NON - LANGUAGESpvsap.weebly.com/uploads/8/2/5/0/8250405/non_languages.1-114.pdf · Trigonometry Similar Triangles Statistics Trigonometry Tangents and Secants of Circles Co-ordinate

10th ClassModel Question Papers

State Council of Educational Research and TrainingAndhra Pradesh

NON - LANGUAGES

10th ClassModel Question Papers

State Council of Educational Research and TrainingAndhra Pradesh

NON - LANGUAGES

I N D E X

1. MATHS 1 - 85

2. PHYSICS 86 - 150

3. BIOLOGY 151 - 212

4. SOCIAL STUDIES 213 - 261

MATHEMATICS

1

S.S.C. Public ExaminationsFrom March - 2017

Division of Syllabus

Paper-I

Ch. No. Chapter Name

1. y�d�ïe d�+K«\T (Real Numbers)

2. d�$TÔáT\T (Sets)

3. �V�Q|�<�T\T (Polynomials)

4. Âs+&�T #ásÁs�Xø�\ýË ¹sFjáT d�MT¿£sÁD²\ ÈÔá (Pair of Linear Equations in two variables)

5. esÁZ d�MT¿£sÁD²\T (Quadratic Equations)

6. çXâ&ó�T\T (Progressions)

10. ¹¿�çÔá$TÜ (Mensuration)

Paper-II

7. �sÁÖ|�¿£ C²«$TÜ (Co-ordinate Geometry)

8. d�sÁÖ|� çÜuó�TC²\T (Similar Triangles)

9. e�Ô�ï�¿ì d�ÎsÁô¹sK\T eT]jáTT #óû<�q ¹sK\T (Tangents and Secants to a circle)

11. çÜ¿ÃD$TÜ (Trigonometry)

12. çÜ¿ÃD$TÜ nqTesÁïH�\T (Applications of Trigonometry)

13. d�+uó²e«Ôá (Probability)

14. kÍ+K«¿£ Xæçd�ï+ (Statistics)

2

Division of Syllabus for SA-I, II & IIIClass : X Subject : Mathematics Paper - I & II

Name of theExam

Paper - I Paper - II

SA-I

upto

September

SA-II

December

SA-III

March

Real Numbers

Sets

Polynomials

Mensuration

Real Numbers

Sets

Polynomials

Pair of linear equations in twovariables

Quadratic equations

Mensuration

Real Numbers

Sets

Polynomials

Pair of linear equations in twovariables

Quadratic equations

Mensuration

Progressions

Similar Triangles

Statistics

Trigonometry

Similar Triangles

Statistics

Trigonometry

Tangents and Secants of Circles

Co-ordinate Geometry

Similar Triangles

Statistics

Trigonometry

Tangents and Secants of Circles

Co-ordinate Geometry

Application of Trigonometry

Probability

3

1. d�eTkÍ« kÍ<ó�q :

>·DìÔá uó²eq\T, |�<�ÆÔáT\T, d�ÖçÔ�\ d�V�äjáT+ÔÃ d�eTd�«\ kÍ<ó�q\T.

�+<�TýË |�<� d�eTd�«\T

|�³ d�eTd�«\T

<�Ô�ï+Xø ne>±V�²q ` $Xâ¢w�D

ç>±|�t |�<�ÆÜ ç|�¿±sÁ+ #ûjáTT kÍ<ó�q\T

d�Ö¿¡��¿£sÁD |�<�ÆÜýË kÍ<ó�q\T

ç|�Ü¹¿�|�D �<ó�]Ôá d�eTd�«\ kÍ<ó�q\T

uó²eq\ ne>±V�²q <�Çs� #áÔáT]Ç<� ç|�ç¿ìjáT\T neT\T

|�{²�� |�]o*+º d�eTd�«\T kÍ~ó+#á&�+

d�eÖqÔ�Ç\T |�]o*+#á&�+

¿£qT>=q+&�, kÍ~ó+#á+&� d�eTd�«\T

2. ¿±sÁD²\T Ôî\Î&�+ :

H <�Xø\y�¯>± >·\ kþbÍH�\Å£� ¿±sÁD²\T Ôî\|�&�+.

H d�eTd�«\ kÍ<ó�qÅ£� >·\ kÍ<ó�«, nkÍ<ó�«\Å£� ¿±sÁD²\T Ôî\|�³+.

H |��*Ô�\qT }V¾²+#á³+

H Èy��T\T d�]#áÖ&�³+

H �s��D kÍ<ó�«, nkÍ<ó�«\Å£� ¿±sÁD+ Ôî\T|�³+

H d¾<�Æ+Ô�\T �sÁÖ|�D #ûjáT³+

H e Z¿£sÁD\T #ûjáT&�+

3. e«¿£ï|�sÁ#á&�+ :

H >·DìÔá uó²eq\T, y�¿±«\T #á<�e>·\>·&�+, s�jáT>·\>·&�+

H >·DìÔá e«¿¡ï¿£sÁD\T sÁÖbõ+~+#á&�+ (ÿ¿£sÁÖ|�+ qT+&� eTsÃ sÁÖ|�+ýË�¿ì)

H >·DìÔá|�sÁ �ýË#áq\qT d�Ç+Ôá eÖ³\ýË $e]+#á&�+

H |�<�ÆÜ� $e]+#á&�+

H �|�jîÖ>±\T Ôî\|�&�+

H >·DìÔá Ô�]Ø¿£ÔáqT $e]+#á&�+

4

H |��*Ô�\ eT<ó�« d�+�+<ó�� e«¿£ï|�sÁ#á&�+

H �<�V�²sÁD\T Ôî\Î&�+

4. nqTd�+<ó�q+ :

H nqT�+<ó� >·DìÔá bÍsÄÁ«$uó²>±\qT nqTd�+<ó��+#á&�+

�<� : uó²>±�¿ì ` �w�ÎÜï¿ì, d�+¿£\H��¿ì ` >·TD¿±s��¿ì)

H �ÈJ$Ôá d�eTd�«\qT >·DìÔ��¿ì nqTd�+<ó��+#á&�+

H yûsÁTyûsÁT d��Å£�¼\ÔÃ >·DìÔ�� nqTd�+<ó��+#á&�+

H >·DìÔá+ýËHû yû¹sÇsÁT bÍsÄ�«+Xæ\qT nqTd�+<ó��+#á&�+

5. <��o«¿£sÁD Ê çbÍÜ�<ó�«|�sÁ#á&�+ :

H |�{ì¼¿£ýË� d�eÖ#�sÁ+ #á<�e&�+

H d�+U²«¹sK�|Õ $$<ó� d�+K«\qT >·T]ï+#á&�+

H 2D, 3D |�{²\qT @sÁÎsÁ#á&�+

H �sÁÖ|�¿£ Ôá\+�|Õ _+<�TeÚ\T >·T]ï+#á&�+

H �s��D²\T

H ç>±|�t\ <�Çs� d�eTd�«\ kÍ<ó�q\T

5

Real Numbers

1. Irrational Number (¿£sÁD¡jáT d�+K«)

1. ç¿ì+~ y��ýË ¿£sÁD¡jáT d�+K«\qT e Z¿£]+º s�jáT+&�. (R.P)

2 , 3 , 5, 5.75, 1.735 ........., 8 , 4 , 16

2. ¿£sÁD¡jáT d�+K«\qT �sÁÇº+#á+&� ? �<�V�²sÁD*eÇ+&� ? (Commu)

3. ¿£sÁD¡jáT d�+K«\Å£� n¿£sÁD¡jáT d�+K«\Å£� >·\ uóñ<�ýñ$ ? (R.P)

4. 2 , 3 , 5 \qT d�+U²«¹sK�|Õ #áÖ|¾+#á+&�. (V.R).R)

5. 2 ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�. (R.P)

6. 2 jîTT¿£Ø $\TeqT H�\TZ <�Xæ+Xø\ esÁÅ£� $\Te ¿£qT>=q+&�. (P.S)

7. ¿£sÁD¡jáT d�+K«\qT �ÈJ$Ôá+ýË m¿£Ø&� �|�jîÖÐkÍïsÁT ?

8. #áÔáTsÁçd�+ýË uó�TC²�¿ì ¿£s��¿ì >·\ d�+�+<ó�+ Ôî\T|�+&� ? (Commu)

9. P $\Te ¿£sÁD¡jáT d�+K« ýñ¿£ n¿£sÁD¡jáT d�+K« ¿±sÁD²\T #î|�Î+&�. (R.P)

Chapter : �V�Q|�<�T\T

Topic : �V�Q|�~ XøSH�«\T

1. x2 + 8x + 15 jîTT¿£Ø �V�Q|�~ XøSH�«\qT ¿£qT>=q+&�.

2. x2 + 8x + 5 �V�Q|�~¿ì >·]w�÷+>± »2µ XøSH�«\T �+&�Tq� mý² #î|�Î>·\eÚ ?

3. x2 + 8x + 5 �V�Q|�~ XøSH�«\qT ç>±|�t <�Çs� ¿£qT>=q+&�.

4. x2 + 8x + 5 Å£� »6µ ÿ¿£ �V�Q|�~ XøSq«eTeÚÔáT+<� ? ýñ<� ? m+<�Te\¢.

5. »»ÿ¿£ d�+K« jîTT¿£Ø esÁZeTTqÅ£� � d�+K«jîTT¿£Ø 8 Âs³T¢ ¿£*|¾q |��*Ôá+ »`5µ n>·TqT. B�

qT|�jîÖÐ+º esÁZd�MT¿£sÁDeTT çy�d¾ � d�+K«qT ¿£qT>=qTeTT.

6. x2 + 8x + 5 �V�Q|�~ eç¿£eTT X`n¿�±�� >·]w�¼+>± m�� _+<�TeÚ\ e<�Ý K+&�+#áe#áTÌqT?

m+<�Te\¢.

7. x2 + 8x + 5 �V�Q|�~� 'y' #ásÁs�¥ <��cÍ¼« Ôî\Î+&�.

8. x2 + 8x + 5 �V�Q|�~ XøSH�«\Å£�, >·TD¿±\Å£� eT<ó�«>·\ d�+�+<ó�� Ôî\Î+&�.

6

Chapter : Âs+&�T #ásÁs�Xø�\ýË ¹sFjáT d�MT¿£sÁD²\ ÈÔá

Topic : ÈÔá ¹sFjáT d�MT¿£sÁD²\ kÍ<ó�q

1. »»>·DìÔá bÍsÄÁ«|�Úd�ï¿£eTT yî\, �+>·¢ |�Úd�ï¿£ K¯<�T jîTT¿£Ø 2 Âs³¢ ¿£H�� 10 sÁÖöö\T ÔáÅ£�Øeµµ B��

¹sFjáT d�MT¿£sÁD+>± çy�jáT+&�.

2. 2x + 3y = 12, 3x + 2y = 13 ¹sFjáT d�MT¿£sÁD²\qT eTÖ\¿±�� Ô=\Ð+#û |�<�ÆÜýË kÍ~ó+#á+&�.

3. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�qqT ç>±|�t <�Çs� kÍ~ó+#á+&�.

4. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�q e«ed¾�Ôá+ neÚÔáT+<�? ýñ<�? >·TD¿±\

�w�ÎÔáTï\ �<ó�sÁ+>± Ôî\Î+&�.

5. »»2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\Å£� kÍ<ó�q\T nq+ÔáeTTµµ neÚH�? ¿±<�? Ôá>·T

¿±sÁD²\ÔÃ Ôî\Î+&�.

6. 2x + 3y = 12, 3x + 2y = 13 \qT ç|�Ü¹¿�|�D |�<�ÆÜýË kÍ~ó+#á+&�.

7. 2x + 3y = 12 ¹sKÅ£� nq+ÔáyîT®q kÍ<ó�q\T �+{²sTT. m+<�Te\¢?

8. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�qÅ£� úeÚ @ |�<�ÆÜ� �|�jîÖÐkÍïeÚ? m+<�Te\¢?

úÅ£� qºÌq |�<�ÆÜýË x, y $\Te\qT ¿£qT>=qTeTT.

Chapter : çXâ&ó�T\T

Topic : n+¿£çXâ&ó�ýË 'n' e |�<�eTT

1. 2, 7, 12, ..... n+¿£çXâ&ó�ýË »13µe |�<�eTT ¿£qT>=qTeTT.

2. n+¿£çXâ&ó�ýË |�<�+ÔásÁeTT »6µ, 7e |�<�eTT 36. B�qT+&� n+¿£çXâ&ó�� çy�jáT&��¿ì M\eÚÔáT+<�?

ýñ<�? m+<�Te\q?

3. n+¿£çXâ&ó�ýË 'n' e |�<�+ 6n + 2 nsTTq yîTT<�{ì H�\T>·T |�<�\qT çy�jáT+&�.

4. n+¿£çXâ&ó�ýË 7e |�<�+ 13, 3e |�<�eTT 7. nsTTq eTÖ\¿±�� Ô=\Ð+#û |�<�ÆÜ <�Çs� a, d \qT

¿£qT>=q+&�.

7

5. n+¿£çXâ&ó�ýË 'n' e |�<�� ýÉ¿ìØ+#áT³Å£� eTqÅ£� @jûT |�<�\T Ôî* �+&�eýÉqT?

6. |�<�+ÔásÁeTT XøSq«+ nsTTq#Ã � çXâ&ó�ýË yîTT<�{ì |�<��¿ì, 'n' e |�<��¿ì >·\ d�+�+<ó�+

Ôî\Î+&�.

7. 2016 ýË sÁÖ. 10,000/` JÔá+ÔÃ �<Ã«>·+ bõ+~q e«¿ìï¿ì ç|�Ü d�+eÔáàsÁ+ sÁÖ.1500/` JÔá+

�|]Ðq#Ã 2020e d�+eÔáàsÁ+ýË � �<Ã«Ð JÔá+ ¿£qT>=q+&�.

8. �+&�� \T|�Ú d��\+ýË ÿ¿£sÃEÅ£� sÁÖ.10/` ��|Õ ç|�ÜsÃEÅ£� sÁT.2/` n<�q+>± #î*¢+#áe\d¾q#Ã

15 sÃE\ Ôás�ÇÔá #î*¢+#áe\d¾q yîTTÔáï+ m+Ôá?

Chapter : �sÁÖ|�¿£ ¹sU²>·DìÔáeTT

Topic : Âs+&�T _+<�TeÚ\ eT<ó�« <�ÖsÁ+

1. (5, 7), (7, 5) _+<�TeÚ\ eT<ó�« <�ÖsÁ+ ¿£qT>=q+&�.

2. (5, 7), (7, 5) _+<�TeÚ\qT �sÁÖ|�¿£Ôá\+�|Õ >·T]ï+º \+�¿ÃD çÜuó�TÈ+ @sÁÎsÁº y�{ì eT<ó�«

<�ÖsÁ+ ¿£qT>=q+&�.

3. (5, 7), (7, 5) _+<�TeÚ\T d�eÖqeÖ? ¿±<�? m+<�Te\¢?

4. (5, 7), (7, 5) \Å£� d�eÖq <�ÖsÁ+ýË >·\ X`n¿£�+�|Õ >·\ _+<�TeÚqT ¿£qT>=qTeTT.

5. (5, 7), (`5, 7), (5, `7), (`5, `7) _+<�TeÚ\T @jûT bÍ<�\ýË �+&�THÃ Ôî\Î+&�.

6. |�³+ýË X`n¿�±�¿ì d�eÖ+ÔásÁ+>± >·\ ¹sK\ bõ&�eÚ\T

�dØ\T �|�jîÖÐ+#áÅ£�+&� ¿£qT>=qTeTT-4 -3 -2 -1 1 2 3 4

8

Chapter : ¹¿�çÔá$TÜ

Topic : Xø+Å£�eÚ yîÕXæ\«eTT

1. 7 �d+.MT. uó�Ö y�«kÍsÁ�eTT, 24 �d+.MT. mÔáTï>·\ Xø+Å£�eÚ �¿±sÁ {Ë|Ó\T »10µ ÔájáÖsÁT

#ûjáT&��¿ì ¿±e\d¾q >·T&�¦ yîÕXæ\«+ ¿£qT>=q+&�.

2. »21µ �d+.MT. y�«kÍsÁ�+ >·\ ÿ¿£ e�Ô�ï�� »3µ d�eÖq uó²>±\T>± $uó��+º Xø+Å£�eÚ\T @sÁÎsÁºq,

Xø+Å£�eÚ uó�Öy�«kÍsÁ�+ m+Ôá?

3. ç¿£eT Xø+Å£�eÚqT �sÁÇº+º, Xø+Å£�eÚ @³y�\T mÔáTïqT ¿£qT>=qT³Å£� d�ÖçÔáeTTqT �Ô�Î~+#áTeTT.

4. Xø+Å£�eÚ �¿±sÁ |�³+ ^º y�«kÍsÁ�+, mÔáTï, @³y�\T mÔáTï\T d�Öº+#á+&�.

5. ç¿ì+~ @ çÜuó�TC²\T çuó�eTD+ #ûd¾q#Ã @sÁ¿£yîT®q Xø+Å£�eÚqT @sÁÎsÁ#áTqT

m) d�eTuó²V�Q çÜuó�TÈ+ _) \+�¿ÃD çÜuó�TÈ+ d¾) $w�eTu²V�Q çÜuó�TÈ+

Chapter : d�sÁÖ|� çÜuó�TC²\T

Topic : çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+ÔáeTT

1. çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+ÔáeTTqT �sÁÇº+º, �sÁÖ|¾+#á+&�.

2. AB R 6 �d+.MT. ¹sU²K+&�� 3:2 �w�ÎÜïýË $uó�Èq #ûd¾ �s��Dç¿£eT+ çy�jáT+&�.

3. D ABC ýË AB, AC \�|Õ _+<�TeÚ\T esÁTd�>± E, F nsTTq ç¿ì+~ ç|�Ü d�+<�sÁÒÛ+ýË EF P BC

neÚHÃ ¿±<Ã Ôî\Î+&�.

a) AE = 3.9 cm, EB = 3 cm, AF = 3.6 cm, CF = 2.4 cmb) AE = 4 cm, BE = 4.5 cm, AF = 8 cm, CF = 9 cm

4. D ABC ýË BC P DE eT]jáTT AD = DB = 3:4 eT]jáTT

AC = 14 cm nsTTq AE, EC \ bõ&�eÚ\T ¿£qT>=qTeTT.

5. D ABC ýË AB, AC \ eT<ó�« _+<�TeÚ\T D, E eT]jáTT BC = 6 cm nsTTq DE bõ&�eÚqT

¿£qT>=qTeTT.

A

D E

CB

9

Chapter : e�Ô�ï\Å£� d�ÎsÁô¹sK\T eT]jáTT #óû<�q¹sK\T

Topic : e�Ôáï K+&� yîÕXæ\«eTT

1. ç|�¿£Ø |�³+ýË e�Ôáï y�«kÍsÁ�+ 21 �d+.MT, nsTTq AOBÐ R 120

nsTTq AYB e�ÔáïK+&� yîÕXæ\«+ ¿£qT>=qTeTT

2. ÿ¿£ >·&�jáÖsÁ+ýË 7 �d+.MT. bõ&�eÚ >·\ �$TcÍ\ eTT\T¢#û 10 �öö\ýË @sÁÎ&û ç|�<ûXø yîÕXæ\«+

Å£qT>=qTeTT.

3. 14 �d+.MT. y�«kÍsÁ�+ >·\ e�Ôáï+ýË n+Ôá]¢Ï+#á�&�q ç¿£eT nw�¼uó�T� yîÕXæ\«+ ¿£qT>=qTeTT.

4. 3 �d+.MT. y�«kÍsÁ�+ >·\ »4µ ¿±«sÁy�TuËsÁT¦ bÍH�\T ÿ¿£<��¿=¿£{ì Ô�Å£�q³T¢ neT]Ìq#Ã y�{ì

eT<ó�« yîÕXæ\«eTTqT ¿£qT>=qTeTT.

Chapter : d�$TÔáT\T (Sets)

Topic : d�yûT�Þøq+ (Union)

1. A, B d�$TÔáT*ºÌ d�eT�Þøq+ ¿£qT>=qeTq&�+.

2. AÌ B njûT«ý² d�$TÔáT*ºÌ ¿£qT>=qeTq&�+. @$T >·eT�+#�sÁT?

3. B Ì A njûT«ý² d�$TÔáT*ºÌ ¿£qT>=qeTq&�+. @$T >·eT�+#�sÁT?

4. A, B \T $jáTT¿£ï d�$TÔáTýÉÕq|�ð&�T AÈ B ¿£qT>=q&�+.

5. yîH� ºçÔ�\ <�Çs� AÈ B � #áÖ|�+&�.

6. AÈ B, B È A \qT ¿£qT>=� @$T >·eT�+#�sÃ çy�jáT+&�.

7. A, B \T AÈ B ¿ì �|�d�$TÔáT\eÚÔ�jáÖ? m+<�TÅ£�?

O

A

Y

B

10

Chapter : çÜ¿ÃD$TÜ

Topic : nqTesÁïH�\T

1. uó�Ö$T¿ì 30 MT. mÔáTïqT+&� 60+ ¿ÃD+ÔÃ C²sÁ&��¿ì C²sÁT&�T�\¢ yûjáTeýÉqT. nsTTq C²sÁT&�T�\¢

bõ&�eÚ m+Ôá �+&�eýÉqT.

2. �{²sÁT>± �\�&�q B|�d��+uó�eTT �|qT>±*¿ì |�P]ï>± $]Ð B|�d�ï+uó�+ ¿=quó²>·+ <�ÖsÁ+>± >·\

e«¿ìï� Ô�¿ìq~ nsTTq $sÁ>·¿£ eTTqT|�Ú � e«¿ìï B|�|�Ú d�ï+uó�eTTÔÃ #ûjáTT ¿ÃD+ ¿£qT>=qTeTT.

3. ÿ¿£ h MT. mÔáTï>·\ uó�eq+�|Õq bõ&�y�{ì çÔ�&�T d�V�äjáTeTTÔÃ m>·TsÁTÔáTq� >±*|�{²�� uó�eq+

ç¿ì+<� x MT. <�ÖsÁ+ýË >·\ u²\T&�T >±*|�{²��, çÔ�&�TqT m>·TsÁyûd�Tïq� e«¿ìï� esÁTd�>± , a b

¿ÃD+ÔÃ |�]o*+#�&�T. � <�Ô�ï+Xæ�� Ôî\T|�Ú |�³+ ^jáT+&�.

4. Âs+&�T uó�eH�\Å£� d�eÖq <�ÖsÁ+ýË >·\ e«¿ìï � uó�eH�\qT esÁTd�>± 35+, 46

+ ¿ÃD²\ÔÃ

|�]o*+ºq#Ã, � Âs+&�T uó�eH�\ýË @~ mÔáïsTTq~? m+<�Te\¢?

5. �<�jáT+ 8 >·+³\ d�eTjáT+ýË 15 MT. mÔáTï>·\ d�ï+uó�+ ú&�bõ&�eÚ 5 3 MT³sÁT¢ nsTTq �

d�eTjáT+ýË d�ÖsÁ«¿ìsÁD²\T uó�Ö$TÔÃ #ûjáTT ¿ÃD+ ¿£qT>=qTeTT.

Chapter : d�+uó²e«Ôá

Topic :

1. ÿ¿£ d�+ºýË 3 mçsÁ�+ÔáT\T, 4 Ôî\¢�+ÔáT\T ¿£\eÚ. jáÖ<��ºÌÛ¿£+>± rd¾q �+Ü (i) mçsÁ�+Ü

n>·T³Å£� (ii) Ôî\¢�+Ü n>·T³Å£� d�+uó²e«ÔáqT ¿£qT>=qTeTT.

2. ÿ¿£ d�+eÔáàsÁeTTýË »53µ �~y�s�\T n>·T³Å£� d�+uó²e«Ôá m+Ôá?

3. 1`20 esÁÅ£� n+Â¿\ >·\ d¾Øq�sYýË

(i) ç|�<ó�q d�+K« (ii) d�+jáTT¿£ï d�+K« (iii) 3 jîTT¿£Ø >·TDìC²\T n>·T³Å£� d�+uó²e«ÔáqT ýÉ¿ìØ+#á+&�.

4. »6µ eTTU²\T >·\ bÍº¿£qT <=]¢+ºq|�Ú&�T (i) 5 ¿£H�� ÔáÅ£�Øe |�&�T³Å£� (ii) 5 ¿£H�� mÅ£�Øe |�&�T

d�+uó²e«ÔáqT ýÉ¿ìØ+#á+&�.

11

5. Âs+&�T bÍº¿£\qT <=]¢+ºq|�Ú&�T y�{ì yîTTÔáï+Å£� d�+uó²e«Ôá |�{ì¼¿£qT |�P]+#á+&�.

Âs+&�T bÍº¿£\�|Õ 2 3 4 5 6 7 8 9 10 11 12

yîTTÔáï+

d�+uó²e«Ôá 1

365

36

B�� sÁÖ|�¿£ Ôá\+�|Õ »u²sYç>±|�tµ >± �]�+#áTeTT.

6. �|¿£eTT¿£Ø\ ¿£³¼qT+&� jáÖ<��ºÌÛ¿£+>± rd¾q �|¿£ &îÕeT+&�s�E n>·T d�+uó²e«Ôá, ¿±� d�+uó²e«Ôá

m+Ôá?

7. 50 eÖsÁTØ\ |� ¿£�ýË �rïsÁT�&�T ne&��¿ì 80% ne¿±Xø+ ¿£\<�T. nsTTq �rïsÁ�Ôá bõ+<�T

d�+uó²e«Ôá m+Ôá?

8. 60 eT+~ >·\ ÔásÁ>·ÜýË 32 eT+~ »Tµ çÔ�Â><�sÁT nsTTq ÿ¿£ çÔ�>·� y�] d�+uó²e«Ôá m+Ôá?

9. ç¿ì+~ |�{ì¼¿£ýË ç|�ÜsÃE �cþ�ç>·Ôá, esÁü+ |�&�q d�+<�sÁÒÛ+ �eÇ�&�q~. @ d�+<�sÁÒÛ+ýË esÁü+ |�&�T

ne¿±Xø+ mÅ£�Øe>±qT, @ d�+<�sÁÒÛ+ýË ÔáÅ£�Øe ¿£\<Ã Ôî\Î+&�.

y�sÁ+ �~ kþeT eT+>·Þø �T<ó� >·TsÁT Xø�ç¿£ Xø�

�cþ�ç>·Ôá 37+

25+

27+

32+

30+

36+

38+

esÁü+ Å£�]d¾+~ ýñ<�T ýñ<�T ºsÁTÈ\T¢ ýñ<�T Å£�]d¾+~ Å£�]d¾+~

10. ç¿ì+~ |�{ì¼¿£qT+&� yîTT<�³ u²«{ì+> #ûd¾q|�Ú&�T @ È³T¼ Â>\Tbõ+<�T³Å£� mÅ£�Øe ne¿±Xø+ ¿£\<�T?

È³T¼ yîTT<�³ u²«{ì+> |��*Ôá+

Â>\T|�Ú z³$T

�+&�jáÖ 30 20 10

bÍ¿ìkÍ�H� 28 12 16

�ç�d¼*jáÖ 44 22 22

ço\+¿£ 50 0 30

kåÔY�ç|�¾¿±

12

Chapter : kÍ+K«¿£ Xæçd�ï+

Topic : d�>·³T

1. 2016 d�+öö yûT Hî\ýË yîTT<�{ìy�sÁ+ �cþ�ç>·Ôá\T esÁTd�>± 36+, 32

+, 34

+, 30

+, 42

+, 40

+, 38

+

>± qyîÖ<�T nsTTq$. nsTTq d�>·³T �cþ�ç>·Ôá m+Ôá?

2. 2016 IPL T-20 bþ{¡ýË ç¿ìÂ¿³sY ¿ÃV¾²¢ 15 eÖ«#Y\ýË 975 |�sÁT>·T\T #ûkÍ&�T. nsTTq nÔáqT

ÿ¿=Ø¿£Ø eÖ«#YýË #ûd¾q |�sÁT>·T\T m��?

3. 22 eT+~ $<�«sÁT�\T sÁT.3300/` \ÔÃ $V�äsÁjáÖçÔáÅ£� �jáT\T<û]H�sÁT. n+<�TýË �<�ÝsÁT $<�«sÁT�\T

y�] y�{² sÁT.500/` \ÔÃ $V�äsÁjáÖçÔáqT+&� �çw�Ø$T+#�sÁT. nsTTq $TÐ*qy�sÁT $V�äsÁjáÖçÔáqT

|�P]ï#ûd¾q#Ã ÿ¿=Ø¿£ØsÁT n<�q+>± #î*¢+#áe\d¾q yîTTÔáïyîT+Ôá?

4. ÔásÁ>·Ü 2 3 4 5 6 7

båq'|�Úq«+ 10 6 9 13 7 8

d�>·³T ýÉ¿ìØ+#á+&�.

5. ç¿ìÂ¿{Ù ç¿¡&�¿±sÁT&� kÍeTs��«�� Ôî*jáTCñ�d ¹¿+çBjáT kÍ�q$\Te @~? m+<�Te\¢?

6. �ÈJ$Ôá+ýË n+¿£>·DìÔá d�>·³T\T @jûT d�+<�s�ÒÛ\ýË �|�jîÖÐkÍïsÁT?

13

qeTÖH� ç|�Xø�\T ` ç|�Xø�\ $<ó�q+

Real Numbers

H @<û� <ó�qd�+K« bq + r sÁÖ|�+ýË �+³T+<�� #áÖ|�&�+.

H jáTÖ¿ì¢&� dÓÇ¿£�Ôá+ �<ó�sÁ+>± >·.kÍ.uó². ýÉ¿ìØ+#á&�+.

H 'x' >·TDìÈ d�+K«\ sÁÖ|�+ bq + 1, bq + 2..... bq + (x-1) sÁÖ|�+ýË �+³T+<�� mý² #î|�Î>·\eÚ.

H ç|�<ó�q ¿±sÁH�+¿±\ \�Ý+ �<ó�sÁ+>± >·.kÍ.uó², ¿£.kÍ.>·T ýÉ¿ìØ+#á&�+.

H jáTÖ¿ì¢&� dÓÇ¿£�Ôá+ �<ó�sÁ+>± ¿±sÁD²+¿£ |�<�ÆÜýË >·Dì+ºq >·.kÍ.uó².ÔÃ d�]#áÖ&�+&�.

H |�sÁd�ÎsÁ ç|�<ó�q d�+K«\ >·.kÍ.uó². »1µ ¿±e&��¿ì ¿±sÁD+ Ôî\Î+&�.

H _óH��\qT uó²>·V�äsÁ+ #ûjáTÅ£�+&� <�Xæ+Xø _óH��\T>± eÖsÁÌ&�+.

H _óq�+ n+Ôá+ njûT« (ýñ<�) n+Ôá+¿±� �esÁïq <�Xæ+Xø+ n>·T³Å£� ¿±sÁD+ Ôî\Î&�+.

H ç|�<ó�q d�+K«\ esÁZeTÖý²\T ¿£sÁD¡jáT d�+K«\T n� #áÖ|�+&�.

H ~Ç|�~ ¿£sÁDT\ #áÔáT]Ç<� ç|�ç¿ìjáT\T n�� d�+<�s�ÒÛ\ýË ¿£sÁDT\T neÚÔ�jáÖ? ýñ<�? �<�V�²sÁD\ÔÃ

d�]#áÖ&�+&�.

H ç|�<ó�q d�+K«\ \�Æ+, eT]jáTT yîTTÔáï+ d�+jáTT¿£ïd�+K« n>·TH�? ýñ<�?

�V�Q|�<�T\T

H d�eÖkÍ\T @$ �V�Q|�<�T\T? @$ ¿±eÚ? ¿±sÁD+ Ôî\Î+&�.

H �V�Q|�~ $\Te\T ýÉ¿ìØ+#á+&�?

H �V�Q|�~ýË >·TD¿±\T, |�]eÖD²\T >·T]ï+#á+&�.

H �V�Q|�~¿ì XøSH�«\T n>·THÃ ¿±<Ã d�]#áÖ&�+&�.

H �V�Q|�~ XøSH�«\T ýÉ¿ìØ+#á+&�?

H �V�Q|�~ XøSH�«\qT ¹sU²ºçÔá+ <�Çs� mý² ¿£qT>=+{²eTT?

H �V�Q|�~ X`n¿�±�� K+&�+#á¿£bþÔû |��*Ôá+ @eTeÚÔáT+~.

H �V�Q|�~ |�]eÖD²�¿ì, XøSH�«\Å£� eT<ó�« d�+�+<ó�+ Ôî\|�+&�?

14

H �V�Q|�<�T\Å£� ¹sU²ºçÔ�\T ^º, XøSH�«\T ¿£qT>=q+&�. |��*Ô�\qT d�]#áÖ&�+&�.

H �V�Q|�~ XøSH�«\T ¿£qT>=�, XøSH�«\Å£�, >·TD²\Å£� eT<ó�«>·\ d�+�+<ó�� d�]#áÖ&�+&�.

H XøSH�«\ �<ó�sÁ+>± �V�Q|�<�T\qT ÔájáÖsÁT#ûjáT&�+.

H �V�Q|�<�T\T uó²>±V�äs�\T, uó²>±V�äsÁ �jáTeT+ d�]#áÖ&�³+.

H uó²>±V�äsÁ �jáTeÖ�� Ôá�|¾ï|�]#û $<ó�+>± $uó²È«+, $uó²È¿£+, uó²>·|��\+, Xâw�eTT\ |�]eÖD²\qT

}V¾²+º, �<�V�²sÁD*eÇ+&�.

4. Âs+&�T #ásÁs�Xø�\ýË ¹sFjáT d�MT¿£sÁD²\ ÈÔá

H �ÈJ$Ôá d�eTd�«\qT ¹sFjáT d�MT¿£sÁD²\T>± eÖsÁÌ&�+.

H @¿£ #ásÁs�¥ ¹sFjáT d�MT¿£sÁD kÍ<ó�q\T.

H ÿ¿£ ~Ç #ásÁs�¥ ¹sFjáT d�MT¿£sÁD²�¿ì nq+ÔáyîT®q kÍ<ó�q\T �+{²sTT. m+<�Te\¢? ¿±sÁD+ Ôî\|�+&�.

H ç>±|�t |�<�ÆÜ <�Çs� ¹sFjáT d�MT¿£sÁD²\ ÈÔáÅ£� kÍ<ó�q\T ¿£qT>=q&�+.

H >·TD¿±\ �<ó�sÁ+>± kÍ<ó�q\ d�Çuó²y�� }V¾²+#á&�+.

H d�MT¿£sÁD²\ ÈÔá d�+>·Ôá d�MT¿£sÁD²ý²? nd�+>·Ôá d�MT¿£sÁD²ý²? d�]#áÖ&�+&�. ç>±|�t <�Çs� kÍ~ó+#á+&�.

H ç|�Ü¹¿�|�D |�<�ÆÜýË kÍ<ó�q\T.

H #ásÁs�¥� Ô=\Ð+#û |�<�ÆÜýË kÍ<ó�q\T.

H ç>±|�t, ç|�Ü¹¿�|�D, #ásÁs�¥� Ô=\Ð+#û |�<�ÆÔáT\ýË @~ �ÔáïeT+? m+<�Te\¢? @<û� d�MT¿£sÁD²\qT

kÍ~ó+#á+&�.

H �w�ÎÔáTï\T, ¿±\eTT`|��, y�«bÍsÁ >·DìÔáeTT d�eTd�«\qT ¹sFjáT d�MT¿£sÁD²\T>± eÖ]Ì kÍ<ó�q\T

¿£qT>=q&�+.

15

çXâ&ó�T\T

H �ºÌq C²_Ô�ýË @$ n+¿£çXâ&ó�T\T? @$ ¿±<�T? m+<�Te\¢?

H n+¿£çXâ&ó�ýË, yîTT<�{ì|�<�+, |�<�+ÔásÁ+\T >·T]ï+º, 'n' e |�<�+ ¿£qT>=q+&�.

H u²sÁTe&�¦ d�eTd�«\qT n+¿£çXâ&ó�\T>± eÖ]Ì kÍ~ó+#á+&�.

H �ÈJ$Ôá d�+|��T³q\qT esÁTd�ç¿£eT+ýË çy�jáT>± @$ n+¿£çyû&ó�T\T neÚÔ�sTT? @$¿±<�T? ¿±sÁD+

Ôî\Î+&�?

H n+¿£çXâ&ó�ýË 'n' e |�<�+ ¿£qT>=q+&�.

H n+¿£çXâ&ó�ýË 'n' |�<�\ yîTTÔáï+ 'x' n>·T³Å£� >·\ ne¿±Xæ\qT #á]Ì+#á+&�.

H n+¿£çXâ&ó�ýË 'x' e |�<�eTT, 'y' e |�<�eTT �ºÌq|�Ú&�T ¹sFjáT d�MT¿£sÁD²\ ÈÔáÅ£� nqTd�+<ó��d�Öï

d�eTd�«\T kÍ~ó+#á&�+.

H Âs+&�T d�+K«\ eT<ó�« >·TDìC²\qT (ýñ<�) >·TDìC²\ yîTTÔáï+ ¿£qT>=q&�+.

H >·TDçXâ&ó�\qT >·T]ï+#á&�+, kÍeÖq« �w�ÎÔáTï\T, 'n' e |�<�\T ýÉ¿ìØ+#á&�+.

H >·TDçXâ&ó�ýË �]Æw�¼|�<�+ mq�e |�<�+ neÚÔáT+<Ã ¿£qT>=q+&�.

¹¿�çÔá$TÜ

H Xø+Å£�eÚ, d�Ö�|�eTT, >ÃÞøeTT\ ç|�¿£ØÔá\, d�+|�PsÁ�Ôá\ yîÕXæý²«\T |��Tq|�]eÖD²\T ¿£qT>=q&�+.

H Âs+&�T yû¹sÇsÁT �¿±s�\ ¿£\sTT¿£ e\¢ @sÁÎ&�q y�{ì�|Õ d�eTd�«\T kÍ~ó+#á&�+.

H �ÈJ$Ôá d�eTd�«\qT (<ó�q«+ Å£�|�Î, CË¿£sY {Ë|¾, >·T&�sÁeTTÅ£� ¿±e\d¾q >·T&�¦) kÍ~ó+#á&�+.

H Xø+Å£�eÚ, d�Ö�|�eTT |��Tq|�]eÖD²\ eT<ó�« d�+�+<ó�+.

H d�Ö�|�+, Xø+Å£�eÚ |��Tq|�]eÖD²\ qT+&� >ÃÞø+ |��Tq|�]eÖD+ s��{ì¼ y�{ì eT<ó�« d�+�+<ó�eTT @sÁÎsÁ#á&�+.

H d�eT|��Tq+, ç¿£eT |¾sÁ$T&� |��Tq|�]eÖD²\ eT<ó�« d�+�+<ó�+ @sÁÎsÁ#á&�+, |��Tq|�]eÖD²\ �w�ÎÜï

d�]#áÖ&�³+.

16

�sÁÖ|�¿£ ¹sU²>·DìÔáeTT

H _+<�TeÚ\qT �sÁÖ|�¿£ Ôá\+ (ç>±|�t) ýË >·T]ï+#á+&�.

H _+<�TeÚ\qT ¿£*�| ¹sK X`n¿�±�¿ì ýñ<� Y`n¿�±�¿ì d�eÖ+ÔásÁ+>± �+³T+<�� mý² #î|�Î>·\eÚ?

(_+<�TeÚ\T ç>±|�t�|Õ >·T]ï+#áÅ£�+&� x, y �sÁÖ|�¿±\ �<ó�sÁ+>±).

H (o, x) (o, y), (o, z) \T @ n¿£�+�|Õ �+{²sTT? m+<�Te\¢?

H �sÁÖ|�¿£ n¿�±\Å£� d�eÖ+ÔásÁ+>± >·\ ¹sK�|Õ _+<�TeÚ\ eT<ó�« <�ÖsÁ+ ¿£qT>=q+&�.

H �sÁÖ|�¿£ Ôá\+ýË� Âs+&�T _+<�TeÚ\ eT<ó�« <�Ös�� d�ÖçÔá d�V�äjáT+ÔÃ ýÉ¿ìØ+#á+&�.

H �ºÌq _+<�TeÚ\ÔÃ @sÁÎ&û |�³+, #áÔáTsÁçd�ï+ ýñ<� BsÁé#áÔáTsÁçd�+ ýñ<� d�eÖ+ÔásÁ #áÔáTsÁTÒÛÈ+, d�eT\+�

#áÔáTsÁTÒÛÈ+ neÚÔáT+<Ã #áÖ&�+&�.

H P, Q, R _+<�TeÚ\ �<ó�sÁ+>± PQRS |�³+ s�+�dt (ýñ<�) #áÔáTsÁçd�+ ¿±e&��¿ì 'S' _+<�TeÚ �sÁÖ|�¿±\T

¿£qT>=q+&�.

H ¹sU²K+&�� m:n �w�ÎÜïýË $uó��+#û _+<�TeÚ �sÁÖ|�¿±\T d�ÖçÔá+ d�V�äjáT+ÔÃ ¿£qT>=q+&�.

H çÜuó�TÈ >·TsÁTÔáÇ¹¿+ç<�+ ýÉ¿ìØ+#á+&�.

H çÜ<ó�¿£sÁD, _+<�TeÚ �sÁÖ|�¿±\T ¿£qT>=q&�+, 4 d�eTuó²>±\T>± $uó��+#á&�+

H d�ÖçÔá+ d�V�äjáT+ÔÃ çÜuó�TÈ yîÕXæ\«+ ¿£qT>=qTeTT.

H çÜuó�TÈ d�ÖçÔá+ �<ó�sÁ+>± #áÔáTsÁTÒÛÈ yîÕXæ\«+ ¿£qT>=qTeTT.

H çÜuó�TÈ yîÕXæý²«\qT d�ÖçÔád�V�äjáT+ÔÃ, �V²s�H� d�ÖçÔá+ �<ó�sÁ+>± ýÉ¿ìØ+º d�]#áÖ&�+&�.

H d�¹sFjáT _+<�TeÚ\T ç>±|�t�|Õ >·T]ï+#á&�+ kÍ<ó�«eÖ? nsTTÔû � _+<�TeÚ\#û @sÁÎ&�T |�³yîÕXæ\«+ m+Ôá?

H Âs+&�T _+<�TeÚ\qT ¿£*�| ¹sK y�\TqT ¿£qT>=q+&�.

H X`n¿�±�¿ì d�eÖ+ÔásÁ+>± >·\ Y`�sÁÖ|�¿±\T @$<ó�+>± �+{²sTT? ¿±sÁD+ Ôî\|�+&�.

17

n+¿£>·DìÔá çbÍ<�$T¿£ �jáTeTeTT (Fundamental theorm of Arithmetic)

H ç|�Ü d�+jáTT¿£ï d�+K«qT ç|�<ó�q ¿±sÁD²+¿±\ \�Æ+>± s�d�Öï �<�V�²sÁD\ÔÃ d�eT]�+#á+&�?

H 210qT ç|�<ó�q ¿±sÁD²+¿±\ \�Æ+>± s�jáT+&�?

H n d�V�²Èd�+K« nsTTq 6n nHû d�+K« jîTT¿£Ø ÿ¿£³¢ kÍ�q$\Te 0 neÚÔáT+<�? MT d�eÖ<ó�q+

d�eT]�+#á+&�.

H 7I11I13G13 eT]jáTT 7I6I5I4I3I2I1G5 d�+jáTT¿£ï d�+K«\� #áÖ|�+&�?

H 306, 657 \ >·.kÍ.uó² 9 nsTTq 306, 657 \ ¿£.kÍ.>·T ¿£qT>=q+&�.

H 45, 75 \ >·.kÍ.uó². jáTÖ¿ì¢&� uó²>·V�äsÁ XâcÍ�� |�jîÖÐ+º ¿£qT>=q+&�.

H 7I11I13G13 eT]jáTT 7I6I5I4I3I2I1G5 @$<ó�+>± d�+jáTT¿£ï d�+K« $e]+#á+&�.

d�+esÁZeÖH�\T (Logerithams)

H �ç¿ì+~ |��ÖÔá¿£sÁÖbÍ\qT d�+esÁZeÖH�\ýË eÖsÁÌ+&�.

(i) 25 R 32 (ii) 33

R 27 (iii) 53 R 125

H 5122log $\Te ¿£qT>=q+&�.

H 0.0110log $\Te ¿£qT>=q+&�.

H d�+esÁZeÖH�\qT |��ÖÔ�+¿£ sÁÖ|�+ýË s�jáT+&�.

1255log R 3

H d�+esÁZeÖH�\ H�«jáÖ\qT �sÁÖ|¾+#á+&�.

Ex : (i) log xy = log x + log y

H Xø+¿£sY y�&û d��TÒ Hydrozen ian >±&ó�Ôá 9.2I10`22

$\Te logorithems �|�jîÖÐ+º ¿£qT>=q+&�.

18

e�Ô�ï\Å£� d�ÎsÁô¹sK\T eT]jáTT #óû<�q¹sK\T

H e�ÔáïeTT, d�ÎsÁô¹sK d¾<�Æ+ÔáeTT\T

H d�ÎsÁô¹sK bõ&�eÚ\T ¿£qT>=qTeTT

H e�Ôáï¹¿+ç<�+ Ôî*jáTq|�Ú&�T d�ÎsÁô¹sK �]�+#á&�+

H u²V�²«_+<�TeÚ qT+&� e�Ô�ï�¿ì d�ÎsÁô¹sK\ �s��D+

H �V�Quó�T�ýË n+ÔásÁe�Ôáï+, u²V�²«e�Ôáï+ �<ó�]Ôá d�eTd�«\T

H #óû<�q¹sKÔÃ e�ÔáïK+&� yîÕXæý²«\T ¿£qT>=q&�eTT

H �ÈJ$Ôá d�+<�sÁÒÛeTT\ýË e�Ô�ï\qT @sÁÎsÁ#û yîÕXæý²«\T ¿£qT>=q&�eTT.

d�sÁÖ|� çÜuó�TC²\T

H çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+Ôá �sÁÇ#áq+, �sÁÖ|�D+

H <ûýÙà d¾<�Æ+Ôá+ �<ó�sÁ+>± ¹sU²K+&�� m : n �w�ÎÜïýË $uó��+#û �s��D+

H <ûýÙà d¾<�Æ+Ôá $|�sÁ«jáT+

H <ûýÙà d¾<�Æ+Ôá+, $|�sÁ«jáT+ �<ó�sÁ+>± #áÔáTsÁTÒÛC²\ýË <ó�s��\ |�]o\q

H |�³ d�eTd�«\T kÍ~ó+#á&�+

H çÜuó�TC²\ d�sÁÖ|�Ôá �jáTeÖ\ �sÁÖ|�D\T

H çÜuó�TC²�¿ì d�sÁÖ|� çÜuó�TÈ+ �]�+#á&�+

H �ÈJ$Ôá d�eTd�«\T kÍ~ó+#á&�+

H d�sÁÖ|� çÜuó�TÈ yîÕXæý²«\ d¾<�Æ+Ôá+ �sÁÖ|�D

H u�<ó�jáTq d¾<�Æ+ÔáeTT, $|�sÁ«jáTeTT �sÁÖ|�D

H d¾<�Æ+Ôá|�sÁ d�eTd�«\T kÍ<ó�q

19

d�+uó²e«Ôá

H �sÁÇ#áH�\T

H �|¿£eTT¿£Ø\ ¿±sÁT¦\ d�+uó²e«Ôá�|Õ $$<ó� sÁ¿±\ ç|�Xø�\T

H &îÕdt <=]¢+ºq|�Ú&�T ne¿±Xæ\ d�+uó²e«Ôá\T

H �ÈJ$Ôá d�+|��T³q\ýË kÍ<ó�«, nkÍ<ó�« |��T³q\ ýÉ¿ìØ+|�Ú

kÍ+K«¿£ Xæçd�ï+

H e Z¿£�Ôá, ne Z¿£�Ôá <�Ô�ï+Xæ\Å£� d�>·³T, eT<ó�«>·Ôá+, u²V�QÞø¿£+ ýÉ¿ìØ+|�Ú

H d�>·³T ýÉ¿ìØ+#áT³ýË >·\ |�<�ÆÔáT\ýË nqTyîÕq |�<�ÆÜ m+|¾¿£? Ôá>·T ¿±sÁD²\ÔÃ kÍ<ó�q.

H ç>±|�t |�<�ÆÜýË eT<ó�«>·Ôá+ ýÉ¿ìØ+|�Ú

H d�+ºÔá båq'|�Úq« eç¿±\ �s��D+

çÜ¿ÃD$TÜ

H çÜ¿ÃD$TrjáT �w�ÎÔáTï\T, $$<ó� ¿ÃD²\Å£� y�{ì $\Te\T

H çÜ¿ÃD$TrjáT �w�ÎÔáTï\ eT<ó�« d�+�+<ó�eTT\T

H çÜ¿ÃD$TrjáT nqTesÁïH�\T

H |�PsÁ¿£ ¿ÃD²\ çÜ¿ÃD$TrjáT �w�ÎÔáTï\ eT<ó�« d�+�+<ó�+

H nqTesÁïH�\T

20

çÜ¿ÃD$TÜ

H �ºÌq y�{ìýË @$ esÁZd�MT¿£sÁD²\T? @$ ¿±<�T? ¿±sÁD+ Ôî\|�+&�.

H esÁZd�MT¿£sÁD²\ �|�jîÖ>±\T.

H |�<� d�eTd�«\qT esÁZd�MT¿£sÁD²\T>± eÖsÁÌ&�+.

H esÁZd�MT¿£sÁD²\qT ¿±sÁD²+¿£ |�<�ÆÜýË kÍ~ó+#á&�+.

H eTÖý²\ �<ó�sÁ+>± esÁZd�MT¿£sÁD²\T çy�jáT+&�.

H �ÈJ$Ôá d�eTd�«\qT esÁZd�MT¿£sÁD²\T>± eÖsÁÌ&�+, kÍ~ó+#á&�+.

H esÁZeTTqT |�P]ï#ûjáT&�+ <�Çs� esÁZd�MT¿£sÁD²�� kÍ~ó+#áT³Å£� kþbÍH�\T çy�jáT+&�.

H esÁZeTTqT |�P]ï#ûjáTT³ <�Çs� esÁZd�MT¿£sÁD kÍ<ó�q\qT ¿£qT>=� ç|�Ü¹¿�|�D |�<�ÆÜýË kÍ<ó�q\qT

d�]#áÖ&�+&�.

H d�ÖçÔá+ <�Çs� esÁZd�MT¿£sÁD kÍ<ó�q\T ¿£qT>=q&�+.

H >·TD¿±\Å£�, kÍ<ó�q\Å£� eT<ó�« d�+�+<ó�+ @sÁÎsÁ#á&�+

H ¹sU²ºçÔ�\ �<ó�sÁ+>± esÁZd�MT¿£sÁD eTÖý²\ d�Çuó²e+ Ôî\Î+&�

H ¹sU²ºçÔ�\ <�Çs� kÍ~ó+#á&�+

H ¹sU²ºçÔ�\ <�Çs� kÍ~ó+#áTq|�Ú&�T @ n¿�±�� K+&�+#áTÅ£�q� $\Te\ �<ó�sÁ+>± eTÖý²\T >·T]ïkÍïeTT?

m+<�Te\¢? ¿±sÁD+ Ôî\Î+&�.

H esÁZd�MT¿£sÁD kÍ<ó�qÅ£� @ |�<�ÆÜ nqTesTTq~? m+<�Te\¢?

21

d�+ç>·V�²D²Ôá�¿£ eTÖý²«+¿£qeTT`1

eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT

ÔásÁ>·Ü ` 10 ` �||�sY I¿±\eTT : 2 >·+öö 45 �öö bÍsÁT¼ ` A & B >·]w�÷ eÖsÁTØ\T : 40

¿±\eTT : 2 >·+öö 15 �öö bÍsÁT¼ ` A >·]w�÷ eÖsÁTØ\T : 30

d�Ö#áq\T : 1. n�� ç|�Xø�\qT çXø<�Æ>± #á<�e+&�.

2. bÍsÁT¼ A Å£� d�+�+~ó+ºq ç|�Xø�\ Èy��T\qT MT¿ì#ûÌ Èy��T |�çÔá+ýË s�jáT+&�.

3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.

4. n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT\T s�jáT+&�.

5. d�eÖ<ó�qeTT\T d�Îw�¼+>±qT, Xø�çuó�+>±qT s�jáT+&�.

6. �d¿£�H� III q+<�* ç|�Xø�\Å£� n+ÔásÁZÔá m+|¾¿£ �+³T+~.

�d¿£�H� ` I

d�Ö#áq\T : 1. n�� ç|�Xø�\Å£� Èy��T\T s�jáT+&�.

2. ç|�Ü ç|�Xø�Å£� 1 eÖsÁTØ. 4I1 R 4 eÖsÁTØ\T

1. jáTÖ¿ì¢&� uó²>·V�äsÁ Xâw��~ó �|�jîÖÐ+º 196 eT]jáTT 2016 \ >·.kÍ.uó². ¿£qT>=q+&�.

2. ç¿ì+~ y�¿±«\qT >·TsÁTï\T|�jîÖÐ+º çy�jáT+&�.

i) 2016 nHû d�+K« ç|�<ó�qd�+K«\ d�$TÜ¿ì #î+~q~.

ii) 28 nHû d�+K« Xø�<�Æd�+U²« d�$T¿ìÜ #î+~q~.

3. ÿ¿£ d�Ö�|�+ jîTT¿£Ø �|�]Ôá\ yîÕXæ\«+ Xø+K+ jîTT¿£Ø eç¿£Ôá\ yîÕXæ\«+qÅ£� d�eÖq+. Âs+&�+{ì jîTT¿£Ø

uó�Öy�«kÍs��\T d�eÖqeTT nsTTq d�Ö�|�+ jîTT¿£Ø mÔáTï Xø+K+ jîTT¿£Ø @³y�\T mÔáTï\ �w�ÎÜï m+Ôá?

4. ÿ¿£ bÍsÄÁXæ\ýË �q� uóËÈqXæ\ BsÁé#áÔáTsÁçkÍ¿±sÁ+ýË �+~. <�� bõ&�eÚ yî&�\TÎÅ£� 32 Âs³T¢ nsTTq

� uóËÈqXæ\ yîÕXæ\«+ m+Ôá?

22

�d¿£�H� ` II



5. (i) {x | x nHû~ MATHEMATICS nHû |�<�+ýË n¿£�sÁ+} � d�$TÜ� sÃw�¼sY sÁÖ|�+ýË s�jáT+&�?

(ii) {5, 25, 125, 625} d�$TÜ jîTT¿£Ø �s��DsÁÖ|�+ s�jáT+&�?

6. ç¿ì+~ |�{²\qT |�]o*+º �V�Q|�~ jîTT¿£Ø XøSH�«\ d�+K«qT Ôî\|�+&�.

(i) (ii)

7. x2 - 9 �V�Q|�~ jîTT¿£Ø XøSH�«\T ¿£qT>=�, XøSH�«\Å£� �V�Q|�~ >·TD¿±\Å£� eT<ó�«>·\ d�+�+<ó�+

d�]#áÖ&�+&�.

8. 4.2 �d+.MT. y�«kÍsÁ�+>·\ nsÁ�>ÃÞø+ jîTT¿£Ø d�+|�PsÁ�Ôá\ yîÕXæ\«+ ç|�¿£ØÔá\ yîÕXæ\«+ ¿£qT>=q+&�.

9. ç¿ì+~ y�� $\Te\T ¿£qT>=q+&� ?

(i) 813log (ii) 2

256log

�d¿£�H� ` III



10. a. A = {1, 3, 5, 7, 9}

B = {2, 3, 5, 7}

C = {2, 4, 6, 8} nsTTq

(i) AÈ B (ii) B Ç C (iii) A - C (iv) AÈ (B È C) ¿£qT>=q+&�?

23

(ýñ<�)

b. P = {2, 4, 6, 8, 10, 12}

Q = {3, 6, 9, 12, 15}

R = {4, 8, 12, 16, 20, 24} nsTTq

(i) P - R (ii) Q - P (iii) P ÇQ (iv) R Ç Q \qT ¿£qT>=q+&�?

11. a. 6cm y�«kÍsÁ�+ >·\ d�Ö�bÍ¿±sÁ C²&�ýË�¿ì ÿ¹¿ y�«kÍsÁ�+ >·\ 64 >Ã°\qT C²sÁ$&�Te>± C²&�ýË�

ú{ìeT³¼+ �|]Ðq~. nsTTq >Ã° �|�]Ôá\ yîÕXæ\«+ ¿£qT>=q+&� ?

(ýñ<�)

11. b. ÿ¿£ Å£�{¡sÁ |�]çXøeTy�sÁT BsÁé |��TH�¿£�ÜýË �q� 66 �d+.MT., 42 �d+.MT., 21 �d+.MT. ¿=\Ôá\T

¿£*Zq yîT®q|�Ú~yîT� �|�jîÖÐ+º 4.2 �d+.MT. y�«d�eTT, 2.8 �d+.MT. mÔáTï ¿£*Zq d�Ö�bÍ¿±sÁ

¿=y=ÇÔáTï\qT ÔájáÖsÁT#ûjáÖ\qTÅ£�H��sÁT. y�sÁT #ûjáT>·*Zq ¿=y=ÇÔáTï\ d�+K«qT ¿£qT>=q+&�.

12. a. 2 3+ ÿ¿£ ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�.

(ýñ<�)

12. b. log ab = log a - log b �sÁÖ|¾+#á+&�.

log Pxx =

1P n� �sÁÖ|¾+#á+&�.

13. a. y = x2 - x - 6 nHû �V�Q|�~ XøSH�«\qT ç>±|�t <�Çs� kÍ~ó+#á+&�.

(ýñ<�)

13. b. x2 + 3x - 4 �V�Q|�~� Ôî*�| eç¿£¹sKqT �sÁÖ|�¿£ Ôá\+�|Õ #áÖ|¾ �V�Q|�~ XøSq«$\Te\T

¿£qT>=q+&�?

24


eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT �||�sY-I

ÔásÁ>·Ü ` 10

¿±\eTT : 2 >·+öö 45 �öö bÍsÁT¼ ` A & B >·]w�÷ eÖsÁTØ\T : 40

¿±\eTT : 30 �öö bÍsÁT¼ ` B >·]w�÷ eÖsÁTØ\T : 10

d�Ö#áq\T : 1. bÍsÁT¼ B q+<�* n�� ç|�Xø�\Å£� y�{ì Â¿<�TsÁT>± sTTeÇ�&�q çu²Â¿³¢jáT+<�T �+>·¢ n¿£�sÁeTT\ýË�

�|<�Ý n¿£�s�\qT A, B, C, D çy�jáTeýÉqT.

2. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ ¹¿{²sTT+#á&�yîT®q~.

3. ¿={ì¼yûÔá\T, ~~ÝyûÔá\T eTÖý²«+¿£qeTT #ûjáT�&�eÚ.

4. n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT sTTeÇeýÉqT.

�d¿£�H� ` IV

d�Ö#áq\T : 1. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ. 20I

1/2 R 10 eÖsÁTØ\T

14. x2+y2 = z2 nsTTÔû 2log yx

- G 2log yx

+ R ................ ( )

A) - 1 B) - 2 C) 1 D) 2

15.343log125

æ öç ÷è ø R ...................... ( )

A) 3 (log 5 - log 7) B) 3 (log 7 - log 5) C) 3 log (7 - 5) D) 3 log 5 - log 7

16. A nqT d�$TÜýË� ç¿£yîÖ|� d�$TÔáT\ d�+K« 32 nsTTq 'A' d�$TÜýË� eTÖ\¿±\ ( )

d�+K« ?

A) 2 B) 5 C) 7 D) 3

17. A £ B nsTTq A - B = ............. ( )

A) f B) A C) B D) m

18. �ç¿ì+~ y��ýË @~ ¹sFjáT d�eÖd�eTT (a¹o) ( )

A) ax + bx2 B) ax2 + bx C) ax + b D) a

25

19. y = x2 + 6x + 9 nqT eç¿£eTT X`n¿�±�� K+&�+#û _+<�TeÚ ( )

A) (`3, 0) B) (0, `3) C) (9, 0) D) (0, `9)

20. �ç¿ì+~ y��ýË @~ ¿£sÁD¡jáT d�+K« ( )

A) x2 + 5 = 0 jîTT¿£Ø kÍ<ó�q B) x2 ` 5 = 0 jîTT¿£Ø kÍ<ó�q

C) x ` 5 = 0 jîTT¿£Ø kÍ<ó�q D) x2 ` 16 = 0 jîTT¿£Ø kÍ<ó�q

21. �w&� #ûjáT�&�q çbÍ+ÔáeTTqT d�Öº+#áTq~ ( )

A) AÇ B B) A eÖçÔáyûT

C) AÈ B D) B eÖçÔáyûT

22. x3 - 6x2 + 11x - 6 �V�Q|�~¿ì XøSq«$\Te ¿±�~ ( )

A) 1 B) 2 C) 3 D) 4

23. ÿ¿£ d�eT|��TqeTT jîTT¿£Ø ¿£sÁ�eTT ( )

A) 3a B) 3a C) 2a D) 2a

24. 15, 21 \ >·.kÍ.uó² R 18 - 3x nsTTq x = ................ ( )

A) 15 B) 3 C) 5 D) - 5

25. MATHEMATICS nqT |�<�eTTýË� n¿£�sÁeTT\ÔÃ @sÁÎ&�T d�$TÜ ( )

A) {M, A, T, H, E, I, S} B) {A, C, E, I, H, M, S, T}

C) {M, A, T, H, E, I, C, S} D) (B) eT]jáTT (C)

26. d�+esÁZeÖqeTT jîTT¿£Ø $\Te m\¢|�ð&�Ö...... ( )

A) <ó�q ýñ<� �TTDd�+K«\T B) <ó�qd�+K«\T

C) �TTDd�+K«\T D) 0

27. p(x) = x2 - 3 nHû esÁZ �V�Q|�~ jîTT¿£Ø XøSq«$\Te\ yîTTÔáïeTT ( )

A) 3 B) 3 C) 0 D) 1

A B

26

28. a , b , g \T eTÖ\¿±\T>± >·\ p(x) = ax3 + bx2 + cx + d (a ¹ o) �V�Q|�~ýË ( )

1 1 1a b g

+ + R ........................

A) - c/d B) - b/d C) bd D)

cd

29. 1) ÿ¿£ >·~ >Ã<�\ jîTT¿£Ø ç|�¿£ØÔá\ yîÕXæ\«eTT ( ) a) 2 P r (h+r)

2) ÿ¿£ Xø+KTeÚ jîTT¿£Ø eç¿£Ôá\ yîÕXæ\«eTT ( ) b) 2 P (l+b)

3) d�Ö�|�eTT jîTT¿£Ø d�+|�PsÁ�Ôá\ yîÕXæ\«eTT ( ) c) P rl

A) 1-a, 2-b, 3-c B) 1-c, 2-a, 3-b ( )

C) 1-b, 2-c, 3-a D) 1-b, 2-a, 3-c

30. �ç¿ì+~y��ýË @~ n|�]$TÔá d�$TÜ neÚÔáT+~ ( )

A) ÿ¿£ Hî\ýË� y�sÁeTT\ d�$TÜ B) ÿ¿£ d�+eÔáàsÁeTTýË� Hî\\ d�$TÜ

C) 100 jîTT¿£Ø ¿±sÁD²+¿±\ d�$TÜ D) 100 jîTT¿£Ø >·TDC²\ d�$TÜÿ¿£

31. ÿ¿£ CË¿£sÁT jîTT¿£Ø Ôá\{Ë|¾ ç¿£eTXø+KTeÚ �¿±sÁeTTýË �q�~. <��jîTT¿£Ø uó�Öy�«kÍsÁ�eTT ( )

7 �d+.MT. eT]jáTT mÔáTï 24 �d+.MT. nsTTq � {Ë|¾� ÔájáÖsÁT#ûjáTT³Å£� ¿±e\d¾q

>·T&�¦ yîÕXæ\«eTT m+Ôá ?

A) 528 cm2 B) 550 cm2 C) 550 cm D) 620 cm3

32. ÿ¿£ ç¿£eTe�Ô�ï¿±sÁ Xø+KTeÚ jîTT¿£Ø y�«kÍsÁ�eTT eT]jáTT mÔáTï\T 2:3 �w�ÎÜïýË �q� ( )

y�{ì |��Tq|�]eÖDeTT\ �w�ÎÜï

A) 2:3 B) 3:2 C) 4:9 D) 8:27

33. �ç¿ì+~y��ýË @~ 3D �¿±sÁeTTqT d�Öº+#áTqT ( )

A) nÐZ�|fÉ¼ B) �||�sÁT C) ¹sK D) @~jáTT ¿±<�T

27

Weightage Table (Paper-II) forAcademic Standard wise

Academic Standard L.A. S.A. V.S.A. M.C.Q. Total %4m 2m 1m 1/2m

PS 2 (4) 2 (2) 1 (1) 6 (1/2) 11 (16) 40%

R.P 1 (4) 1 (2) - 4 (1/2) 6 (8) 20%

Communication - 1 (2) 1 (1) 2 (1/2) 4 (4) 10%

Connections - 1 (2) 2 (1) 4 (1/2) 7 (6) 15%

Representation & 1 (4) - - 4 (1/2) 5 (6) 15%Visual Form

Total 4 (4) 5 (2) 4 (1) 20 (1/2) 33 (40) 100%

28


eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT �||�sY-II

ÔásÁ>·Ü ` 10





3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.



6. �d¿£�H� III q+<�* ç|�Xø�\Å£� n+ÔásÁZÔá m+|¾¿£ (Internal Choice) �+³T+~.

�d¿£�H� ` I



1. çÜ¿ÃD$TÜ $\Te\ |�{ì¼¿£ �|�jîÖÐ+#áÅ£�+&�

2 2

2 2

sec cot 40sin 20 sin 70

o

o o

-+

$\Te ¿£qT>=q+&�?

2. ç|�¿£Ø |�³eTTýË x $\Te m+Ôá ?

3. ÜsÁT|�Ü |�³¼D+ýË yûT Hî\ 2016 yîTT<�{ìy�sÁ+ýË qyîÖ<�sTTq �cþ�ç>·Ôá\T esÁTd�>± 38+, 41

+, 42

+,

43+, 45

+, 39

+, 40

+ qyîÖ<�sTTq$. � y�sÁ+ýË� d�>·³T �cþ�ç>·Ôá m+Ôá?

4.

�|Õ |�{ì¼¿£ d�V�äjáT+ÔÃ MT çbÍ+ÔáeTTýË ç¿=Ôáï>± Âs&�yûT&� <�T¿±D<�sÁT�¿ì mÅ£�Øe neT�¿£+ ÈsÁ>·&��¿ì

úeÚ �#ûÌ d�\V�ä @$T?

P

Q

R

x T

S

36 12

9

(

jáTÖ�b�Íy�T �dÕE 18 20 22 24

$<�«sÁT�\ d�+K« 12 16 50 22

29

�d¿£�H� ` II



5. 5 �d+.MT, 12 �d+.MT, 13 �d+.MT ¿=\Ôá\T >·\ \+�¿ÃD çÜuó�TÈ yîÕXæ\«+ýË 4e e+ÔáT ¿£*Zq d�sÁÖ|�

çÜuó�TÈ ¿£sÁ�+ bõ&�eÚ ¿£qT>=qTeTT.

6. 6 �d+.MT. y�«kÍsÁ�+ >·\ e�Ôáï+ýË ÿ¿£ C²« ¹¿+ç<�+ e<�Ý 60+ ¿ÃD+ #ûd�Tï+~. C²« bõ&�eÚ ¿£qT>=q+&�.

7. Sin 60o Cas 30 + Sin 30o Cas 60 eT]jáTT Sin (60+30) $\Te\T d�eÖqeÖ ¿±<�? M{ìqT+&� MT¹s$T

ç>·V¾²+#�sÁT?

8. e Z¿£�Ôá <�Ô�ï+Xø u²V�QÞø¿£ d�ÖçÔá+ s�d¾ |�<�\T $XøB¿£]+#á+&�?

9.

�|Õ |�{ì¼¿£qT+&� $<�«sÁT�\ d�s�d�] �sÁTeÚqT ¿£qT>=q+&�.

�d¿£�H� ` III


2. ç|�Ü ç|�Xø�Å£� 4 eÖsÁTØ\T. 4I4 R 16 eÖsÁTØ\T

10 (a) çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+Ôá+ �sÁÇº+º �sÁÖ|¾+#á+&�

(ýñ<�)

10 (b) çÜuó�TÈ\+ ABD ýË \+�¿ÃDeTT A e<�Ý ¿£\<�T

eT]jáTT AC ^ BD nsTTq

(i) AB2 = BC.BD (ii) AC2 = BC.DC

(iii) AD2 = BD.CD n� #áÖ|�+&�.

$<�«sÁT�\ �sÁTeÚ Kg\ýË 20 25 30 35

d�+K« 2 7 10 6

B A

D

C

30

11 (a) (Sin A + Cosec A)2 + (Cos A + Sec A)2 = 7 + tan2A + Cot2A n� #áÖ|�+&�.

(ýñ<�)

11 (b) Sec q + Tan q = P nsTTq Sin q $\Te ¿£qT>=q+&�.

12 (a) |¾\¢\ sÃEy�] Cñ�T KsÁTÌ\T $es�\T ç¿ì+~ båq'|�Úq« $uó²È¿£ |�{ì¼¿£ýË �eÇ�&�q$. |¾\¢\

d�>·³T #ûÜKsÁTÌ 18 sÁÖöö nsTTq ç¿ì+~ |�{ì¼¿£ýË ýË|¾+ºq båq'|�Úq«eTT ( f ) qT ¿£qT>=qTeTT.

(ýñ<�)

12 (b) ç¿ì+~ båq'|�Úq« $uó²Èq |�{ì¼¿£Å£� eT<ó�«>·Ôá+ ¿£qT>=q+&�?

13 (a) 5 �d+.MT., 6 �d+.MT., 7 �d+.MT. ¿=\Ôá\ÔÃ çÜuó�TC²�� ]�+º B�¿ì d�sÁÖ|�+>± �+³Ö �

çÜuó�TÈ uó�TC²\Å£� 75 Âs³T¢ nqTsÁÖ|� uó�TC²\T ¿£*Ðq çÜuó�TC²�� ]�+#á+&�.

(ýñ<�)

13 (b) 3 �d+.MT, 4 �d+.MT uó�TC²\T>± >·\ \+�¿ÃD çÜuó�TC²�� ]�+º B�¿ì d�sÁÖ|�+>± �+³Ö �

çÜuó�TÈ uó�TC²\Å£� 53 Âs³T¢ nqTsÁÖ|� uó�TC²\T ¿£*Zq çÜuó�TC²�� ]�+#á+&�?

|¾\¢\ #ûÜKsÁTÌ 11`13 13`15 15`17 17`19 19`21 21`23 23`25

|¾\¢\ d�+K« 7 6 9 13 f 5 4

$\Te\T < 100 100`200 200`300 300`400 > 400

båq'|�Úq«+ 50 90 158 68 134

31



ÔásÁ>·Ü ` 10



d�Ö#áq\T : 1. bÍsÁT¼ B q+<�* n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT\T çy�jáT+&�.

2. ç|�Ü ç|�Xø�Å£� d�+�+~ó+ºq Èy��TqT d�Öº+#áT �+>·¢ �|<�Ý n¿£�sÁeTTqT ç|�¿£Øq sTTºÌq

çu²Â¿³¢ýË çy�jáT+&�.

3. ¿={ì¼yûÔá\T, ~<�TÝu²³¢Å£� eÖsÁTØ\T sTTeÇ�&�eÚ.

4. n�� ç|�Xø�\Å£� eÖsÁTØ\T d�eÖqeTT.

�d¿£�H� ` IV



14. DABC ~ DDEF eT]jáTT ÐA R 37+, ÐE R 64

+ nsTTq ÐC R ? ( )

A) 59+ B) 69

+ C) 79+ D) 101

+

15. 4 �d+.MT uó�TÈeTT ¿£*Zq ÿ¿£ s�+�dt jîTT¿£Ø ¿£sÁ�eTT\ jîTT¿£Ø es�Z\ yîTTÔáïeTT ( )

A) 16 �d+.MT. B) 36 �d+.MT. C) 56 �d+.MT. D) 64 �d+.MT

16. �ç¿ì+~ y��ýË d�sÁÖbÍ\T ¿±�$ ( )

A) @yîÕH� Âs+&�T q\¢�\¢\T

B) eT�w¾ eT]jáTT nÔá� ú&�

C) |�]eÖD²\T ÔáÐZ+ºq eT]jáTT �|+#á�&�q b�þ{Ë\T

D) <�sÁÎDeTTýË� ed�TïeÚ eT]jáTT <�� ç|�Ü_+�eTT

17. ÿ¿£ çÜuó�TÈeTTq+<�T eT<ó�«>·Ôá ¹sK\ $T[Ôá_+<�TeÚ ................ ( )

A) n+ÔásÁe�Ôáï ¹¿+ç<�eTT B) |�]e�Ôáï ¹¿+ç<�eTT

C) >·TsÁTïe¹¿+ç<�eTT D) \+�¹¿+ç<�eTT

32

18. ÿ¿£ çÜuó�TÈeTTq+<�T eTÖ&�T uó�TC²\ es�Z\ yîTTÔáïeTT <��jîTT¿£Ø eT<ó�«>·Ôá¹sK\ es�Z\ ( )

yîTTÔáïeTTqÅ£� .................... Âs³T¢

A) Âs{ì¼+|�Ú B) H�\T>·T C) d�>·eTT D) d�eÖqeTT

19. ÿ¿£ e«¿ìï 20 MT. ÔáÖsÁTÎ>± ç|�jáÖDì+º n¿£Ø&�qT+&� 15 MT. �ÔáïsÁ ~Xø>± yî[ßq#Ã ( )

ç|�d�TïÔáeTT yîTT<�{ì kÍ�qeTT qT+&� m+Ôá <�ÖsÁeTTýË �H��&�T

A) 5 MT. B) 35 MT. C) 25 MT. D) 10 5 MT.

20. ABC çÜuó�TÈeTTq+<�T 'C' osÁüeTT e<�Ý \+�¿ÃDeTT @sÁÎ&�q~. CD ^ AB eT]jáTT ( )

�ç¿ì+~ y��ýË @~ d�Ôá«eTT

A) 1 1 1p a b

= + B) p = a+b

C) 2 2 2

1 1 1p a b

= + D) p2 = a2+b2

21. Sin 2q = Cos 3q nsTTq Tan 2q R .............. ( )

A) 1 B) 0 C) 12 D) ¥

22. 'Sin q' qT 'Sec q' |�<�\ýË e«¿£ï|�sÁ#áTeTT. ( )

A) 2 1

Sec

Secq

q-

B) 2 1

SecSec

qq- C)

2

2

1

SecSec

qq- D)

1

SecSec

qq-

23. Sin2 30o, Sin2 45o, Sin2 60o \T .................... çXâ&ó�ýË �+{²sTT. ( )

A) n+¿£çXâ&ó� B) >·TDçXâ&ó�

C) n+¿£çXâ&ó� D) n+¿£çXâ&ó�, >·TDçXâ&ó�\T ¿±<�T

24.

2 2

2

18 7245

o o

o

Sin SinCos

+ R ................... ( )

A) 0 B) 1 C) 2 D) 3

25. Sin q . Sec q . Cos q . Cosec q R .............. ( )

A) Sin2 q B) Cos2 q C) Sec2 q D) Sin2 q+Cos2 q

A D B

a

C

b p

33

26. Cos405o R ................... ( )

A) 1 B) 12 C)

12 D) �|Õ @$jáTT ¿±eÚ

27. ç|�¿£Ø |�³eTTq+<�T tan C = ..................... ( )

A) 12 B)

13

C) 2 D) 3

28. 10`25 ÔásÁ>·Ü jîTT¿£Ø eT<ó�«$\Te ...................... ( )

A) 15 B) 17 C) 17.5 D) 19.5

29. yîTT<�{ì 15 ç|�<ó�q d�+K«\ jîTT¿£Ø eT<ó�«>·ÔáeTT ( )

A) 17 B) 19 C) 23 D) 29

30. �ç¿ì+<� sTTºÌq <�Ô�ï+XøeTTq+<�T d�]jî®Tq~ ( )

12, 9, 15, 15, 18, 7, 24

A) n+¿£ eT<ó�«eTeTT R eT<ó�«>·ÔáeTT B) n+¿£eT<ó�«eTeTT R 15

C) n+¿£eT<ó�«eTeTT R �V�QÞø¿£eTT D) eT<ó�«>·ÔáeTT R �V�QÞø¿£eTT

31. e Z¿£�Ôá <�Ô�ï+XøeTTq+<�T eT<ó�«>·ÔáeTT ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )

A) 2N f

l hF

-+ ´ B) 2

F Nl h

f

-+ ´ C) 2

N Fl h

f

-+ ´ D) 2

N hl h

f

-+ ´

32. ~>·Te båq'|�Úq« $uó²Èq |�{ì¼¿£ýË 10`15 ÔásÁ>·Ü u²V�QÞø¿£eTT m+Ôá ?

A) f = 15 eÖçÔáyûT B) f ³ 15 C) f < 7 D) f < 15 ( )

33. ÿ¿£ ÔásÁ>·ÜjáT+<�T 30 eT+~ u²\TsÁT, 20 eT+~ u²*¿£\T >·\sÁT. MsÁT >·DìÔá |� ¿£�Å£� ( )

V�äÈsÁT¿±>± u²\TsÁ d�>·³TeÖsÁTØ 15, u²*¿£\ d�>·³TeÖsÁTØ 10, nsTTq yîTTÔáïeTT ÔásÁ>·Ü

d�>·³TeÖsÁTØ m+Ôá?

A) 25 B) 30 C) 13 D) 20

A

B C

1 2

(

ÔásÁ>·Ü 0`5 5`10 10`15 15`20 20`25

båq'|�Úq«+ 11 14 f 10 07

34



ÔásÁ>·Ü ` 10 ` �||�sY I¿±\eTT : 2 >·+öö 45 �öö bÍsÁT¼ ` A & B >·]w�÷ eÖsÁTØ\T : 40




3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.




�d¿£�H� ` I



1. (A - B) È (B - A) = AADB eT]jáTT N nHû~ d�V�²È d�+U²«d�$TÜ, W nHû~ |�Ps��+¿±\ d�$TÜ nsTTÔû

NDW qT ¿£qT>=q+&�.

2. jáTÖ¿ì¢&� uó²>·V�äsÁ Xâw�$~ó qT|�jîÖÐ+º 90, 70\ >·.kÍ.uó². ¿£qT>=q+&�.

3. d�eÖq y�«kÍsÁ�eTT, mÔáTï >·\ d�Ö�|�eTT, >ÃÞøeTT\ |��Tq|�]eÖD²\ �w�ÎÜï� ¿£qT>=qTeTT.

4. Âs+&�T <ó�q eTÖý²\T �+&û ÿ¿£ esÁZd�eÖkÍ\qT çy�jáT+&�.

�d¿£�H� ` II



5. (2.3)x = (0.23)y R 1000 nsTTq 1 1x y

- $\Te ¿£qT>=q+&�.

6. p(x) = x3 - 8 nsTTq p(2), p( - 2), p(3), p( - 3) $\Te\T ¿£qT>=q+&�.

35

7. 4x - 6y = 15, 2x - 3y = 5 d�MT¿£sÁD²\Å£� kÍ<ó�q kÍ<ó�«eÖ? ¿±<�? |�]o*+º kÍ<ó�«eTsTTÔû ¿£qT>=q+&�.

8. XøSq«d�$TÜ¿ì Âs+&�T �<�V�²sÁD*eÇ+&�? MT Èy��TqT d�eT]�+#á+&�.

9. ç¿£eT e�Ô�ï¿±sÁ Xø+KTeÚ �¿±sÁeTTýËqTq� CË¿£sY {Ë|¾ uó�Öy�«kÍsÁ�+ 7 �d+.MT. eT]jáTT mÔáTï 24

�d+.MT. �³Te+{ì 15 {Ë|Ó\qT ÔájáÖsÁT#ûjáT&��¿ì m+Ôá n³¼ ¿±eýÉqT.

�d¿£�H� ` III



10.2 3 17

3 2 3 2 5x y x y+ =

+ - eT]jáTT 5 1 2

3 2 3 2x y x y+ =

+ - \qT kÍ~ó+#á+&�.

(ýñ<�)

>·DìÔá+ýË CË«Üw�, Èd¾�Ôá\ eÖsÁTØ\ yîTTÔáï+ 50 ÿ¿£yûÞø CË«w¾ÔáÅ£� 3 eÖsÁTØ\T mÅ£�Øe>±qT Èd¾�ÔáÅ£�

3 eÖsÁTØ\T ÔáÅ£�Øe>±qT eºÌeÚ+fñ y�] eÖsÁTØ\ \�Æ+ 625 nsTTq y�] eÖsÁTØ\T m��?

11. 20 MT. ýËÔáT, 7 MT. y�«d�eTT �+&û³³T¢ ÿ¿£ u²$� çÔá$Ç]. çÔáeÇ>± eºÌq eT{ì¼� 22 MT I

14 MT. ¿=\Ôá\T >·\ ÿ¿£ bÍ¢{Ùb�Í+>± d�eÖq+>± (#á<�TqT>±) bþd¾q � b�Í¢{Ùb�ÍsÁ+ mÔáTï m+Ôá?

(ýñ<�)

11. ÿ¿£ |��Tq �V�Q|�~ jîTT¿£Ø XøSH�«\ yîTTÔáï+, Âs+&ûd¾ XøSH�«\ \u²Ý\ yîTTÔáï+ eT]jáTT XøSH�«\ \�Æ+\T

esÁTd�>± 2, - 7, - 14 nsTTq � |��Tq�V�Q|�~� ¿£qT>=q+&�.

12. (a) 5 2+ nHû~ ÿ¿£ ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�.

(ýñ<�)

12. (b) ç¿ì+~ y��ýË d�$TÔáTýñ$? MT Èy��TqT d�eT]�+#á+&�.

(i) uó²sÁÔá<ûXø+ýË� 10 eT+~ n+<�yîT®q e«Å£�ï\ d�eTT<�jáT+.

(ii) uó²sÁÔá<ûXø+ýË� n�� q<�T\ d�eTT<�jáTeTT.

(iii) uó²sÁÔá ç¿ìÂ¿{Ù È³¢ýË� eT+º u²«{ÙàyîTH�\ d�eTT<�jáTeTT.

(iv) uó²sÁÔá eTV¾²Þ² ç�|d¾&î+{Ù\ (n<ó�«Å£��\) d�eTT<�jáTeTT.

36

13. (a) eTÖ&�T Å£�¯Ì\T, Âs+&�T fñ�TÞøß $\Te sÁÖ.2,250/`. Âs+&�T Å£�¯Ì\T eTÖ&�T fñ�TÞøß $\Te

sÁÖ. 2,750/`. ç|�r Å£�¯Ìyî\, fñ�TýÙ yî\\qT ç>±|�t <�Çs� ¿£qT>=qTeTT.

(ýñ<�)

13. (b) x2 - 2x - 8 �V�Q|�~� ç>±|�t |�<�ÆÜ <�Çs� kÍ~ó+#áTeTT.

37



ÔásÁ>·Ü ` 10



d�Ö#áq\T : 1. bÍsÁT¼ B q+<�* n�� ç|�Xø�\Å£� y�{ì Â¿<�TsÁT>± sTTeÇ�&�q çu²Â¿³¢jáT+<�T �+>·¢ n¿£�sÁeTT\ýË�

�|<�Ý n¿£�s�\qT A, B, C, D çy�jáTeýÉqT.

2. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ ¹¿{²sTT+#á&�yîT®q~.

3. ¿={ì¼yûÔá\T, ~~ÝyûÔá\T eTÖý²«+¿£qeTT #ûjáT�&�eÚ.

4. n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT sTTeÇeýÉqT.

�d¿£�H� ` IV



14. 632016log G 32

2016log jîTT¿£Ø $\Te R ................ ( )

A) 632016log B) 95

4032log C) 1 D) 0

15. 2 2 2 Sin+ + + ¥ R ...................... ( )

A) 2 B) 8 C) 2 2 D) 2

16. a, b \ eT<ó�« n¿£sÁD¡jáT d�+K« ( )

A) ab B) 2a b+

C) .a b D) ab

17. 3, 6, 9, 12, ......... 30 jîTT¿£Ø d�$TÜ �s��D sÁÖ|�eTT ( )

A) {3x | x = 1, 2, 3, 4, .......10, xÎn} B) {x : x nqTq~ ç|�<ó�qd�+K«}

C) {x2 | xÎn} D) {x : x nqTq~ 30 ¿£+fÉ ÔáÅ£�ØyîÕq uñd¾d�+K«}

18. P, Q nHû$ Âs+&�T $jáTT¿£ï d�$TÔáT\T nsTTq P - Q = ................... ( )

A) P È Q B) P Ç Q C) P D) Q

38

19. ç|�¿£Ø |�³eTT d�Öº+#áTq~ :` ( )

A) P Ç Q Ç R B) (P Ç Q)`R C) P`(Q Ç R) D) Q`(R Ç P)

20. 2017 jîTT¿£Ø |�]eÖDeTT ( )

A) 2017 B) 0 C) 1 D) 7

21. ax2 + bx + c esÁZ �V�Q|�~ jîTT¿£Ø XøSq«$\Te\ yîTTÔáïeTT eT]jáTT \�ÝeTT ( )

d�eTqeT>·T³Å£�

A) a = b B) a = c C) b = - c D) b = c

22. ç|�¿£Øq �q� ¹sU²ºçÔáeTT y = p(x) XøSq«$\Te\ d�+K« ( )

A) 2 B) 3 C) 0 D) 1

23. Âs+&�T <ó�qd�+K«\jîTT¿£Ø yîTTÔáïeTT 27, eT]jáTT y�{ì \�ÆeTT 180 nsTTq � ( )

<ó�qd�+K«qT

A) 11, 16 B) 10, 17 C) 12, 15 D) 10, 18

24. ax+by+c = 0, a, b, cÎr nqT ¹sFjáT d�MT¿£sÁDeTTýË a, b \qT Ôá�|¾ï|�sÁ#áTq~. ( )

A) a2+b2 = 0 B) a2+b2 ¹ 0 C) a+b ¹ 0 D) a+b = 0

25. ¹sFjáT d�MT¿£sÁD²\ ÈÔá d�+>·Ôá d�MT¿£sÁD²\T eT]jáTT |�sÁd�ÎsÁ �<ó�]Ôá d�MT¿£sÁD²\T ( )

nsTTq

A) 1 1

2 2

a ba b

= B) 1 1

2 2

a ba b

¹ C) 1 1 1

2 2

a b ca b c

= ¹ D) 1 1 1

2 2 2

a b ca b c

= =

26. lx2 - mx - n = 0 esÁZ d�MT¿£sÁDeTT jîTT¿£Ø eTÖý²\T a , b nsTTq a 2, b 2 = .......... ( )

A) 2

mnl B)

2lmn

C) 2

2

2m nll+

D) 2n

lm

27. 6x2 - px + 15 = 0 jîTT¿£Ø $#á¿ì�Dì 81 nsTTq p $\Te R ................... ( )

A) 21 B) 31 C) 18 D) 41

P Q R m

39

28. �ç¿ì+~ y��ýË b2 - 4ac Ü 0 ( )

A) B)

C) D)

29. yîTT<�{ì 'n' d�V�²È d�+K«\ yîTTÔáïeTT 465 nsTTq n $\Te m+Ôá ? ( )

A) 25 B) 29 C) 30 D) 31

30. ÿ¿£ uË\T >ÃÞøeTT jîTT¿£Ø |��Tq|�]eÖDeTT ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )

A) ( )3 343

R rP - B) ( )3 323

R rP - C) ( )3 3R rP - D) ( )3 313

R rP -

31. d�eÖq y�«d�eTT eT]jáTT d�eÖq mÔáTï\T ¿£*Zq d�Ö�|�eTT, Xø+KTeÚ eT]jáTT >ÃÞøeTT\ ( )

jîTT¿£Ø |��Tq|�]eÖDeTT\ �w�ÎÜï

A) 2:3:1 B) 1:3:2 C) 3:1:2 D) 3:2:1

32. ................ �¿±sÁeTTqT <�� ÿ¿£ uó�TÈeTT �<ó�sÁeTT>± çuó�eTDeTT #ûd¾q#Ã d�Ö�|�eTT ( )

@sÁÎ&�TqT.

A) s�+�dt B) BsÁé#áÔáTsÁçd�eTT C) \+�¿ÃD çÜuó�TÈeTT D) e�ÔáïeTT

33. ç|�¿£Ø |�³eTTq+<�T l, h, r \ jîTT¿£Ø d�+�+<ó�eTT ( )

A) l + h = r2 B) l = r2 + h2 C) l2 = h2 - r2 D) l2 = h2 + r2

40



ÔásÁ>·Ü ` 10





3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.




�d¿£�H� ` I



1. #ûÜ >±E d�V�äjáT+ÔÃ ^ºq e�Ô�ï�¿ì ¹¿+ç<�eTTqT mý² ¿£qT>=+{²eÚ?

2. Cos q + Tan q.Sinq = Sec q n� #áÖ|�+&�.

3. eTÖ\_+<�TeÚ ¹¿+ç<�eTT>± >·\ e�Ôáïy�«d�eTT jîTT¿£Ø ÿ¿£ ºe] _+<�TeÚ (3, 2) nsTTq �+¿=¿£ ºe]

_+<�TeÚ �sÁÖ|�¿£eTT ¿£qT>=qTeTT.

4. 3 �d+.MT, 4 �d+.MT, 5 �d+.MT ¿=\Ôá\T>·\ \+�¿ÃD çÜuó�TÈ yîÕXæý²«�� V²s�H� d�ÖçÔáeTT <�Çs�

d�]#áÖ&�+&�.

41

�d¿£�H� ` II



5. ç¿ì+~ |�{ì¼¿£ýË �ºÌq çÜuó�TÈ+ ABC ýË� uó�TC²\ bõ&�eÚ\ �<ó�sÁ+>± @~ d�sÁÖbÍ\eÚÔ�jîÖ Ôî\|�+&�?

6. ( )5 3, 7 , ( )3 3, 1 _+<�TeÚ\qT ¿£*�| d�sÁÞø¹sK X-n¿£�+ÔÃ 60+ ¿ÃD+ #ûd�Tï+<�� ¿±e« #î|¾Î+~. �~

d�ÂsÕq<ûH� ú d�eÖ<ó�q+ d�eT]�+#á+&�.

7. A (a, b) eT]jáTT B (b, a) \qT ¿£*�| ¹sK�|Õ C (x, y) @<û� _+<�TeÚ nsTTÔû x + y $\Te ¿£qT>=q+&�?

8. 5 Tan A = 12 nsTTq Sin A, Cas A $\Te\T ¿£qT>=qTeTT?

9. AB y�«d�eTT>± >·\ e�Ôáï+ýË BC, AC \ bõ&�eÚ\T esÁTd�>± 8 �d+.MT, 6 �d+.MT

nsTTq �w&� #ûd¾q ç|�<ûXø yîÕXæý²«�� ¿£qT>=qTeTT ?

�d¿£�H� ` III



10 (a) �|Õ<�>·sÁdt (C²<�ÝjáTq) d¾<�Æ+ÔáeTTqT �sÁÇº+º �sÁÖ|¾+#á+&�.

(ýñ<�)

10 (b) eTÖ\_+<�TeÚ ¹¿+ç<�eTT>± 5�d+.MT y�«kÍsÁ�+ÔÃ ^ºq e�Ô�ï�¿ì A (13, 0) eT]jáTT

C ( - 13, 0) _+<�TeÚ\ qT+&� ^ºq d�ÎsÁô¹sK\T B, D e<�Ý K+&�+#áT¿=q&�+ e\q

@sÁÎ&�q #áÔáTsÁTÒÛÈ |�³ yîÕXæý²«�� ýÉ¿ìØ+#á+&�?

AB BC AC

1e çÜuó�TÈ+ 2�d+.MT 5�d+.MT 6�d+.MT



A B

C

42

11 (a) ç¿ì+~ <�Ô�ï+Xæ�¿ì eT<�«>·Ôá+ ¿£qT>=q+&�.

(ýñ<�)

11 (b) Cos q + Cot q = K nsTTq Cos q + Sec q $\Te ¿£qT>=q+&�.

12 (a) ( - 2, 4) (8, - 1) \#û @sÁÎ&�T ¹sU²K+&�� nd�eÖq uó²>±\T>± $uó��+#û _+<�TeÚ\ �sÁÖ|�¿±\T

¿£qT>=q+&�.

(ýñ<�)

12 (b) A (2, 4) B (6, 8) C (8, 3) D (5, 1) _+<�TeÚ\#û @sÁÎ&�T #áÔáTsÁTÒÛÈ yîÕXæ\«+ ¿£qT>=qTeTT.

13 (a) 5 �d+.MT., 6 �d+.MT., 7 �d+.MT. ¿=\Ôá\ÔÃ çÜuó�TC²�� ]�+º <��¿ì d�sÁÖ|�+>± �+³Ö

çÜuó�TÈ uó�TC²\Å£� 23 Âs³T¢ nqTsÁÖ|� uó�TC²\T ¿£*Ðq çÜuó�TC²�� ]�+#á+&�.

(ýñ<�)

13 (b) e�Ôáï y�«kÍsÁ�+ 5 �d+.MT eT]jáTT Âs+&�T d�ÎsÁô¹sK\ eT<�«¿ÃD+ 60+ nsTTq � e�Ô�ï�¿ì

d�ÎsÁô¹sK\T ^jáT+&�.

ÔásÁ>·Ü n+<�sÁ+ 5`15 15`25 25`35 35`45 45`55 55`65

båq'|�Úq«+ 8 7 6 12 9 8

43



ÔásÁ>·Ü ` 10








�d¿£�H� ` IV



14. Y n¿£�eTT jîTT¿£Ø y�\T ...................... ( )

A) 0 B) 1 C) - 1 D) �sÁÇº+#á�&�<�T

15. ÿ¿£ ¹sU²K+&�� <�� eT<ó�« _+<�TeÚ $uó��+#áT �w�ÎÜï ( )

A) 1:1 B) 1:2 C) 2:1 D) 1:3

16. 2x - 3y + 7 = 0, 6x - ky + 18 = 0 nqT ¹sK\T d�eÖ+ÔásÁeTTýÉÕq#Ã 'k' $\Te ........ ( )

A) 3 B) 6 C) 9 D) 25

17. ÿ¿£ esÁTd�ç¿£eTeTTýË rd�T¿=q�&�q d�eÖ+ÔásÁ #áÔáTsÁTÒÛÈeTT jîTT¿£Ø osÁüeTT\T A (6, 1), ( )

B (8, 2), d (9, 4), D (p, 3) os�ü\T>± >·*Zq#Ã p $\Te .....................

A) 6 B) 7 C) 9 D) - 4

18. (6, 2), (0, 0) eT]jáTT (4, - 7) os�ü\T>± >·*Zq çÜuó�TÈeTTjîTT¿£Ø >·TsÁTÔáÇ ¹¿+ç<�eTT ( )

A) 10 7, 3 3

æ öç ÷è ø B)

10 5, 3 3

æ öç ÷è ø C)

10 5, 3 3

-æ öç ÷è ø D) @~jáTT ¿±<�T

44

19. eTÖ&�T _+<�TeÚ\ÔÃ @sÁÎ&�q çÜuó�TÈ yîÕXæ\«eTT d�TH�� nsTTq#Ã � eTÖ&�T ( )

_+<�TeÚ\qT ................. _+<�TeÚ\T n+<�TsÁT.

A) d�¹sFjáÖ\T ¿±� B) @¿¡uó�$+#û C) d�¹sFjáT D) @B¿±<�T

20. DABC ýË DEP BC, AD = x; DB = x - 2, AE = x+2, ( )

eT]jáTT EC = x - 1 nsTTq x $\Te

A) 2 B) 4 C) 6 D) 8

21. ABC çÜuó�TÈeTTq+<�T AB = AC eT]jáTT 'D' nqT _+<�TeÚ BC �|Õ �q�~. nsTTq ( )

AB2 - AD2 =

A) BD2 B) AC2 C) BD2.CD D) AB.AC

22. m\¢|�ð&�Ö d�sÁÖ|�eTT¿±� |�³eTT\T ( )

A) e�Ô�ï\T B) çÜuó�TC²\T C) #áÔáTsÁçd�eTT\T D) @~jáTT ¿±<�T

23. ÿ¿£ e�Ôáï yîÕXæ\«eTTqT y�«d�eTTqT �|�jîÖÐ+º ¿£qT>=qTeTT. ( )

A) Pd2 B) 2

4dP

C) 2Pd2 D) 23 Pd2

24. 8 �d+.MT y�«kÍsÁ�eTT>± >·\ e�Ô�ï�¿ì <�� ¹¿+ç<�eTTqT+&� 17 �d+.MT <�ÖsÁeTTýË ( )

ÿ¿£ _+<�TeÚ ¿£\<�T. nsTTq <��¿ì ^jáT�&�q d�ÎsÁô¹sK bõ&�eÚ m+Ôá?

A) 9 �d+.MT B) 25 �d+.MT C) 15 �d+.MT D) 136 �d+.MT

25. r1, r2 y�«kÍs��\T>± ¿£*Zq Âs+&�T e�Ô�ï\T u²V�²«eTT>± d�Î]ô+#áT¿=�q#Ã y�{ì ¹¿+ç<�\ ( )

eT<ó�« <�ÖsÁeTT 'd' nsTTq#Ã

A) d = r1.r2 B) d = r1 - r2 C) d = r1 + r2 D) r1 - r2

26. ç|�¿£Ø |�³eTTq+<�T e�Ôáï y�«kÍsÁ�eTT 14 �d+.MT eT]jáTT ( )

e�Ôáï¹¿+ç<�eTT e<�Ý 120+ ¿ÃD²\T @sÁÎsÁºq#Ã � e�Ôáï C²«

bõ&�eÚ m+Ôá?

A) 14 �d+.MT B) 21 �d+.MT C) 28 �d+.MT D) 14 3 �d+.MT

A D B

C

E

A B

o14 14)

120o

45

27. 7 �d+.MT y�«kÍsÁ�eTT, e�Ôáï¹¿+ç<�eTT e<�Ý 144+ @sÁÎsÁ#áT ÿ¿£ �d¿£¼sÁT yîÕXæ\«eTT ( )

A) 214 5

cmP B) 298 5

cmP C) 249 5

cmP D) 294 5

cmP

28. ABC çÜuó�TÈeTTq+<�T 2

A BCos +æ öç ÷è ø $\Te ................... ( )

A) 2ASin B)

2ACos C)

2CSin D)

2CCos

29. Cot q + tan q qT d�Ö¿¡��¿£]+#á>±...... ( )

A) Sec q.cosec q B) Sec q C) Cosec q D) Cos q

30. Sec q - tan q = 1x nsTTq Sec q + tan q $\Te m+Ôá ? ( )

A) 1 B) 2x C) x D) 2

1x

31. d�+¿ì�|�ï $#á\q |�<�ÆÜýË im $\Te ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )

A) ix ha-

B) ix ah-

C) ia xh-

D) i

a hx-

32. 'n' |�]o\H�+XøeTT\T �sÃV�²D ç¿£eT+ýË neTsÁÌ�&� �q�$. 'n' uñd¾d�+K« nsTTq|�ð&�T ( )

� |�]o\H�+XøeTT\ eT<ó�«>·Ôá+ ..............................

A) 2n

e e+ÔáT B) 12næ ö+ç ÷è ø e |�<�+

C) 1

2n +æ ö

ç ÷è ø e |�<�+ D) , 12 2n næ ö+ç ÷è ø |�<�\ d�s�d�]

33. a - 3d, a - d, a + d, a + 3d çXâDì jîTT¿£Ø d�>·³T m+Ôá? ( )

A) 4a B) 4d C) 4ad D) a

46

SUMMATIVE ASSESSMENT - IIIMODEL PAPER

X CLASS MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40

WEIGHTAGE TABLES & BLUE PRINT

TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage

Alloted1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15

TOTAL 40 100

S.No. Academic Standards No. of Marks PercentageQuestions Alloted

1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25

TOTAL 33 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS

TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL

1 Problem Solving 1 2 2 6 112 Reasoning Proof - 1 1 4 63 Communication 1 1 - 2 44 Connection 2 1 - 4 75 Visualization /Representation - - 1 4 5

TOTAL 4 5 4 20 33

TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL %

1 Real Numbers - 1 1 3 52 Sets 1 - 1 2 43 Polynomials 1 1 1 3 64 Linear Equations in 2 Variables 1 1 2 3 75 Quadratic Equations 1 1 1 3 6

6 Progressions - - 1 3 4

7 Mensuration - 1 1 3 5

47



ÔásÁ>·Ü ` 10





3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.




�d¿£�H� ` I



1. 2x2 + 7x + 5 nHû esÁZ �V�Q|�~ jîTT¿£Ø XøSH�«\T , a b nsTTq, a b ab+ + $\Te ¿£qT>=qTeTT?

2. A = {a, r, e} nsTTq d�$TÜ A qT �s��D sÁÖ|�+ýË s�jáT+&�?

3. Âs+&�T |�PsÁ¿£ ¿ÃD²\ýË �|<�Ý¿ÃDeTT, ºq�¿ÃDeTT ¿£H�� 18+ mÅ£�Øe, nsTTq � ¿ÃD²\qT ¿£qT>=q+&�?

4. ÿ¿£ BsÁé#áÔáTsÁçkÍ¿±sÁ >·~jîTT¿£Ø mÔáTï eT]jáTT >·~ n&�T>·Tuó²>·+ #áT³T¼¿=\Ôá esÁTd�>± 8 MT. eT]jáTT

20 MT. nsTTq � >·~ jîTT¿£Ø H�\T>·T >Ã&�\ yîÕXæ\«+ ¿£qT>=qTeTT.

�d¿£�H� ` II



5. 3x = 5x-2 d�MT¿£sÁDeTTqT kÍ~ó+#áTeTT.

6. 5x2 - 6x - 2 = 0 nHû esÁZd�MT¿£sÁDeTTqT esÁZeTT |�P]ï#ûjáTT³ |�<�ÆÜ� �|�jîÖÐ+º eTÖý²\T

¿£qT>=q+&�.

48

7. 6 �d+.MT. y�«kÍsÁ�+, 24 �d+.MT. mÔáTï>·\ eT{ì¼Xø+U²�� ÿ¿£ u²\T&�T >ÃÞø+ �¿±sÁ+ýË¿ì eÖ]Ìq �

>ÃÞø+ y�«kÍsÁ�+ m+Ôá?

8. @ |�]eÖDeTTýËHîÕH� Âs+&�T �V�Q|�<�T\T s�d¾, y�{ì�|Õ Âs+&�T ç|�Xø�\T s�jáT+&�?

9. ×<�T d�+eÔáàsÁeTT\ eTT+<�T qÖ] ejáTd�Tà kþú ejáTd�Tà¿£+fñ eTÖ&�TÂs³T¢ mÅ£�Øe. 10 d�+öö Ôás�ÇÔá

qÖ] ejáTd�Tà kþú ejáTd�TàÅ£� Âs{ì¼+|�Úµµ. �|Õ d�eÖ#�s�� d�Öº+#û ¹sFjáT d�MT¿£sÁD²\qT Ôî\T|�+&�?

�d¿£�H� ` III


2. ç|�Ü ç|�Xø�Å£� 4 eÖsÁTØ.

10a10 2 4

x y x y+ =

+ - eT]jáTT 15 5 2

x y x y+ = -

+ - d�MT¿£sÁDeTT\qT kÍ~ó+#á+&�?

(ýñ<�)

10b ÿ¿£ �qT|� d�ï+uó�+ d�Ö�|�+�|Õ Xø+K+ uË]¢+ºq³T¢>± �+~. <�� d�Ö�bÍ¿±sÁ uó²>·|�Ú mÔáTï 2.8 MT. y�«d�+

20 �d+.MT. eT]jáTT Xø+U²¿±sÁ uó²>·+ mÔáTï 42 �d+.MT. ÿ¿£ |��Tq �d+.MT. �qTeTT �sÁTeÚ 7.5ç>±.

nsTTq �qT|�d�ï+uó�+ �sÁTyî+Ôá?

11a ÿ¿£ uó�eq �s��D ¿±+ç{²¿£¼sY �]�w�¼ d�eTjáT+ýË |�� |�P]ï#ûjáT¿£bþÔû nÔá�¿ì $~ó+#û n|�s�<ó� sÁTd�TeTT

yîTT<�{ìsÃEÅ£� sÁÖ.200/` eTsÁTd�{ì ç|�ÜsÃEÅ£� sÁÖ.50/` #=|�ðq �|sÁT>·TÔáT+~. 30 sÃE\T |��

�\d�«+ nsTTq+<�Tq � uó�eq �s��D ¿±+ç{²¿£¼sY #î*¢+#áe\d¾q n|�s�<ó� sÁTd�TeTT m+Ôá ?

(ýñ<�)

11b ÿ¿£ BsÁé#áÔáTsÁçkÍ¿±sÁ bÍsÁTØ ÔájáÖsÁT#ûjáT�&�TÔáT+~. B� yî&�\TÎ bõ&�eÚ ¿£+fñ 3 MT. ÔáÅ£�Øe. B�

yîÕXæ\«+ B� yî&�\TÎÅ£� d�eÖqyîT®q, uó�Ö$T eT]jáTT 12 MT. mÔáTï>·\ ÿ¿£ d�eT~Çuó²V�Q çÜuó�TÈ

yîÕXæ\«+ ¿£+fñ 4 #á.MT. mÅ£�Øe nsTTq BsÁé#áÔáTsÁçkÍ¿±sÁ|�Ú bÍsÁTØ jîTT¿£Ø bõ&�eÚ, yî&�\TÎ ¿£qT>=qTeTT?

12a 3 2 5+ ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�.

(ýñ<�)

12b A = {x | x �sÁyîÕ¿£+fñ ÔáÅ£�Øe >·\ ç|�<ó�qd�+K«\T}

B = {x | 2x+1, xÎw eT]jáTT x£ 9} nsTTq

(i) AÈ B (ii) AAÇ B (iii) A - B (iv) B - A A \qT ¿£qT>=qTeTT.

49

13a ÿ¿£ ç¿ìÂ¿{Ù ¿Ã#Y 3 u²«{Ù\T eT]jáTT 6 �+ÔáT\qT 3900 sÁÖbÍjáT\Å£� ¿=HîqT. Ôás�ÇÔá ÿ¿£ u²«{Ù

eT]jáTT 2 �+ÔáT\qT 1300 sÁÖbÍjáT\Å£� ¿=HîqT. � d�+<�s�ÒÛ�� ç>±|�t <�Çs� kÍ~ó+#áTeTT.

(ýñ<�)

13b x2 - 3x - 4 esÁZ �V�Q|�~� ç>±|�t <�Çs� kÍ~ó+#áTeTT.

50



ÔásÁ>·Ü ` 10








�d¿£�H� ` IV



14. 31, 43, 47 \ >·.kÍ.uó². m+Ôá ? ( )

A) 121 B) 1 C) 31 D) 43

15. a b+ ÿ¿£ ¿£sÁD¡jáT d�+K« nsTTq ...................... ( )

A) 'a' eT]jáTT 'b' \T ç|�<ó�q d�+K«\T B) 'a' ýñ<� 'b' ç|�<ó�q d�+K«

C) 'a' eT]jáTT 'b' \T |�PsÁ�d�+K«\T D) 'a' ýñ<� 'b' \T KºÌÔá esÁZd�+K«\T ¿±eÚ

16. x2 + y2 = z2 nsTTÔû 1 1

log logx xz y z y+ -

+ = ................... ( )

A) 1 B) 2 C) `2 D) `1

17. n(A) = 14; n(B) = 11; n(AÈ B) = 19 nsTTq n(AÇ B) = ............. ( )

A) 6 B) 16 C) 22 D) 25

18. ç|�¿£Ø |�³eTTq+<�T »�w&�µ #ûjáT�&�q çbÍ+ÔáeTTqT d�Öº+#áTq~ ( )

A) A - B B) B - A C) AÇ B D) (AÈ B) - (AÇ B)

A B

51

19. a , b , g \T 3x3 - 5x2 - 11x1x - 3 nqT |��Tq �V�Q|�~¿ì eTÖ&�T XøSq«$\Te\T nsTTq ( )

a b + b g +g a = ...............................

A) 5/3 B) 11/3 C) `11/3 D) `1

20. p(x) = g(x) - q(x)+r(x) nsTTÔû p(x), q(x) |�]eÖDeTT\T d�eÖqeTT nsTTq ( )

g(x) jîTT¿£Ø |�]eÖDeTT

A) 0 B) 1 C) 2 D) 3

21. y = ax+b nqT ¹sU²ºçÔáeTT ÿ¿£ d�sÁÞø¹sKqT d�Öºd�Öï X`n¿�±�� K+&�+#û _+<�TeÚ ( )

A) 0, ba

æ öç ÷è ø B) , 0b

aæ öç ÷è ø C) 0, b

a-æ ö

ç ÷è ø D) , 0ba

-æ öç ÷è ø

22. x - y = 2; x+y = 0 d�MT¿£sÁD²\ kÍ<ó�q _+<�TeÚ .............. bÍ<�eTTýË �+&�TqT. ( )

A) yîTT<�{ì B) H�\T>·e C) Âs+&�e D) eTÖ&�e

23. nd�+>·Ôá ¹sK\T ................ ( )

A) K+&�+#áT¿=qTqT B) K+&�+#áTqT ýñ<� @¿¡uó�$+#áTqT

C) d�eÖ+ÔásÁeTT>± �+&�TqT D) @¿¡uó�$+#áTqT

24. ÿ¿£ _óq�eTT jîTT¿£Ø \eeTTqÅ£� 9 ¿£\T|�>± 2 e#áTÌqT eT]jáTT V�äsÁeTTqT+&� »2µ ( )

rd¾yûd¾q 1 e#áTÌqT. nsTTq � _óq�eTT

A) 5/8 B) 8/5 C) 5/7 D) 7/9

25. Âs+&�T esÁTd� <ó�qd�] d�+K«\ esÁZeTT\ yîTTÔáïeTT 340. nsTTq � <ó�q d�]d�+K«\T ( )

A) 12, 14 B) 10, 12 C) 14, 16 D) 16, 18

26. x2+ax+b = 0; x2+bx+a = 0 \T �eT�&� eTÖý²\T ¿£*Ð�q�#Ã ( )

A) a+b = 0 B) a - b = 1 C) a+b = 1 D) a+b+1 = 0

27. ÿ¿£ \+�¿ÃD çÜuó�TÈeTT jîTT¿£Ø mÔáTï, uó�Ö$T¿£+fÉ 7 �d+.MT. ÔáÅ£�Øe eT]jáTT ( )

<�� ¿£sÁ�eTT 17 �d+.MT. nsTTq $TÐ*q uó�TC²\ bõ&�eÚ ..............

A) 15 �d+.MT., 8 �d+.MT. B) 12 �d+.MT., 5 �d+.MT.

C) 24 �d+.MT., 17 �d+.MT. D) �|Õ n��jáTT

52

28. 3, 3 3 , 9, ..... >·TDìçXâ&ó� jáT+<�T 243 mq�e |�<�eTT neÚÔáT+~ ( )

A) 6 B) 7 C) 8 D) 9

29. (n - 1), (n - 2), (n - 3), ................. çXâ&ó�ýË an = ................. ( )

A) n B) (n+1) C) 0 D) (n - 1)

30. log a, log b, log c \T n+¿£çXâ&ó�ýË a, b, c \T @ çXâ&ó�ýË �+&�TqT. ( )

A) n+¿£çXâ&ó� B) >·TDçXâ&ó�

C) n+¿£çXâ&ó� eT]jáTT >·TDçXâ&ó� D) n+¿£çXâ&ó�, >·TDçXâ&ó� @~jáTT ¿±<�T

31. 22�d+.MT.I15�d+.MTI7.5�d+.MT ¿=\Ôá\T ¿£*Zq ÿ¿£ ýËV�²|�Ú BsÁé|��TqeTTqT ¿£sÁÐ+º, ( )

14 �d+.MT mÔáTï>± >·\ d�Öï|�eTT>± eT*ºq#Ã d�Öï|�eTT y�«kÍsÁ�eTT ....................

A) 15�d+.MT B) 7.5�d+.MT C) 22.5�d+.MT D) 7�d+.MT

32. BsÁé|��TqeTT jîTT¿£Ø ¿£sÁ�eTT ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )

A) 2 2l b+ B) l b h+ + C) 2 2 2l b h+ + D) ( )2l b h+ +

33. dÓkÍýË� bÍ\ |�]eÖDeTTqT d�Öº+#áTq~ ( )

A) yîÕXæ\«eTT B) |��Tq|�]eÖDeTT C) kÍ+ç<�Ôá D) d�+|�PsÁ�Ôá\ yîÕXæ\«eTT

53



WEIGHTAGE TABLES & BLUE PRINT

TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage

Alloted1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15

TOTAL 40 100

S.No. Academic Standards No. of Marks PercentageQuestions Alloted

1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25

TOTAL 33 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS

TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL

1 Problem Solving 1 2 2 6 112 Reasoning Proof - 1 1 4 63 Communication 1 1 - 2 44 Connection 2 1 - 4 75 Visualization /Representation - - 1 4 5

TOTAL 4 5 4 20 33

TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL %

1 Co-ordinate Geometry 1 2 2 3 72 Similar Triangles - 1 1 2 53 Tangents & Secants of circles 1 - 1 3 54 Trigonometry - 1 1 3 55 Application of trigonometry 1 - 1 2 4

6 Probability 1 1 1 3 5

7 Statistics - 1 1 3 5

54



ÔásÁ>·Ü ` 10





3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.




�d¿£�H� ` I



1. A (6, - 5), B ( - 2, 11) ¹sU²K+&�� ¿£*�| eT<ó�«_+<�TeÚ C(2, P) nsTTÔû P $\Te m+Ôá?

2. ÿ¿£ u²\T&�T Ôáq ú&� bõ&�eÚ Ôáq mÔáTïÅ£� d�eÖqeT� >·eT�+#îqT. � d�eTjáT+ýË uó�Ö$TÔÃ d�ÖsÁ«¿ìsÁD²\T

#û�d }sÁ�Ç¿ÃD+ m+Ôá?

3. ÿ¿£ ÔásÁ>·ÜýË 35 eT+~ $<�«sÁT�\Å£�>±qT 25 eT+~ nH�sÃ>·«¿£sÁyîT®q ºsÁTÜ+&�¢qT Ôî#áTÌÅ£�+{²sÁT.

�sÃ>·«¿£sÁyîT®q |�<�sÁ�eTT\qT Ôî#áTÌ¿=Hû y�] d�+uó²e«Ôá m+Ôá?

4. ÿ¿£ e�Ôáï|�]~ó <�� y�«d�eTT¿£H�� 16.8 �d+.MT. mÅ£�Øe nsTTq � e�Ôáï|�]~ó m+Ôá?

�d¿£�H� ` II



5. What is the relationship between the areas of two equilateral triangles those are constructed on side

of a square and its diagonal.

55

6. Mr. Gopal aged 70 lives in his house at (4, 5). He goes to shop which is located at (5, 2) and then

to a park located at (3, 6). Find the distance travelled by Gopal.

7. Simplify (1 - Sin q) (1+Sin q) (1+tan2 q)

8. Find the median of the following distribution

C.I 65-85 85-105 105-125 125-145 145-165 165-185 185-205

f 3 4 12 15 14 12 8

9. A box contain 25 balls numbered as 1, 2, 3, ......, 25 a ball is drawn at random. What is the

probability for getting the ball bearing the number

(i) is divisible by 6

(ii) is a prime number

�d¿£�H� ` III



10a çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+Ô�� sÁÇº+º, �sÁÖ|¾+#á+&�?

(ýñ<�)

10b A (3, 5), B ( - 7, 4), C (10, 8) os�ü\T >·\ çÜuó�TÈ uó�TC²\T BC, CA eT]jáTT AB \ eT<ó�« _+<�TeÚ\T

esÁTd�>± D, E, F nsTTq DABC eT]jáTT DDEF \ >·TsÁTÔáÇ ¹¿+ç<�\T d�eÖqeÖ ¿±<�?

11a Tan x = 5

12 nsTTq Sec x eT]jáTT x+1 x-1

SecSec $\Te\T ¿£qT>=qTeTT.

(ýñ<�)

11b sÁVÓ²y�T ÿ¿£ ³esY �|ÕqT+º, ³esY ¿ìsÁTyîÕ|�Úý² �q� A, B nHû ¿±sÁ¢qT 30+, 60

+ �eT� ¿ÃD+ÔÃ

|�]o*+#îqT. � ¿±sÁT¢ ³esÁT bÍ<�eTTyîÕ|�Ú 10 m/s eT]jáTT 5 m/s @¿£ Ü yû>·+ÔÃ ç|�jáÖDìd�TïH��sTT.

³esY mÔáTï 100 3 MT. nsTTq @¿±sÁT eTT+<�T>± #ûsÁTÔáT+~. Âs+&�e ¿±sÁT yîTT<�{ì ¿±sÁT ¿£+fñ m��

�d¿£qT¢ �\d�«+>± #ûsÁTÔáT+~.

56

12a ÿ¿£ u²«>´ýË 6 |�d�T|�Ú �+ÔáT\T ¿=�� Å£�|�#áÌ �+ÔáT\T ¿£\eÚ. �Å£�|�#áÌ �+Ü e#ûÌ d�+uó²e«Ôá |�d�T|�Ú

�+Ü e#ûÌ d�+uó²e«ÔáÅ£� 3 Âs³T¢ nsTTq d�+ºýË� �Å£�|�#áÌ �+ÔáTýÉ��? ç|�Ü sÁ+>·T�+Ü e#ûÌ

d�+uó²e«Ôá m+Ôá?

(ýñ<�)

12b s�eTT¿ì çÜuó�TC²¿£sÁ d��\+ �+~. ÿ¿£#Ã³TqT+&� >·eT�+ºq|�ð&�T � çÜuó�TÈ eTÖ\\T (2, 3) (4, 1)

( - 2, 5) >± >·T]ï+#�&�T. � uó�TC²\ eT<ó�« _+<�TeÚ\qT ¿£\T|�ÚÔáÖ ÿ¿£ �Ôá¿=\qT �]�+#�&�T. <��

yîÕXæ\«+ m+Ôá?

13a ç¿ì+~ |�{ì¼¿£ýË 80 eT+~ $<�«sÁT�\ S.A-2 >·DìÔá+ýË eºÌq eÖsÁTØ\T �eÇ�&�¦sTT. <��¿ì �sÃV�²D

d�+ºÔá båq'|�Úq«+ z�y� eç¿±�� ^jáT+&�?

eÖsÁTØ\T 0`10 10`20 20`30 30`40 40`50 50`60 60`70 70`80

$<�«sÁT�\T 04 06 11 20 16 10 08 05

(ýñ<�)

13b ÿ¿£ #ûÜ >±E d�V�äjáT+ÔÃ e�Ô�ï�� ^º <�� u²V�²« _+<�TeÚqT+&� e�Ôáï+�|Õ¿ì ÿ¿£ ÈÔá d�ÎsÁô¹sK\qT

^º ¿=\e+&�. @$T >·eT�+#�sÁT?

57



ÔásÁ>·Ü ` 10








�d¿£�H� ` IV

d�Ö#áq\T : ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ. 20I


14. ÿ¿£ d�sÁÞø¹sK jîTT¿£Ø y�\T »lµ nsTTq �¹sK X`n¿£�eTTÔÃ <ó�q~XøýË #ûjáTT ( )

<ó�H�Ôá�¿£ ¿ÃDeTT

A) 30+ B) 45

+ C) 60+ D) 90

+

15. (0, 0), (1, 0), (0, 3) os�ü\T>± >·*Zq çÜuó�TÈeTT ............. çÜuó�TÈeTT neÚÔáT+~. ( )

A) \+�¿ÃD B) d�eT~Çu²V�Q

C) \+�¿ÃD d�eT~Çu²V�Q D) d�eTu²V�Q

16. ç|�¿£Øq sTTeÇ�&�q e�ÔáïeTTq+<�T Âs+&�e ºe]_+<�TeÚ........... ( )

A) (2, 3) B) (`2, `3) C) (`3, `2) D) (6, 4)

17. ABd çÜuó�TÈeTTq+<�T DE nqTq~ Bd ¿ì d�eÖ+ÔásÁeTT>± �q�~. D, AB �, AC �|Õq ( )

>·\ _+<�TeÚ\T

1) = AD AEDB Ed 2) = AB AC

AD AE 3) = AB AdDB Ed

A) 1`T, 2`T, 3`T B) 1`T, 2`F, 3`T C) 1`F, 2`T, 3`F D) 1`F, 2`F, 3`T

A(3, 2)B(0, 0)

58

18. DPQR eT]jáTT DXYZ \T d�sÁÖbÍ\T, eT]jáTT PQ : XY = 5:8 nsTTq � çÜuó�TC²\ ( )

eT<ó�«>·Ôá ¹sK\ �w�ÎÜï

A) 25:64 B) 2.5:4 C) 5:8 D) 8:5

19. ç|�¿£Øq �q� ABC çÜuó�TÈeTT q+<�T ÐB n~ó¿£ ¿ÃDeTT nsTTq AC2 ............. ( )

A) AB2+BC2`BD2

B) AB2+BC2

C) AB2+BC2+2BC.DB

D) AB2+BC2`2BC.DB

20. � ~>·Te sTTeÇ�&�q |�³eTTýË �jáT³ e�Ôáïy�«kÍsÁ�eTT 7 jáTÖ�³T¢ nsTTq ýË|�* ( )

e�Ôáï y�«kÍsÁ�eTTqT ¿£qT>=qTeTT.

A) 7 2 jáTÖ�³T¢ B) 7 2 1- jáTÖ�³T¢

C) 72 jáTÖ�³T¢ D) ( )

142 1+ jáTÖ�³T¢

21. ~>·Te |�³eTTq+<�T ÐAPB = 70o nsTTq ÐAOB = ........................ ( )

A) 70o B) 90o

C) 160o D) 110o

22. e�Ô�ï�¿ì eT]jáTT d�sÁÞø¹sKÅ£� ÿ¹¿ �eT�&� _+<�TeÚ ¿£*Zq n³Te+{ì ¹sKqT ............. ( )

n+<�TsÁT.

A) y�«kÍsÁ�eTT B) d�ÎsÁô¹sK C) #óû<�q¹sK D) C²«

23. ÈÔá|�sÁ#áTeTT

1) cos (180+q) ( ) a) - cot q

2) sec (270+q) ( ) a) - cos q

3) tan (90+q) ( ) a) - cosec q

A) 1 - b, 2 - c, 3 - a B) 1 - c, 2 - b, 3 - a ( )

C) 1 - a, 2 - b, 3 - c D) 1 - c, 2 - a, 3 - b

A

D B C

)

)

A

B

O70oP

59

24.

4 4

2 2

tantan

sec A Asec A A

--

( )

A) 0 B) 1/2 C) - 1 D) 1

25. �ç¿ì+~ y��ýË @~ d�]¿±�~ ( )

A) sin q = 0.5 B) cos q = 0 C) tan q = 2 D) sec q = 2

26. ÿ¿£ ³esY jîTT¿£Ø ú&� <�� mÔáTï¿£+fÉ 3 Âs³T¢ mÅ£�Øe �q�~. nsTTq }sÁ�Ç¿ÃDeTT ( )

m+Ôá?

A) 45o B) 30o C) 60o D) 90o

27. h1, h2 mÔáTï\T ¿£*Zq Âs+&�T e�¿�±\T m<�TÂs<�TsÁT>± �q�$. y�{ì eT<ó�«_+<�TeÚqT+&� ( )

30+, 60

+ }sÁ�Ç¿ÃDeTTÔÃ #î³T¼\ osÁüuó²>·eTTqT #áÖºq#Ã � mÔáTï\ �w�ÎÜï (h1:h2) .........

A) 3 :1 B) 1: 3 C) 3:1 D) 1:3

28. eTÖ&�T H�DÉeTT\qT ÿ¹¿kÍ] m>·TsÁyûd¾q ¿£úd�eTT ÿ¿£ØkÍÂsÕH� u¤sÁTd�T (n#áTÌ) ( )

d�+uó�$+#áT d�+uó²e«Ôá

A) 3/4 B) 1/3 C) 7/8 D) 2/3

29. ÿ¿£ kÍ+|�¾T¿£Xæçd�ï |�Úd�ï¿£eTT 250 �|J\T ¿£*Ð�q�~. � |�Úd�ï¿£eTTqT+&� KºÌÔáesÁZeTT ( )

>·\ �|J\ d�+K«qT mqT�¿=qT³Å£� >·\ d�+uó²e«Ôá

A) 3

50 B) 9

50 C) 1

250 D) 249250

30. ÿ¿£ kÍ<ó�sÁD d�+eÔáàsÁeTTýË 53 �~y�s�\T e#áTÌ³Å£� >·\ d�+uó²e«Ôá ( )

A) 5253 B)

152 C)

17 D)

67

31. 25 n+XøeTT\ d�>·³T 40. n+<�TýË ÿ¿£ n+XøeTT 53 Å£��<�T\T>± »28µ n� ( )

ýÉ¿ìØ+#á�&�q~. nsTTq KºÌÔáyîT®q d�>·³T m+Ôá?

A) 26 B) 39 C) 41 D) 46

60

32. �ç¿ì+~ y��ÔÃ d�]nsTTq~ ( )

A) ÔásÁ>·Ü eT<ó�« $\Te R 2ÿ¿ £ ÔásÁ>Ü· m>·Te ne~ ó - ÿ¿ £ Ôsá >Á ·Ü ~>·Te ne~ó

B) ÔásÁ>·Ü eT<ó�« $\Te R 2Ôsá >Á ·Ü m>T· e ne~ ó G Ôsá >Á ·Ü ~>T· e ne~ó

C) ÔásÁ>·Ü eT<ó�« $\Te R m>·Te ne~ó - ~>·Te ne~ó

D) ÔásÁ>·Ü eT<ó�« $\Te R m>·Te ne~ó + ~>·Te ne~ó

33. �ç¿ì+<� sTTeÇ�&�q bå'q$uó²È¿£ |�{ì¼¿£ jîTT¿£Ø �V�QÞø¿£ ÔásÁ>·Ü ¿£qT>=qTeTT ( )

ejáTd�Tà 0`10 10`20 20`30 30`40 40`50 50`60

sÃ>·T\ d�+K« 12 09 05 10 25 18

A) 10`20 B) 20`30 C) 30`40 D) 40`50

61



SYLLABUS: 1. Real Number2. Sets3. Polynomials4. Linear Equations in 2 Variables5. Quadratic Equations6. Progressions10. Mensuration

TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15

TOTAL 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONSS.No. Academic Standards No. of Questions Marks Alloted Percentage1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25

Total 33 40 100

NOTE ; 1. There is weightage to only academic standards and type of questions.2. There is no fixed weightage to content, but all chapters must be covered in each question paper.3. Student should answer the questions as per the academic standard required.4. Answer scripts shall be in the view of achievement of academic standards.

62


MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40

Time : 2 hrs 15 min. PART - A Max. Marks : 30

Instructions : 1. Read all questions.2. Part A answers should be written in separate answers book.3. There are three sections in Part A.4. Answer all questions.5. Every answer should write visibly and neatly.6. There is internal choice in Section-III.

SECTION - IInstructions : 1. Answer all questions.

2. Each question carries 1 mark. 4I1 R 4 marks

1. If a, b are zeroes of the polynomial 2x2 + 7x + 5, find the value of a+b+ab ?

2. If A = {1, 4, 9, 5, 16, 25, . . . . . .} then write it in set builder form.

3. The larger of two complimentary angles is double the smaller. Find the angles.

4. The height of a rectangular stockroom is 5m and perimeter of its floor is 50m. Find the outer area of thefour walls to be painted.

SECTION – IInstructions : 1. Answer all questions.


5. Solve the equation 3x = 5x+2

6. Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing square.

7. A cone of height 24cm and radius of base 6cm is made up modeling clay. A child reshapes it into a

sphere. Find the radius of the sphere.

8. If a, b and g are the zeroes of a polynomial of degree 3, then give the relations between the zeroes and

the coefficients of the polynomial.

9. Find whether the equations x2 – 4x + 1.5 = 0 and 2x2 + 3 = 8x are consistent or not

63

SECTION - III

Instructions : 1. Answer all questions.

2. Choice any one from each question. 4I4 R 16 marks

Each question carries 4 marks

10a Solve the equations 10 2 4

x y x y+ =

+ - and 15 5 2

x y x y+ = -

+ -

(or)

10b An iron pillar consists of a cylindrical portion of 2.8 cm height and 20 cm in diameter and a cone of 42

cm height surmounting it. Find the weight of the pillar if 1cm3 of iron weighs 7.5 gram.

11a A contractor construction job specifies a penalty for delay of completion beyond a certain date asfollows. Rs. 200 for the first day. The penalty for each succeeding day being Rs.50 more than thepreceding day. How much money does the contractor pay as penalty if he has delayed the work by 30

days.

(or)

11b A Rectangular park is to be designed. Its breadth is 3m less than its length. Its area is to be 4 squaremeters more than the area of park that has already been made in the shape of an isosceles triangle with

base as the breadth of the rectangular park and altitude 12m. Find the length and breadth.

12a Proove that 3 2 5+ is irrational

(or)

12b If A = {x | x is a prime number and x 20}

B = {x | 2x+1, xew and x<9} then

Find (i) AB (ii) AB (iii) A-B (iv) B-A. What do you observe?

13a The Coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later he buys another bat and two

more balls of the same kind for Rs.1300. What is the cost price of each? Solve the situation graphically.

(or)

13b Solve the quadratic polynomial x2 - 3x - 4 graphically.

64

A) 6 B) 7 C) 8 D) 9

20. If a b+ is an irrational number, then which of the following is false ? ( )

A) ‘a’ and ‘b’ are prime B)’a’ or ‘b’ is primeC)’a’ and ‘b’ are any integers D)one of ‘a’ or ‘b’ is not a perfect square

21. If p(x) = g(x)q(x)+r(x) if deg {p(x)} = deg {q(x)} then deg {g(x)} = .............. ( )

A) 0 B) 1 C) 2 D) 3

22. The graph of y = ax+b is a straight line which intersects the X-axis at exactly one ( )

point namely, ..................

A) 0, ba

æ öç ÷è ø B) , 0b

aæ öç ÷è ø C) 0, b

a-æ ö

ç ÷è ø D) , 0ba-æ ö

ç ÷è ø

23. If x2+ax+b = 0; x2+bx+a = 0 have a common roots then ( )

A) a+b = 0 B) ab = 1 C) a+b = 1 D) a+b+1 = 0

24. Coefficient of x in a polynomial ax2 + bx + c is ‘o’. Then its zeroes are ( )

A) equal B)additive inverses to one anotherC)multiplicative inverses to one another D)none

25. The series (n-1), (n-2), (n-3), ................. is a type of ( )

A) AP B) GP C) may be both D) none

26. A metal cuboid of dimensions 22cm I 15cm I 7.5cm was melted and cast into a ( )

cylinder of height 14cm. Its radius is .............................

A) 15cm B) 7.5cm C) 22.5cm D) 7cm

27. If log a, log b, log c are in A.P. then a, b, c are ( )

A) A.P. B) G.P. C) Both A.P and G.P D) neither A.P. nor G.P.

28. To calculate the quantity of milk inside a bottle, we need to find out ............. ( )

A) Area B) Valume C) Density D) Total surface area

29. The height of right angle triangle is 7cm less than the base, the length of the diagonal ( )

is 17cm, then the length of remaining two sides are .........................

A) 15cm, 8cm B) 12cm, 5cm C) 24cm, 17cm D) All above

30. Length of the dark line given in the diagram ( )

A) 2 2l b+ B) l b h+ +

C) 2 2 2l b h+ + D) ( )2l b h+ +

65

31. The shaded area in the figure shows ( )

A) A-B B) B-A C) AÇB D) (AÈB)-(AÇB)

32. Solution of x-y = z; x+y = 0 lies in ................. quadrant. ( )

A) I B) IV C) II D) III

33. Inconsistent equations may represent. ( )

A) intersect line B) parallel lines C) coinciding lines D) B or C

66


X CLASS MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40

SYLLABUS: 7. Co-ordinate Geometry8. Similar Triangles9. Tangents and Secants to a circle11. Trigonometry12. Applications of Trigonometry13. Probability14. Statistics

TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15

TOTAL 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONSS.No. Academic Standards No. of Questions Marks Alloted Percentage1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25

Total 33 40 100

NOTE ; 1. There is weightage to only academic standards and type of questions.2. There is no fixed weightage to content, but all chapters must be covered in each question paper.3. Student should answer the questions as per the academic standard required.4. Answer scripts shall be in the view of achievement of academic standards.

67


MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40


Instructions : 1. Read all questions.2. Part A answers should be written in separate answers book.3. There are three sections in Part A.4. Answer all questions.5. Every answer should write visibly and neatly.6. There is internal choice in Section-III.

SECTION - IInstructions : 1. Answer all questions.


1. If C (2, P) is a point on the line segment joining the points A (6, 5) and B (2, 11). Explain condition for

the point C to become the mid point of AB.

2. A boy observes that the length of his shadow is equal to his height. What is the angle of elevation of the

Sun rays?

3. In a class of 35, 28 students brought Junk food for their lunch. What was the probability that a student

at random would have brought healthy food?

4. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.

SECTION - II



5. Compare the areas of two equilateral triangles which are constructed on side of a square and its diagonal.

6. An ant is at (4, 5) on graph sheet mounted of a wall. If it moves to a point (5, 2) and turns to reach

another point (3, 6). Find the distance travelled by the ant.

7. Show that (1-Sin q) (1+Sin q) (1+tan2 q) =1

68

8. Find the median of the following distribution

CI 65-85 85-105 105-125 125-145 145-165 165-185 185-205

f 3 4 12 15 14 12 8

9. A box contains 25 balls numbered as 1, 2, 3, ......, 25. A ball is drawn from the box at random.What is the probability for getting the ball bearing the number, that

(i) is divisible by 6 (ii) is a prime number

SECTION - IIIInstructions : 1. Answer all questions.


10a Prove that a line drawn through the mid-point of one side of a triangle parallel to another side

bisects the third side.

(OR)

10b Vertices of a triangle ABC are A (3, 5), B (7, 4) and C (10, 8). The mid point of the side BC, CA

and AB are D, E and F respectively. Are the centroids of DABC and DDEF are same or not?

11a If tan x = 512 , then find the value of sec x and x+1

x-1SecSec

(OR)

11b There is a tower beside the road, Rahim standing at the top of the tower observes two cars A and B oneither side of the tower at an angle of depression 30o and 60o are approaching the foot of the tower witha uniform speed of 10m/s and 5m/s respectively. If the height of the tower is 100 m, then find which

car reaches the tower first and how many seconds the other car is late by the first one.

12a A bag contains 6 yellow balls and some green balls. The probability of getting a green ball is triple thatof a yellow ball. Determine number of Green balls in the bag and find the probability of each colour ball

when a ball is drawn at time randomly.

(OR)

12b Ramu has a triangular site. He observes the corners of the triangular site are (2, 3), (4, 1), (�2, 5). Find

the area of the swimming pool dug by joining of the mid points of the sides of the site.

13a The following distribution gives the marks of 80 students in S.A-2 of Mathematics. Draw ogive curvefor the distribution.

69

Marks scored 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No.of Students 04 06 11 20 16 10 08 05

(OR)13b Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct the pair of

tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.


MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40

Time : 30 min. PART - B Max. Marks : 10

Instructions : 1. Answer all the questions in Part-B.2. Each question has 4 options. Write the capital letter indicating the answer in the given

brackets.3. Marks are not awarded for over writing answers.4. All questions carry equal marks.

SECTION - IV


2. Each question carries 1/2 mark. 20I1/2 R 10 marks

14. If the slope of a line is »lµ then the angle made by it with X-axis in positive direction is ( )

A) 30+ B) 45+ C) 60+ D) 90+

15. If DPQR ~ DXYZ and PQ : XY = 5:8, then the ratio of their corresponding median is .. ( )

A) 5:8 B) 64:25 C) 25:64 D) 8:5

16.4 4

2 2

tantan

sec A Asec A A

--

= ........................ ( )

A) 0 B) 1/2 C) 1 D) 1

17. If the shadow of a tower is times its height then attitude of the Sun is ( )

A) 45o B) 30o C) 60o D) 90o

70

18. Three coins are tossed simultaneously, then probability of getting at least one tail is ( )

A) 3/4 B) 1/3 C) 7/8 D) 2/3

19. The mean of a data consisting 25 observations is 40. In doing so observation 53 ( )

was wrongly recorded as 28. Then the correct mean is

A) 26 B) 39 C) 41 D) 46

20. From the figure if ÐAPB = 70o then ÐAOB = ........................ ( )

A) 70o B) 90o

C) 160o D) 110o

21. The following line has only one point in common to the circle ( )

A) diameter B) tangent C) secant D) chord

22. Which of the following is not possible ( )

A) sin q = 0.5 B) cos q = 0 C) tan q = 2 D) sec q = 0.3

23. Which of the following is correct ? ( )

A) Class mark = Class Limit - Lower Class Limit2

Upper

B) Class mark = Class Limit + Lower Class Limit2

Upper

C) Class mark = Upper Boundary � Lower Boundary

D) Class mark = Upper Boundary + Lower Boundary

24. In the figure ÐB is an obtuse angle, then AC2 = ................ ( )

A) AB2+BC2�BD2 B) AB2+BC2

C) AB2+BC2+2BC.DB D) AB2+BC2�2BC.DB

25. Modal class of the following distribution is ( )

Age 0-10 10-20 20-30 30-40 40-50 50-60

No. of Patients 12 09 05 10 25 18

26. In the given figure, the radius of the outer circle is ‘7’ units; ( )

then the radius of the inner circle is

A) 7 2 units B) 7 2 1- units

C) 72 units D) ( )

142 1+ units

71

27. A Social Studies text book contains 250 pages. A page is selected at random. ( )

What is the probability that the number on the page selected is a perfect square?

A) 1

250 B) 1

125 C) 3

50 D) None

28. The probability of getting 53 Sundays in an ordinary year is .................... ( )

A) 5253 B) 1

52 C) 17 D) 6

7

29. Match the following

1) cos (180+q) ( ) a) cot q

2) sec (270+q) ( ) b) cos q

3) tan (90+q) ( ) c) cosec q

A) 1b, 2c, 3a B) 1c, 2b, 3a C) 1a, 2b, 3c D) 1c, 2a, 3b ( )

30. (0, 0), (1, 0), (0, 3) are vertices of a ......................... triangle. ( )

A) Right angle B) Isosceles C) Right isosceles D) Equilateral

31. Co –ordinates of second end of the diameter is ........................ ( )

A) (2, 3) B) (�2, �3) C) (�3, �2) D) (6, 4)

32. In a DABC, DE//BC and intersects AB at D and AC at E, then ( )

1) = AD AEDB Ed 2) =

AB ACAD AE 3) = AB Ad

DB Ed

A) 1�T, 2�T, 3�T B) 1�T, 2�F, 3�T C) 1�F, 2�T, 3�F D) 1�F, 2�F, 3�T

33. If the two trees of heights h1 and h2 subtended angles of 30o and 60o respectively ( )

at the mid point of the line joining their feet then h1 : h2 is ...........................

A) 3 :1 B) 1: 3 C) 3:1 D) 1:3

72

73

SUMMATIVE ASSESSMENT - III MODEL PAPER

X CLASS MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40

SYLLABUS: 1. Real Number 2. Sets 3. Polynomials 4. Linear Equations in 2 Variables 5. Quadratic Equations 6. Progressions 10. Mensuration TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDS

S.No. Academic Standards Marks Percentage 1 Problem Solving 16 40 2 Reasoning Proof 8 20 3 Communication 4 10 4 Connection 6 15 5 Visualization /Representation 6 15 TOTAL 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS S.No. Academic Standards No. of

Questions Marks Alloted Percentage

1 Very Short Answer 4 4 10 2 Short Answer 5 10 25 3 Essay/Long Answer 4 16 40 4 Multiple Choice 20 10 25 Total 33 40 100

NOTE ; 1. There is weightage to only academic standards and type of questions.

2. There is no fixed weightage to content, but all chapters must be covered in each question paper.

3. Student should answer the questions as per the academic standard required.

4. Answer scripts shall be in the view of achievement of academic standards.

74


MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40


Instructions : 1. Read all questions. 2. Part A answers should be written in separate answers book. 3. There are three sections in Part A. 4. Answer all questions. 5. Every answer should write visibly and neatly. 6. There is internal choice in Section-III.

SECTION - I Instructions : 1. Answer all questions. 2. Each question carries 1 mark. 4I1 R 4 marks 1. If a, b are zeroes of the polynomial 2x2 + 7x + 5, find the value of a+b+ab ?

2. If A = {1, 4, 9, 5, 16, 25, . . . . . .} then write it in set builder form. 3. The larger of two complimentary angles is double the smaller. Find the angles. 4. The height of a rectangular stockroom is 5m and perimeter of its floor is 50m. Find the

outer area of the four walls to be painted. SECTION – I

Instructions : 1. Answer all questions. 2. Each question carries 2 mark. 5I2 R 10 marks 5. Solve the equation 3x = 5x+2 6. Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing square. 7. A cone of height 24cm and radius of base 6cm is made up modeling clay. A child reshapes

it into a sphere. Find the radius of the sphere. 8. If a, b and g are the zeroes of a polynomial of degree 3, then give the relations between the

zeroes and the coefficients of the polynomial. 9. Find whether the equations x – 4y + 1.5 = 0 and 2x – 8y+ 3=0 are consistent or not

SECTION - III

Instructions : 1. Answer all questions. 2. Choice any one from each question. 4I4 R 16 marks Each question carries 4 marks

10a Solve the equations and

(or)

10 2 4x y x y

+ =+ -

15 5 2x y x y

+ = -+ -

75

10b An iron pillar consists of a cylindrical portion of 2.8m height and 20 cm in diameter and a cone of 42 cm height surmounting it. Find the weight of the pillar if 1cm3 of iron weighs 7.5 gram.

11a A contractor construction job specifies a penalty for delay of completion beyond a certain date as follows. Rs. 200 for the first day. The penalty for each succeeding day being Rs.50 more than the preceding day. How much money does the contractor pay as penalty if he has delayed the work by 30 days.

(or) 11b A Rectangular park is to be designed. Its breadth is 3m less than its length. Its area is to be

4 square meters more than the area of park that has already been made in the shape of an isosceles triangle with base as the breadth of the rectangular park and altitude 12m. Find the length and breadth of rectangular park.

12a Proove that is irrational (or)

12b If A = {x | x is a prime number and x < 20} B = {x | 2x+1, xew and x<9} then Find (i) AÈB (ii) AÇB (iii) A-B (iv) B-A. What do you observe? 13a The Coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later he buys another bat

and two more balls of the same kind for Rs.1300. What is the cost price of each? Solve the situation graphically.

(or) 13b Solve the quadratic polynomial x2 - 3x - 4 graphically.

3 2 5+

76


MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40


Instructions : 1. Answer all the questions in Part-B. 2. Each question has 4 options. Write the capital letter indicating the answer in

the given brackets. 3. Marks are not awarded for over writing answers. 4. All questions carry equal marks.

SECTION - IV Instructions : 1. Answer all questions. 2. Each question carries 1/2 mark. 20I1/2 R 10 marks 14. The H.C.F. of 31, 43 and 47 is ....................... ( )

A) 121 B) 1 C) 31 D) 43

15. If x2 + y2 = z2 then ................... ( )

A) 1 B) 2 C) `2 D) `1

16. n(A) = 14; n(B) = 11; n(AÈB) = 19 then n(AÇB) = ............. ( )

A) 6 B) 16 C) 22 D) 25

17. If a fraction becomes 2 when 9 is added to its numerator and 1 when 2 is subtracts ( )

from its denominator then the fraction is ................................. A) 5/8 B) 8/5 C) 5/7 D) 7/9 18. The sum of squares of two consecutive positive even numbers is 340, then the ( )

numbers are ............................. A) 12, 14 B) 10, 12 C) 14, 16 D) 16, 18

19. Which term of the G.P 3,3 √3, 9, . . . .. is 243 ? ( )

A) 6 B) 7 C) 8 D) 9

20. If is an irrational number, then which of the following is false ? ( )

A) 'a' and 'b' are prime B)'a' or 'b' is prime C)'a' and 'b' are any integers D)one of 'a' or ‘b' is not a perfect square 21. If p(x) = g(x)q(x)+r(x) if deg {p(x)} = deg {q(x)} then deg {g(x)} = .............. ( )

A) 0 B) 1 C) 2 D) 3 22. The graph of y = ax+b is a straight line which intersects the X-axis at exactly one ( ) point namely, ..................

1 1log logx x

z y z y+ -

+ =

a b+

77

A) B) C) D)

23. If x2+ax+b = 0; x2+bx+a = 0 have a common roots then ( )

A) a+b = 0 B) ab = 1 C) a+b = 1 D) a+b+1 = 0 24. Coefficient of x in a polynomial ax2 + bx + c is ‘o’. Then its zeroes are ( )

A) equal B)additive inverses to one another C)multiplicative inverses to one another D)none 25. The series (n-1), (n-2), (n-3), ................. is a type of ( ) A) AP B) GP C) may be both D) none 26. A metal cuboid of dimensions 22cm I 15cm I 7.5cm was melted and cast into a ( )

cylinder of height 14cm. Its radius is .............................

A) 15cm B) 7.5cm C) 22.5cm D) 7cm

27. If log a, log b, log c are in A.P. then a, b, c are ( )

A) A.P. B) G.P. C) Both A.P and G.P D) neither A.P. nor G.P. 28. To calculate the quantity of milk inside a bottle, we need to find out ............. ( )

A) Area B) Volume C) Density D) Total surface area 29. The height of right angle triangle is 7cm less than the base, the length of the diagonal ( ) is 17cm, then the length of remaining two sides are .........................

A) 15cm, 8cm B) 12cm, 5cm C) 24cm, 17cm D) All above 30. Length of the dark line given in the diagram ( )

A) B)

C) D)

31. The shaded area in the figure shows ( )

A) A-B B) B-A C) AÇB D) (AÈB)-(AÇB) 32. Solution of x-y = 2; x+y = 0 lies in ................. quadrant. ( ) A) I B) IV C) II D) III 33. Inconsistent equations may represent. ( ) A) intersect lines B) parallel lines C) coinciding lines D) B or C

0, ba

æ öç ÷è ø

, 0ba

æ öç ÷è ø

0, ba-æ ö

ç ÷è ø, 0b

a-æ ö

ç ÷è ø

2 2l b+ l b h+ +

2 2 2l b h+ + ( )2l b h+ +

78

Q. No Chapter Academic standard wise marks

AS 1 AS 2 AS 3 AS 4 AS 5 Very short answer questions

1 Polynomials 1 2 Sets 1 3 Linear Equations in 2 Variables 1 4 Mensuration 1 Short answer questions

5 Real Number 2 6 Quadratic Equations 2 7 Mensuration 2 8 Polynomials 2 9 Linear Equations in 2 Variables 2 Essay answer type questions

10 Linear Equations in 2 Variables 4 Mensuration

11 Progressions 4 Quadratic Equations

12 Real Numbers 4 Sets

13 Linear Equations in 2 Variables 4 Polynomials

Part B: Objective type questions 14 Real Number 0.5 15 Real Number 0.5 16 Sets 0.5 17 Quadratic Equations 0.5 18 Quadratic Equations 0.5 19 Progressions 0.5 20 Real Number 0.5 21 Polynomials 0.5 22 Linear Equations in 2 Variables 0.5 23 Quadratic Equations 0.5 24 Polynomials 0.5 25 Progressions 0.5 26 Mensuration 0.5 27 Real Number 0.5 28 Mensuration 0.5 29 Mensuration 0.5 30 Mensuration 0.5 31 Sets 0.5 32 Linear Equations in 2 Variables 0.5 33 Linear Equations in 2 Variables 0.5

Total 16 8 4 6 6

79


X CLASS MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40

SYLLABUS: 7. Co-ordinate Geometry 8. Similar Triangles 9. Tangents and Secants to a circle 11. Trigonometry 12. Applications of Trigonometry 13. Probability 14. Statistics TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDS

S.No. Academic Standards Marks Percentage 1 Problem Solving 16 40 2 Reasoning Proof 8 20 3 Communication 4 10 4 Connection 6 15 5 Visualization /Representation 6 15 TOTAL 40 100

TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS S.No. Academic Standards No. of

Questions Marks Alloted Percentage

1 Very Short Answer 4 4 10 2 Short Answer 5 10 25 3 Essay/Long Answer 4 16 40 4 Multiple Choice 20 10 25 Total 33 40 100

NOTE ; 1. There is weightage to only academic standards and type of questions.

2. There is no fixed weightage to content, but all chapters must be covered in each question paper.

3. Student should answer the questions as per the academic standard required.

4. Answer scripts shall be in the view of achievement of academic standards.

80


MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40


Instructions : 1. Read all questions. 2. Part A answers should be written in separate answers book. 3. There are three sections in Part A. 4. Answer all questions. 5. Every answer should write visibly and neatly. 6. There is internal choice in Section-III.

SECTION - I Instructions : 1. Answer all questions. 2. Each question carries 1 mark. 4I1 R 4 marks 1. If C (2, P) is a point on the line segment joining the points A (6, 5) and B (2, 11). Explain

condition for the point C to become the mid point of AB. 2. A boy observes that the length of his shadow is equal to his height. What is the angle of

elevation of the Sun rays? 3. In a class of 35, 28 students brought Junk food for their lunch. What was the probability

that a student at random would have brought healthy food? 4. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of

the circle.

SECTION - II

Instructions : 1. Answer all questions. 2. Each question carries 2 mark. 5I2 R 10 marks 5. Compare the areas of two equilateral triangles which are constructed on side of a square

and its diagonal. 6. An ant is at (4, 5) on graph sheet mounted of a wall. If it moves to a point (5, 2) and turns

to reach another point (3, 6). Find the distance travelled by the ant. 7. Show that (1-Sin q) (1+Sin q) (1+tan2 q) =1 8. Find the median of the following distribution

CI 65-85 85-105 105-125 125-145 145-165 165-185 185-205

f 3 4 12 15 14 12 8

9. A box contains 25 balls numbered as 1, 2, 3, ......, 25. A ball is drawn from the box at random. What is the probability for getting the ball bearing the number, that

(i) is divisible by 6 (ii) is a prime number

81

SECTION - III Instructions : 1. Answer all questions. 2. Each question carries 4 mark. 4I4 R 16 marks 10a Prove that “ If a line is drawn parallel to one side of a triangle , will divide other to sides in

the same ratio. (OR)

10b Vertices of a triangle ABC are A (3, 5), B (7, 4) and C (10, 8). The mid point of the side BC, CA and AB are D, E and F respectively. Are the centroids of DABC and DDEF are same or not?

11a If tan x = , then find the value of sec x and

(OR) 11b There is a tower beside the road, Rahim standing at the top of the tower observes two cars

A and B on either side of the tower at an angle of depression 30o and 60o are approaching the foot of the tower with a uniform speed of 10m/s and 5m/s respectively. If the height of the tower is 100√3m, then find which car reaches the tower first and how many seconds the other car is late by the first one.

12a A bag contains 6 yellow balls and some green balls. The probability of getting a green ball is triple that of a yellow ball. Determine number of Green balls in the bag and find the probability of each colour ball when a ball is drawn at time randomly.

(OR) 12b Ramu has a triangular site. He observes the corners of the triangular site are (2, 3), (4, 1),

(`2, 5). Find the area of the swimming pool dug by joining of the mid points of the sides of the site.

13a The following distribution gives the marks of 80 students in S.A-2 of Mathematics. Draw ogive curve for the distribution. Marks scored 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No.of Students 04 06 11 20 16 10 08 05

(OR) 13b Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct the pair of

tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.

512

x+1 x-1

SecSec

82


MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40


Instructions : 1. Answer all the questions in Part-B. 2. Each question has 4 options. Write the capital letter indicating the answer in

the given brackets. 3. Marks are not awarded for over writing answers. 4. All questions carry equal marks.

SECTION - IV

Instructions : 1. Answer all questions. 2. Each question carries 1/2 mark. 20I1/2 R 10 marks 14. If the slope of a line is »lµ then the angle made by it with X-axis in positive direction is ( ) A) 30+ B) 45+ C) 60+ D) 90+

15. If DPQR ~ DXYZ and PQ : XY = 5:8, then the ratio of their corresponding median is .. ( ) A) 5:8 B) 64:25 C) 25:64 D) 8:5

16. = ........................ ( )

A) 0 B) 1/2 C) 1 D) 1

17. If the shadow of a tower is √3 times its height then attitude of the Sun is ( )

A) 45o B) 30o C) 60o D) 90o 18. Three coins are tossed simultaneously, then probability of getting at least one tail is ( )

A) 3/4 B) 1/3 C) 7/8 D) 2/3 19. The mean of a data consisting 25 observations is 40. In doing so observation 53 ( )

was wrongly recorded as 28. Then the correct mean is A) 26 B) 39 C) 41 D) 46

20. From the figure if ÐAPB = 70o then ÐAOB = ........................ ( ) A) 70o B) 90o C) 160o D) 110o

21. The following line has only one point in common to the circle ( )

A) diameter B) tangent C) secant D) chord 22. Which of the following is not possible ( )

A) sin q = 0.5 B) cos q = 0 C) tan q = 2 D) sec q = 0.3

4 4

2 2

tantan

sec A Asec A A

--

83

23. Which of the following is correct ? ( )

A) Class mark =

B) Class mark = C) Class mark = Upper Boundary ` Lower Boundary D) Class mark = Upper Boundary + Lower Boundary 24. In the figure ÐB is an obtuse angle, then AC2 = ................ ( )

A) AB2+BC2`BD2 B) AB2+BC2 C) AB2+BC2+2BC.DB D) AB2+BC2`2BC.DB

25. Modal class of the following distribution is ( )

Age 0-10 10-20 20-30 30-40 40-50 50-60

No. of Patients 12 09 05 10 25 18

A) 10`20 B) 20`30 C) 30`40 D) 40`50

26. In the given figure, the radius of the outer circle is '7' units; ( ) then the radius of the inner circle is

A) units B) units

C) units D) units 27. A Social Studies text book contains 250 pages. A page is selected at random. ( )

What is the probability that the number on the page selected is a perfect square?

A) 1

250 B)

1125

C) 3/50 D) None

28. The probability of getting 53 Sundays in an ordinary year is .................... ( )

A) B) C) D)

29. Match the following 1) cos (180+q) ( ) a) cot q 2) sec (270+q) ( ) b) cos q 3) tan (90+q) ( ) c) cosec q A) 1b, 2c, 3a B) 1c, 2b, 3a C) 1a, 2b, 3c D) 1c, 2a, 3b ( ) 30. (0, 0), (1, 0), (0, 3) are vertices of a ......................... triangle. ( )

A) Right angle B) Isosceles C) Right isosceles D) Equilateral 31. Co –ordinates of second end of the diameter is ........................ ( )

A) (2, 3) B) (`2, `3) C) (`3, `2) D) (6, 4)

32. In a DABC, DE//BC and intersects AB at D and AC at E, then ( )

Class Limit - Lower Class Limit2

Upper

Class Limit + Lower Class Limit2

Upper

7 2 7 2 1-

72 ( )

142 1+

5253

152

17

67

84

1) AD AEDB ED

= 2) 3) AB ADDB ED

=

A) 1`T, 2`T, 3`T B) 1`T, 2`F, 3`T C) 1`F, 2`T, 3`F D) 1`F, 2`F, 3`T

33. If the two trees of heights h1 and h2 subtended angles of 30o and 60o respectively ( ) at the mid point of the line joining their feet then h1 : h2 is ...........................

A) :1 B) 1: C) 3:1 D) 1:3

Q. No Chapter Academic standard wise marks

AS 1 AS 2 AS 3 AS 4 AS 5 Very short answer questions

1 Co-ordinate Geometry 1 2 Applications of Trigonometry 1 3 Probability 1 4 Tangents and Secants to a circle 1 Short answer questions

5 Similar Triangles 2 6 Co-ordinate Geometry 2 7 Trigonometry 2 8 Statistics 2 9 Probability 2 Essay answer type questions

10 Similar Triangles 4 Co-ordinate Geometry

11 Trigonometry 4 Applications of Trigonometry

12 Probability 4 Co-ordinate Geometry

13 Statistics 4 Tangents and Secants to a circle

Part B: Objective type questions 14 Co-ordinate Geometry 0.5 15 Similar Triangles 0.5 16 Trigonometry 0.5 17 Applications of Trigonometry 0.5 18 Probability 0.5 19 Statistics 0.5 20 Tangents and Secants to a circle 0.5 21 Tangents and Secants to a circle 0.5 22 Trigonometry 0.5 23 Statistics 0.5 24 Similar Triangles 0.5 25 Statistics 0.5

= AB ACAD AE

3 3

85

26 Tangents and Secants to a circle 0.5 27 Probability 0.5 28 Probability 0.5 29 Trigonometry 0.5 30 Co-ordinate Geometry 0.5 31 Co-ordinate Geometry 0.5 32 Similar Triangles 0.5 33 Applications of Trigonometry 0.5

Total 16 8 4 6 6

1

dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3

10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT

>∑DÏ‘·+ ` ù||üsY I

ø±\eTT : 2 >∑+ˆˆ 45 ìˆˆ bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40

ø±\eTT : 2 >∑+ˆˆ 15 ìˆˆ bÕs¡Tº ` A >∑]wü e÷s¡Tÿ\T : 30

dü÷#·q\T : 1. nìï Á|üXï\qT ÁX<äΔ>± #·<äe+&ç.

2. bÕs¡Tº A ≈£î düe÷<ÛëqeTT\qT MTøÏe«ã&çq »yêãT |üÁ‘·+˝À sêj·T+&ç.

3. bÕs¡Tº A q+<äT eT÷&ÉT $uÛ≤>±\T e⁄HêïsTT.

4. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.

5. Á|ü‹ »yêãTqT <ädü÷ÔØ>±, ns¡úeTjT´$<Ûä+>± sêj·T+&ç.

6. ôdø£åHé III q+<ä* Á|üXï\≈£î n+‘·s¡Z‘· m+|æø£ ñ+≥T+~.

ôdø£åHé ` I

dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.

2. Á|ü‹ Á|üXï≈£î 1 e÷s¡Tÿ. 4I1 R 4 e÷s¡Tÿ\T

1. 2x2 + 7x + 5 nH ãVüQ|ü~øÏ α, β \T XSqéTT\T nsTTq#√ α G β G αβ $\Te ø£qT>=q+&ç.

2. A = {1, 4, 9, 16, 25, ....} qT dü$T‹ ìsêàD s¡÷|ü+˝À sêj·T+&ç.

3. |üPs¡ø£ ø√D≤\˝À ô|<ä›ø√D+ ∫qï<ëìøÏ ¬s{Ïº+|ü⁄ nsTTq Ä ø√D≤\qT ø£qT>=q+&ç.

4. ˇø£ Bs¡È#·‘·Ts¡ÁkÕø±s¡ >∑~ H\ #·T≥Tºø=\‘· 50 MT., eT]j·TT m‘·TÔ 5 MT. nsTTq <ëì Hê\T>∑T >√&É\≈£î

s¡+>∑Tyùd Á|ü<X+ yÓ’XÊ\´+ ø£qT>=q+&ç.

ôdø£åHé ` II



5. 3x = 5x+2 düMTø£s¡D≤ìï kÕ~Û+#·+&ç.

6. 5x2 − 6x − 2 nqT düMTø£s¡D≤ìøÏ |ü]|üPs¡íes¡Z |ü<äΔ‹˝À eT÷˝≤\T ø£qT>=q+&ç.

2

7. eT{Ïº‘√ ‘·j·÷¬s’q ˇø£ X+KTe⁄ jÓTTø£ÿ uÛÑ÷yê´kÕs¡ú+ 6 ôd+.MT. eT]j·TT m‘·TÔ 24 ôd+.MT. Bìì ˇø£

|æ\¢yê&ÉT >√fi≤ø±s¡+˝À e÷]Ãq, <ëì yê´kÕs¡ú+ m+‘· ?

8. αβ eT]j·TT γ nH$ 3e |ü]e÷D ãVüQ|ü~ XSHê´ …’q#√, Ä ãVüQ|ü~ XSHê´\≈£î, >∑TDø±\≈£î eT<Ûä

dü+ã+<Ûëìï ‘Ó\Œ+&ç.

9. x + 4y + 1.5 = 0 eT]j·TT 2x − 8y + 3 = 0 düMTø£s¡D≤\ kÕ<Ûäq eéd”úø£è‘·yÓ÷ ø±<√ ø£qT>=q+&ç.

ôdø£åHé ` III


2. Á|ür Á|üXï˝À n+‘·s¡Z‘· m+|æø£ ø£\<äT. @<Ó’Hê ˇø£<ëìì m+|æø£ #düTø=qe#·TÃqT.


10 (a)10 2

4x y x y

+ =+ − eT]j·TT

15 52

x y x y+ = −

+ − kÕ~Û+#·+&ç.

( Ò<ë)

(b) ˇø£ dü÷úbÕø±s¡ ÇqT|ü düú+ã+ m‘·TÔ 2.8 ôd+.MT. eT]j·TT 20 ôd+.MT. yê´dü+ ø£*–j·TTqï~.

<ëìô|’ 42 ôd+.MT. m‘·TÔ X+KTe⁄ Äø±s¡ uÛ≤>∑eTTqï~. ˇø£ |òüTq|ü⁄ ôd+.MT. ÇqTeTT jÓTTø£ÿ

ãs¡Te⁄ 7.5 Á>±eTT\T nsTT‘ Ä ÇqT|ü düú+ãeTT jÓTTø£ÿ ãs¡Te⁄ m+‘· ?

11 (a) ˇø£ |üìì |üP]Ô#˚j·TT≥≈£î ìπsú•+∫q ø±\+qT n<äqeTT>± düeTj·T+ rdüTø=H˚ >∑T‘˚Ô<ës¡T≈£î

ÁøÏ+~$<Ûä+>± n<äq|ü⁄ s¡TdüTeTT (ô|Hê©º) edü÷\T≈£î ìs¡ísTT+#·&ÉyÓTÆq~. yÓTT<ä{Ï ~qeTTq≈£î

r 200, ‘·sê«‘· Á|ü‹ n<äq|ü⁄ ~HêìøÏ, eTT+<äTs√Eø£Hêï r 50 #=|üq m≈£îÿe. Ä >∑T‘Ô<ës¡T

ìπsΔ•+∫q ø±\+ ø£Hêï 30 s√E\T n<äqeTT>± |üì |üP]Ô#dæq ô|Hê©ºøÏ+<ä edü÷\jT´ yÓTT‘·Ô+

m+‘· ?

( Ò<ë)

(b) ˇø£ ¬s’\T 360 øÏ.MT. <ä÷s¡eTTqT @ø£Ø‹ y>∑+‘√ Á|üj·÷DÏ+#·TqT. Bì y>∑eTT >∑+≥≈£î 5 øÏ.MT.

ô|]–q n< <ä÷s¡eTTqT Á|üj·÷DÏ+#·T≥≈£î |ü≥Tº ø±\eTT 1 >∑+≥ ‘·>∑TZqT. nsTTq ¬s’\T y>∑eTTqT

ø£qT>=qTeTT.

3

12 (a) 3 2 5+ ˇø£ ø£s¡D°j·T dü+K´ nì ìs¡÷|æ+#·+&ç.

( Ò<ë)

(b) A = {x | x nH~ ˇø£ Á|ü<Ûëqdü+K´ eT]j·TT x < 20}

B = {2x+1 | x∈w eT]j·TT x < 9} nsTTq#√

(i) A∪B (ii) A∩B (ii) A − B (iv) B − A ø£qT>=q+&ç. MTs¡T @$T >∑eTì+#ês¡T?

13 (a) ˇø£ ÁøÏ¬ø{Ÿ »≥Tº jÓTTø£ÿ •ø£å≈£î&ÉT 3 u≤´≥T¢, 6 ã+‘·T\qT r 3900 \≈£î ø=Hêï&ÉT. ‘·sê«‘·

n<s¡ø£+q≈£î #Ó+~q 1 u≤´{Ÿ eT]j·TT 2 ã+‘·T\qT r 1300 \≈£î ø=Hêï&ÉT. á dü+<äsê“¤\qT

πsU≤∫Á‘· |ü<äΔ‹˝À kÕ~Û+∫ u≤´{Ÿ eT]j·TT ã+‹ jÓTTø£ÿ yÓ\qT ø£qT>=q+&ç.

( Ò<ë)

(b) x2 − 3x − 4 nH ãVüQ|ü~ XSHê´\qT πsU≤∫Á‘· |ü<äΔ‹˝À ø£qT>=q+&ç.

4


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT

>∑DÏ‘·eTT ù||üsY-I


ø±\eTT : 30 ìˆˆ bÕs¡Tº ` B >∑]wü e÷s¡Tÿ\T : 10

dü÷#·q\T : 1. bÕs¡Tº B q+<äT nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.

2. Á|ü‹ Á|üXï≈£î 4 düe÷<ÛäqeTT\T ø£\e⁄. dü]jÓÆTq düe÷<ÛëqeTTqT m+|æø£#dæ, <ëì nø£åsêìï

Áu≤¬ø≥¢ À sêj·T+&ç.

3. ~~›y‘·\T, ø={Ïºy‘·\‘√ ≈£L&çq düe÷<ÛëqeTT\≈£î e÷s¡Tÿ\T Çe«ã&Ée⁄.

4. nìï Á|üXï\≈£î e÷s¡Tÿ\T düe÷q+.

ôdø£åHé ` IV

dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛäqeTT\T sêj·T+&ç.

2. Á|ü‹ Á|üXï≈£î 1/2 e÷s¡Tÿ πø{≤sTT+#·ã&çq~. 20I

1/2 R 10 e÷s¡Tÿ\T

14. 31, 43 eT]j·TT 17 \ jÓTTø£ÿ >∑.kÕ.uÛ≤. ( )

A) 121 B) 1 C) 31 D) 43

15. x2 + y2 = z2 nsTTq 1 1

log logx xz y z y+ −

+ R .................. ( )

A) 1 B) 2 C) − 2 D) − 1

16. n(A) = 14, n(B) = 11, n(A∪B) = 19 nsTTq#√ n(A∩B) = ................. ( )

A) 6 B) 16 C) 22 D) 25

17. ˇø£ _Ûqï+ jÓTTø£ÿ \e+q≈£î 9 ø£*|æq n~ 2 n>∑TqT eT]j·TT <ëì Vü‰s¡+qT+&ç ( )

2 rdæydæq Ä _Ûqï+ 1 n>∑TqT. nsTTq Ä _Ûqï+ ....................

A) 5

8B)

8

5C)

5

7D)

7

9

18. ¬s+&ÉT es¡Tdü <Ûäq dü]dü+K´\ esêZ\ yÓTT‘·Ô+ 340 nsTTq Ä dü+K´\T ( )

A) 12, 14 B) 10, 12 C) 14, 16 D) 16, 18

5

19. >∑TDÁX‚&Ûç 3, 3 3 , 9, ........... ˝À mqïe|ü<ä+ 243 n>∑TqT ? ( )

A) 6 B) 7 C) 8 D) 9

20. a b+ nH~ ˇø£ ø£s¡D°j·T dü+K´ nsTTq#√ ÁøÏ+~yêì˝À @~ ndü‘· + ( )

A) 'a' eT]j·TT 'b' Á|ü<ÛëHê+ø±\T

B) 'a' Ò<ë 'b' \T Á|ü<ÛëHê+ø±\T

C) 'a' eT]j·TT 'b' \T @yì |üPs¡ídü+K´\T

D) 'a' eT]j·TT 'b' \˝À @<ì ˇø£{Ï |ü]|üPs¡í dü+K´ ø±<äT

21. p(x) = g(x), q(x) + r(x) eT]j·TT p(x), q(x) |ü]e÷D≤\T düe÷qeTT nsTTq#√ ( )

g(x) jÓTTø£ÿ |ü]e÷D+

A) 0 B) 1 C) 2 D) 3

22. y = ax + b nH πsU≤∫Á‘·+ ˇø£ düs¡fiπsK. Ç~ x-nøå±ìï K+&ç+# _+<äTe⁄ ìs¡÷|üø±\T ( )

A) 0, b

a B) , 0

b

a C) 0,

b

a

− D) , 0

b

a

−

23. x2+ax+b = 0 eT]j·TT x2+bx+a = 0 \≈£î ñeTà&ç eT÷\+ ñqï#√ ( )

A) a+b = 0 B) ab = 1 C) a+b = 1 D) a+b+1 = 0

24. ax2+bx+c nH ãVüQ|ü~˝À x`>∑TDø£+ ªdüTqïμ nsTTq#√ <ëì XSHê´\T ( )

A) düe÷q+ B) ˇø£<ëìø=ø£{Ï dü+ø£\q $˝Àe÷\T

C) ˇø£<ëìø=ø£{Ï >∑TDø±s¡ $˝Àe÷\T D) @Bø±<äT

25. (n-1), (n-2), (n-3) ........... nH ÁX‚&ç @s¡ø£+ ( )

A) n+ø£ÁX‚&Ûç B) >∑TDÁX‚&Ûç (GP) C) ¬s+&ÉTq÷ D) @Bø±<äT

26. 22 ôd+.MT I 15 ôd+.MT I 7.5 ôd+.MT ø=\‘·\T ø£*–q ˇø£ Bs¡È|òüTHêø±s¡ ˝ÀVü≤|ü⁄ ( )

ø£&û¶ì ø£]–+∫ 14 ôd+.MT m‘·TÔ>∑\ dü÷ú|ü+>± #dæq <ëì yê´kÕs¡ú+

A) 15 ôd+.MT. B) 7.5 ôd+.MT C) 22.5 ôd+.MT D) 7 ôd+.MT

27. log a, log b, log c \T A.P ˝À ñqï#√ a, b, c \T ñ+& ÁX‚&Ûç ( )

A) A.P B) G.P C) ¬s+&ÉTq÷ D) @Bø±<äT

6

28. ˇø£ bÕÁ‘· À |üfÒº bÕ\T |ü]e÷D+ ‘Ó\TdüTø=qT≥≈£î ø£qT>=qe*‡q$ ( )

A) yÓ’XÊ\´+ B) |òüTq|ü]e÷D+ C) kÕ+Á<ä‘· D) dü+|üPs¡í‘·\ yÓ’XÊ\´+

29. ˇø£ \+ãø√D Á‹uÛÑT»+ jÓTTø£ÿ m‘·TÔ, <ëì uÛÑ÷$Tø£Hêï 7 ôd+.MT ‘·≈£îÿe. <ëì ø£s¡í+ ( )

bı&Ée⁄ 17 ôd+.MT nsTTq $T–*q ¬s+&ÉT uÛÑTC≤\ bı&Ée⁄\T

A) 15 ôd+.MT, 8 ôd+.MT B) 12 ôd+.MT, 5 ôd+.MT

C) 24 ôd+.MT, 17 ôd+.MT D) ô|’eìïj·TT

30. Á|üø£ÿ |ü≥+˝À eTT<ä›>± ^∫q πsK bı&Ée⁄ ( )

A) 2 2l b+ B) l b h+ +

C) 2 2 2l b h+ + D) ( )2l b h+ +

31. Á|üø£ÿ |ü≥+˝À ùw&é #dæq Á|ü<X yÓ’XÊ\´+ ‘Ó ÒŒ~ ( )

A) A − B B) B − A

C) A∩ B D) (A ∪ B) − (A ∩ B)

32. x+y = 2 eT]j·TT x − y = 0 jÓTTø£ÿ kÕ<Ûäq @ bÕ<ä+˝À e⁄+≥T+~. ( )

A) I B) IV C) II D) III

33. eéd”úø£è‘·+ ø±ì düMTø£s¡D≤\T ÁbÕ‹ì<Ûä |ü]#$ ( )

A) K+&ÉqπsK\T B) düe÷+‘·s¡ πsK\T C) @ø°uÛÑ$+# πsK\T D) B Ò<ë C

h

lb

A B

7


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT

>∑DÏ‘·eTT ù||üsY-II









ôdø£åHé ` I



1. A(6, 5) eT]j·TT B(2, 11) _+<äTe⁄\qT ø£*ù| πsU≤K+&É+ô|’q C(2, p) nH _+<äTe⁄ ø£\<äT. AB jÓTTø£ÿ

eT<Ûä _+<äTe⁄ 'C' n>∑T≥≈£î ø±e*‡q ìã+<Ûäq ‘Ó\Œ+&ç.

2. ˇø£ u≤\T&ÉT ‘·q ˙&É bı&Ée⁄, ‘·q jÓTTø£ÿ m‘·TÔ≈£î düe÷qyÓTÆq≥T¢>± >∑eTì+#ê&ÉT. Ä düeTj·T+˝À

dü÷s¡ øÏs¡D≤\ jÓTTø£ÿ }s¡ú«ø√D+ m+‘· ?

3. 35 eT+~ $<ë´s¡Tú\T >∑\ ‘·s¡>∑‹˝À 28 eT+~ $<ë´s¡Tú\T düeT‘·T\´+ø±ì ÄVü‰s¡+ eT<Ûë´Vü≤ï uÛÀ»q+>±

‹Hêïs¡T. nsTTq Äs√E düeT‘·T\ýÓTÆq ÄVü‰s¡+ rdüT≈£îqï $<ë´s¡Tú\ dü+uÛ≤e´‘· m+‘· ?

4. ˇø£ eè‘·Ô|ü]~Û <ëì yê´dü+ø£Hêï 16.8 ôd+.MT n~Ûø£yÓTÆq, Ä eè‘·Ô |ü]~Û m+‘· ?

ôdø£åHé ` II



5. ˇø£ #·‘·Ts¡Ádü uÛÑT»+ô|’q eT]j·TT <ëì ø£s¡í+ô|’q ^j·Tã& ¬s+&ÉT düeTu≤VüQ Á‹uÛÑTC≤\ yÓ’XÊ˝≤´\qT

b˛\Ã+&ç.

8

6. ˇø£ >√&Éô|’q >∑\ Á>±|òt ø±–‘·+ô|’ ˇø£ NeT (4, 5) _+<äTe⁄qT+&ç (5, 2) _+<äTe⁄q≈£î yÓ[fl, ‹]–

(3, 6) _+<äTe⁄≈£î #]+~. nsTTq Ä NeT Á|üj·÷DÏ+∫q <ä÷s¡+ m+‘· ?

7. (1 − Sinθ) (1+Sinθ)(1+tan2θ) = 1 nì #·÷|ü+&ç.

8. øÏ+~ <ä‘êÔ+X+q≈£î eT<ä >∑‘·+ ø£qT>=q+&ç.

‘·s¡>∑‹ n+‘·s¡+ 65`85 85`105 105`125 125`145 145`165 165`185 185`205

bÂq'|ü⁄q´+ 3 4 12 15 14 12 8

9. ˇø£ ô|f…º À 1, 2, 3 ......... 25 dü+K´\T >∑\ 25 ã+‘·T\T e⁄HêïsTT. <ëìqT+&ç j·÷<äè∫Ã¤ø£+>± ˇø£

ã+‹ì rdæq dü+<äs¡“¤+˝À

(i) 6 # uÛ≤–+#·ã&$ (ii) Á|ü<Ûëq dü+K´ njT´ dü+K´\ dü+uÛ≤e´‘· ø£qT>=q+&ç

ôdø£åHé ` III


2. Á|ü‹ Á|üXï≈£î 4 e÷s¡Tÿ\T. 4I4 R 16 e÷s¡Tÿ\T

10 (a) ˇø£ Á‹uÛÑT»+˝À ˇø£ uÛÑTC≤ìøÏ düe÷+‘·s¡+>± ^j·Tã& πsK, $T–*q ¬s+&ÉT uÛÑTC≤\qT πø

ìwüŒ‹Ô À $uÛÑõdüTÔ+<äì ìs¡÷|æ+#·+&ç.

( Ò<ë)

10 (b) A(3, 5), B(7, 4) eT]j·TT C(10, 8) nH$ ABC Á‹uÛÑT» osê¸\T. D, E eT]j·TT F \T es¡Tdü>±

BC, CA eT]j·TT AB \ eT<ä _+<äTe⁄\T. ΔABC eT]j·TT ΔDEF Á‹uÛÑTC≤\ >∑Ts¡T‘·«πø+Á<ë\

ìs¡÷|üø±\T ˇø£fÒHê? ø±<ë? ‘Ó\Œ+&ç.

11 (a) tan x = 5

12 nsTTq#√ sec x $\Te ø£qT>=q+&ç. BìqT+&ç

sec x+1

sec x-1 $\Te >∑DÏ+#·+&ç.

( Ò<ë)

(b) ˇø£ s¡Vü≤<ë]ì ÄqTø=ì e⁄qï ≥esY ô|’qT+&ç s¡V”≤yéT, s¡Vü≤<ë]øÏ Çs¡TyÓ’|ü⁄\qT+&ç e#Ã ¬s+&ÉTø±s¡T¢

A eT]j·TT B \qT 30+ eT]j·TT 60

+ n<Ûä'ø√D+‘√ |ü]o*düTÔHêï&ÉT. ¬s+&ÉTø±s¡¢ À yÓTT<ä{Ï~ 10

MT/ôd y>∑+‘√q÷, ¬s+&Ée~ 5 MT/ôd y>∑+‘√q÷ ≥es¡TqT düMT|ædüTÔHêïsTT. ≥esY jÓTTø£ÿ m‘·TÔ

9

100 3 MTˆˆ nsTTq#√ @ø±s¡T ≥es¡TqT yÓTT<ä≥ #s¡T‘·T+~? ¬s+&Ée~, yÓTT<ä≥ #]q ø±s¡Tø£Hêï

mìï ôdø£qT¢ ‘·sê«‘· #s¡T‘·T+~?

12 (a) ˇø£ dü+∫˝À 6 |üdüT|ü⁄s¡+>∑T ã+‘·T\T eT]j·TT ø=ìï Ä≈£î|ü#·Ã ã+‘·T\T e⁄HêïsTT. dü+∫qT+&ç

rùd ã+‘·T\˝À Ä≈£î|ü#·Ã ã+‹ dü+uÛ≤e´‘·, |üdüT|ü⁄|ü#·Ã ã+‹ dü+uÛ≤e´‘·≈£î 3 ¬s≥T¢ nsTTq#√

Ä≈£î|ü#·Ãì ã+‘·T\ dü+K´ ø£qT>=q+&ç. n<$<Ûä+>± dü+∫qT+&ç j·÷<äè∫Ã¤ø£+>± m+|æø£#ùd Á|ü‹

s¡+>∑T ã+‹jÓTTø£ÿ dü+uÛ≤e´‘· ‘Ó\|ü+&ç.

( Ò<ë)

(b) ABC Á‹uÛÑT» osê¸\T es¡Tdü>± (2, 3), (4, 1) eT]j·TT ( − 2, 5). Á‹uÛÑT» uÛÑTC≤\T AB, BC

eT]j·TT CA \ eT<Ûä _+<äTe⁄\T es¡Tdü>± D, E, F \T nsTTq#√, eT<Ûä _+<äTe⁄\‘√ @s¡Œ&

Á‹uÛÑT» yÓ’XÊ\´+ ø£qT>=q+&ç. Ç<$<Ûä+>± ΔABC eT]j·TT ΔDEF yÓ’XÊ˝≤´\ ìwüŒ‹Ô ‘Ó\Œ+&ç.

13 (a) ˇø£ ‘·s¡>∑‹˝À 80 eT+~ $<ë´s¡Tú\≈£î SA-2 |üØø£å À >∑DÏ‘·+˝À e∫Ãq e÷s¡Tÿ\T øÏ+~ Çe«ã&çq$.

á <ä‘êÔ+X+q≈£î bÂq'|ü⁄qéÁø£+ (zõyéeÁø£+) ^j·T+&ç.

( Ò<ë)

(b) 6 ôd+.MT yê´kÕs¡ú+‘√ ˇø£ eè‘·Ô+ ^j·T+&ç. πø+Á<ä+qT+&ç 10 ôd+.MT <ä÷s¡+˝À>∑\ _+<äTe⁄

qT+&ç eè‘êÔìøÏ ˇø£ »‘· düŒs¡ÙπsK\qT ^∫, yê{Ï bı&Ée⁄\T ø£qT>=q+&ç. ô|’<∏ë>∑s¡dt dæ<ëΔ+‘·+

Á|üø±s¡+ dü]#·÷&É+&ç.

e÷s¡Tÿ\T 0`10 10`20 20`30 30`40 40`50 50`60 60`70 70`80

$<ë´s¡Tú\ dü+K´ 04 06 11 20 16 10 08 05

10


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT









ôdø£åHé ` IV



1/2 R 10 e÷s¡Tÿ\T

14. x-nø£å+‘√ <ÛäHê‘·àø£ ~X˝À ø£<äT\T‘·Tqï ˇø£ πsK yê\T ª|μ nsTTq n~ #j·TT ø√D+ ( )

A) 30+ B) 45+ C) 60+ D) 90+

15. ΔPQR ∼ ΔXYZ eT]j·TT PQ : XY = 5:8 nsTTq yê{Ï düs¡÷|ü eT<ä >∑‘· πsK\ ìwüŒ‹Ô ( )

A) 5 : 8 B) 10 : 16 C) 25 : 64 D) 8 : 5

16.

4 4

2 2

sec tan

sec tan

A A

A A

−−

R ................. ( )

A) 0 B) 1

2C) 1 D) 2

17. ˇø£ düú+ã+ jÓTTø£ÿ ˙&É, <ëì m‘·TÔ≈£î 3 ¬s≥T¢ ø£\<äT. nsTTq dü÷s¡T´&ÉT <ëì m‘·TÔ‘√ ( )

#˚j·TT ø√D+

A) 45+ B) 30+ C) 60+ D) 90+

11

18. eT÷&ÉT HêD≤\T πøkÕ] m>∑Ts¡yj·Tã&çq$. nsTTq ø£ dü+ ˇø£ u§s¡TdüT (tail) e#Ã ( )

dü+uÛ≤e´‘·

A) 3

4B)

1

3C)

7

8D)

2

3

19. 25 |ü]o\Hê+XÊ\ dü>∑≥T 40. á dü+<äs¡“¤+˝À ˇø£ |ü]o\Hê+X+ 53 ≈£î ã<äT\T>± 28 >± qyÓ÷<Ó’q~

nsTTq dü]jÓÆTq dü>∑≥T ( )

A) 26 B) 39 C) 41 D) 46

20. Á|üø£ÿ |ü≥+˝À ∠APB = 70o nsTTq ∠AOB = ( )

A) 70+ B) 90+

C) 160+ D) 110+

21. øÏ+~ yêì˝À @πsK, eè‘·Ô+q≈£î πø _+<äTe⁄ e<ä› K+&çdüTÔ+~ ( )

A) yê´dü+ B) düŒs¡ÙπsK C) #Û<äqπsK D) C≤´

22. øÏ+~ yêì˝À @~ nkÕ<Ûä + ? ( )

A) sin θ = 0.5 B) cos θ = 0 C) tan θ = 2 D) sec θ = − 1

23. øÏ+~ yêì˝À @~ dü‘· + ? ( )

A) ‘·s¡>∑‹ e÷s¡Tÿ R

B) ‘·s¡>∑‹ e÷s¡Tÿ R

C) ‘·s¡>∑‹ e÷s¡Tÿ R m>∑Te Vü≤<äT› − ~>∑Te Vü≤<äT›

D) ‘·s¡>∑‹ e÷s¡Tÿ R m>∑Te Vü≤<äT› G ~>∑Te Vü≤<äT›

24. Á|üø£ÿ |ü≥+˝À ∠B n~Ûø£ ø√D+ nsTTq AC2 = ................. ( )

A) AB2 + BC2 − BD2

B) AB2 + BC2

C) AB2 + BC2 + 2BC.DB

D) AB2 + BC2 − 2BC.DB

)P

A

B

O

m>∑Te ne~Û ` ~>∑Te ne~Û

2

m>∑Te ne~Û G ~>∑Te ne~Û

2

A

D B C

)

12

25. øÏ+~ bÂq'|ü⁄q´ $uÛ≤»q+˝À u≤VüAfiø£ ‘·s¡>∑‹ ( )

A) 10`20 B) 20`30 C) 30`40 D) 40`50

26. Á|üø£ÿ|ü≥+˝À u≤Vü≤éè‘êÔ\ yê´kÕs¡ú+ 7 j·T÷ˆˆ nsTTq n+‘·s¡eè‘·Ô yê´kÕs¡ú+ ( )

A) 7 2 j·T÷ˆˆ B) 7 2 1− j·T÷ˆˆ

C) 7

2 j·T÷ˆˆ D) ( )

14

2 1+ j·T÷ˆˆ

27. kÕ+|òæTø£XÊÁdüÔ |ü⁄düÔø£+˝À 250 ù|J\T ø£\e⁄. j·÷<äè∫Ã¤ø£+>± @<ì ˇø£ù|Jì m+|æø£ #dæq|ü⁄&ÉT Ä ù|J

dü+K´ dü+|üPs¡íes¡Z+ njT´ dü+uÛ≤e´‘· m+‘·? ( )

A) 8

125B)

3

25C)

3

50D) 1

28. ˇø£ kÕ<Ûës¡D dü+e‘·‡s¡+˝À 53 Ä~yêsê\T e#Ã dü+uÛ≤e´‘· ( )

A) 52

53B)

1

52C)

1

7D)

6

7

29. øÏ+~ yêìì »‘· |üs¡Ã+&ç. ( )

1) cos (180+θ) ( ) a) cot θ

2) sec (270+θ) ( ) a) cos θ

3) tan (90+θ) ( ) a) cosec θ

A) 1(b), 2(c), 3(a) B) 1(c), 2(b), 3(a) C) 1(a), 2(b), 3(c) D) 1(c), 2(a), 3(b)

30. (0, 0), (1, 0), (0, 3) nH$ @ Á‹uÛÑT»eTTjÓTTø£ÿ osê¸\T ne⁄qT? ( )

A) \+ãø√D Á‹uÛÑT»eTT B) düeT~«u≤VüQ Á‹uÛÑT»eTT

C) düeT~«u≤VüQ \+ãø√D Á‹uÛÑT»eTT D) düeTu≤VüQ Á‹uÛÑT»eTT

31. Á|üø£ÿ |ü≥+˝À eè‘·Ôyê´dü+ jÓTTø£ÿ ¬s+&Ée ∫e] _+<äTe⁄ ( )

A) (2, 3) B) ( − 2, − 3) C) ( − 3, − 2) D) (6, 4)

ej·TdüT‡ 0`10 10`20 20`30 30`40 40`50 50`60

s√>∑T\ dü+K´ 12 09 05 10 25 18

13

32. ΔABC ˝À DE � BC eT]j·TT DE πsK AB ì D e<ä›, AC ì E e<ä› K+&ç+∫q#√ ( )

1) AD

DB R

AE

ED2)

AB

AD R

AC

AE3)

AB

DB R

AD

ED

A) 1-T, 2-T, 3-T B) 1-T, 2-F, 3-T C) 1-F, 2-T, 3-F D) 1-F, 2-F, 3-T

33. h1 eT]j·TT h

2 m‘·TÔ>∑\ ¬s+&ÉT #Ó≥T¢ yê{Ï bÕ<äeTT (yÓTT<ä\T) \T ø£\T|ü>± @s¡Œ&çq πsU≤ ( )

eT<ä _+<äTe⁄ e<ä› 30+ eT]j·TT 60

+ ø√DeTT\T #dæq, yê{Ï m‘·TÔ\ ìwüŒ‹Ô

A) 3 :1 B) 1: 3 C) 3 : 1 D) 1 : 3

14


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT

>∑DÏ‘·eTT ù||üsY I









ôdø£åHé ` I



1. 6410log $\Te ø£qT>=q+&ç. ( 2

10log = 0.3010)

2. XSq´dü$T‹øÏ ì»J$‘·+˝À ¬s+&ÉT ñ<ëVü≤s¡D\T Çe«+&ç.

3. ª|üsêe\j·T+μ nq>±H$T?

4. ˇø£ {≤ø°‡øÏ yÓTT<ä{Ï øÏ ÀMT≥sY Á|üj·÷D≤ìøÏ r 40 #=|üq ‘·s¡Tyê‘· Á|ür øÏ.MT ≈£î r 10 #=|üq

#Ó*¢+#·e\dæj·TTqï~. yÓTT<ä{Ï 5 øÏ.MT es¡≈£î es¡Tdü>± #Ó*¢+#·e\dæq kıeTTà\qT sêj·T+&ç.

ôdø£åHé ` II



5. 65 eT]j·TT 117 \ >∑.kÕ.uÛ≤ 65x − 117 nsTTq x $\Te ø£qT>=qTeTT.

6. A = {2, 5, 6, 8}, B = {1, 5, 7, 9} nsTTq n(A ∩ B) eT]j·TT n(A ∪ B) \qT ø£qT>=qTeTT.

15

7. ˇø£ Á‹uÛÑT» ø√DeTT\T x, y eT]j·TT 50+ ø√DeTT\T x, y \ uÛÒ<äeTT 30

+ nsTTq x, y $\Te\qT

ø£qT>=qTeTT.

8. es¡ZdüMTø£s¡D+ ax2 + bx + c = 0 (a≠0, a, b, c∈R) jÓTTø£ÿ eT÷˝≤\ dü«uÛ≤eeTTqT $e]+#·+&ç.

9. πø m‘·TÔ >∑\ ˇø£ dü÷ú|üeTT eT]j·TT X+≈£îe⁄\, uÛÑ÷yê´kÕsêú\T düe÷qeTT. yê{Ï |òüTq|ü]e÷D≤\ ìwüŒ‹Ô

3 : 1 nì ˙e⁄ m˝≤ #Ó|üŒ>∑\e⁄.

ôdø£åHé ` III

dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç. Á|ür Á|üXï≈£î n+‘·s¡Z‘·eTT>± a Ò<ë b m+|æø£

#˚düTø=qe#·TÃqT.


10 (a) A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8} \T ¬s+&ÉT dü$T‘·T\T nsTTq

(i) (A ∪ B) − (A ∩ B) (ii) (A − B) ∪ (B − A) \qT ø£qT>=qTeTT. @$T >∑eTì+#ês¡T?

( Ò<ë)

(b) es¡ZdüMTø£s¡D+ x2 + 2x − 143 = 0 jÓTTø£ÿ eT÷˝≤\qT, es¡ZeTTqT |üP]Ô#˚j·TT≥ <ë«sê

es¡ZdüMTø£s¡DeTTqT kÕ~Û+# |ü<äΔ‹˝À ø£qT>=qTeTT.

11 (a) ˇø£ bÕsƒ¡XÊ\˝À bÕsƒ¡ $wüj·Tø£ dü+ã+~Û‘· $wüj·÷\˝À n‘·T´qï‘· Á|ü‹uÛÑ ø£qã]∫q yê]øÏ yÓTT‘·Ô+

700 s¡÷bÕj·T\≈£î 7 ãVüQeT‘·T\T Çyê«\ì uÛ≤$+#ês¡T. Á|ü‹ ãVüQeT‹ $\Te <ëìeTT+<äTqï

<ëìøÏ r 20 ‘·≈£îÿe nsTTq Á|ü‹ ãVüQeT‹ $\TeqT ø£qT>=qTeTT.

( Ò<ë)

(b) ˇø£ Ä≥edüTÔe⁄ ns¡ú>√fieTTô|’ ì{≤s¡T>± ì\T|üã&çq X+KTe⁄ e … j·TTqï~. X+KTe⁄ jÓTTø£ÿ

uÛÑ÷ýê´dü+ 6 ôd+.MT. eT]j·TT m‘·TÔ 4 ôd+.MT. nsTTq#√ Ä≥edüTÔe⁄ jÓTTø£ÿ ñ|ü]‘·\

yÓ’XÊ\éTT m+‘·? (π R 3.14 >± rdüTø=qTeTT)

12. (a) 2 ˇø£ ø£s¡D°j·T dü+K´ nì |üs√ø£å |ü<äΔ‹ <ë«sê ìs¡÷|æ+#·+&ç.

16

( Ò<ë)

(b) #·T≥Tºø=\‘· 80MT. yÓ’XÊ\éTT 400 #·.MT ñ+&ÉTq≥T¢ ˇø£ Bs¡È#·‘·Ts¡ÁkÕø±s¡ bÕs¡TÿqT ‘·j·÷s¡T

#j·T>∑\e÷? #j·T>∑*–‘ <ëì bı&Ée⁄, yÓ&É\TŒ\qT ø£qT>=qTeTT.

13. (a) ˇø£ es¡Z ãVüQ|ü~ p(x) = x2 − 9 jÓTTø£ÿ πsU≤∫Á‘·eTTqT ^j·TTeTT. πsU≤∫Á‘·+ qT+&ç ãVüQ|ü~ p(x)

jÓTTø£ÿ XSHê´\qT ø£qT>=qTeTT. dü]#·÷&É+&ç.

( Ò<ë)

(b) düMTø£s¡D eédüú x + y − 16 = 0, x − 2y + 2 = 0 qT πsU≤∫Á‘·|ü<äΔ‹ <ë«sê kÕ~Û+#·+&ç. kÕ<Ûäqô|’

˙ n_ÛÁbÕj·T+ yêÚ≤´ì+#·+&ç.

17


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT

>∑DÏ‘·eTT ù||üsY-I








ôdø£åHé ` IV



1/2 R 10 e÷s¡Tÿ\T

14. ¬s+&ÉT dü+K´\T 144 eT]j·TT 420 \ >∑.kÕ.uÛ≤. 12 nsTTq yê{Ï ø£.kÕ.>∑T. m+‘·? ( )

A) 6040 B) 5040 C) 4200 D) 1440

15. n(A) = 12, n(B) = 5 eT]j·TT A∩ B = φ nsTTq n(A ∪ B) = ................. ( )

A) 17 B) 7 C) 60 D) 0

16. ãVüQ|ü~ 2x2 − 9 jÓTTø£ÿ XSHê´\ yÓTT‘·Ô+ .............. ( )

A) 0 B) 1 C) − 1 D) 2

17. a + b = 5 eT]j·TT 3a + 2b = 20 nsTTq 3a + b R .............. ( )

A) 25 B) 20 C) 15 D) 10

18. n+ø£ÁX‚&Ûç 1

3,

1

2,

2

3, .........

11

6 ˝À >∑\ |ü<ë\ dü+K´ ................... ( )

A) 8 B) 10 C) 12 D) 13

18

19. x ôd+.MT, 6 ôd+.MT eT]j·TT 8 ôd+.MT yê´kÕsêú\T>± >∑\ eT÷&ÉT >√fieTT\qT ( )

ø£]–+#·>± 9 ôd+.MT yê´kÕs¡ú+>± >∑\ >√fieTT>± ‘·j·÷¬s’q~. yÓTT<ä{Ï >√fieTT

yê´kÕs¡ú+ x = ........................

A) 1

4ôd+.MT B)

1

3ôd+.MT C)

1

2ôd+.MT D) 1 ôd+.MT

20. ÁøÏ+~ yêì˝À n+‘·+ø±ì Äes¡ÔqeTjT´ <äXÊ+X_Ûqï+ @~ ? ( )

A) 24

1600B)

171

800C) 2 3

123

2 5× D) 3 2 2

145

2 5 7× ×

21. πsFj·T düMTø£s¡D≤\ »‘· 2x − 3y = 8 eT]j·TT 4x − 6y = 9 @ düMTø£s¡D eédüú≈£î ( )

#Ó+~q~

A) dü+>∑‘· düMTø£s¡D eédüú B) ndü+>∑‘· düMTø£s¡D eédüú

C) ndü«‘·+Á‘· eédüú D) dü«‘·+Á‘· düMTø£s¡D eédüú

22. es¡ZdüMTø£s¡D+ ax2 + bx + c = 0 øÏ yêdüÔe eT÷˝≤\T Òe⁄. nsTTq#√ ÁøÏ+~ yêì˝À ( )

@~ dü‘· +

A) b2 − 4ac < 0 B) b2 − 4ac = 0 C) b2 − 4ac > 0 D) b2 − 4ac ≠ 0

23. 4 # ìX‚Ùwü+>± uÛ≤–+|üã& ¬s+&É+¬ø\ dü+K´\T mìï ø£\e⁄ ? ( )

A) 20 B) 16 C) 25 D) 22

24. dü$T‹ A = 1 1 1 1

1, , , , 2 4 8 16

jÓTTø£ÿ ìsêàDs¡÷|üeTT ( )

A) 1

: , y N, y 42

y

x x ε = ≤

B) 1

: , y W, y 42 yx x ε = ≤

C) { } : 2 , y W, y 4yx x ε= ≤ D) 1

: x N, y 5x

ε

≺

25. yÓTT<ä{Ï n uÒdædü+K´\ yÓTT‘·ÔeTT ( )

A) ( )12

nn + B) n2 C) n(n+1) D) [ ]2 ( 1)

2

na n d+ −

19

26. log2(5x+7) = 5 nsTTq x $\Te ( )

A) 5 B) 6 C) 7 D) 10

27. 3 ≈£îØÃ\T eT]j·TT 2 u…+N\ yÓ\ r 1850. 5 ≈£îØÃ\T eT]j·TT 3 u…+N\ yÓ\ ( )

r 2850. nsTTq#√ ˇø£ ≈£îØÃ eT]j·TT ˇø£ u…+N yÓ\ m+‘· ?

A) r 800 B) r 850 C) r 900 D) r 950

28. ˇø£ r>∑qT ñ|üjÓ÷–+∫ l ôd+.MT bı&Ée⁄, 1 ôd+.MT. yÓ&É\TŒ >∑\ Bs¡È#·‘·Ts¡ÁkÕ\qT ( )

‘·j·÷s¡T#düTÔHêïs¡T. Bs¡È#·‘·Ts¡ÁkÕ\ bı&Ée⁄qT 1 ôd+.MT. #=|üq ô|+#·T≈£î+≥÷ es¡Tdü>±

5 Bs¡È#·‘·Ts¡ÁkÕ\qT ‘·j·÷s¡T#dæq yê{ÏøÏ ø±e\dæq r>∑ bı&Ée⁄ m+‘·?

A) 10(l + 1) B) 10(l + 2) C) 10(l + 3) D) 5(l + 2)

29. ˇø£ |òüTq>√fieTT eT]j·TT ˇø£ |òüTq ns¡ú>√fieTT\T πø dü+|üPs¡í‘·\ yÓ’XÊ\´+qT ( )

ø£*–j·TTqï$. nsTTq yê{Ï |òüTq|ü]e÷D≤\ ìwüŒ‹Ô

A) 3 :1 B) 3 3 : 5 C) 3 3 : 4 D) 1: 3

30. |ü≥+˝À ùw&é #j·Tã&çq ÁbÕ+‘·eTT <ìì dü÷∫düTÔ+~? ( )

A) A − B B) B − A

C) A Δ B D) A ∩ B

31. ÁøÏ+~ yêì˝À @ πsU≤∫Á‘·eTT ˇø£ es¡ZãVüQ|ü~ì dü÷∫düTÔ+~ ? ( )

A) B) C) D)

32. πsU≤∫Á‘·+ qT+&ç ' l ' jÓTTø£ÿ düMTø£s¡D+ ( )

A) x = 2 B) y = 2 C) x = − 2 D) y = − 2

33. ˇø£ |òüTqedüTÔe⁄ jÓTTø£ÿ |òüTq|ü]e÷D+ 21

3V r h= Π nsTTq Ä |òüTqedüTÔe⁄ @~? ( )

A) B) C) D)

A

B

y

x

l

0

-2

r

h

h r

rh

20


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT `










ôdø£åHé ` I



1. ( − 3, 2), (1, 5) eT]j·TT (11, − 19) \T osê¸\T>± >∑\ Á‹uÛÑT» >∑Ts¡T‘·«πø+Á<äeTT ø£qT>=q+&ç.

2. ÁbÕ<∏ä$Tø£ nqTbÕ‘· dæ<ëΔ+‘·eTTqT ìs¡«∫+|ü⁄eTT.

3. 50 MTˆˆ bı&Ée⁄ >∑\ <ës¡+‘√ ø£≥ºã&çq ˇø£ >±*|ü≥+ uÛÑ÷$T‘√ 60+ ø√D+ #dü÷Ô m>∑Ts¡T#·Tqï~.

nsTTq Ä >±*|ü≥+ uÛÑ÷$TqT+&ç m+‘· m‘·TÔ À ñqï<√ ø£qT>=q+&ç.

4. ¬s+&ÉT HêDÒ\qT m>∑Ts¡yùd Á|üjÓ÷>∑+˝À e#·TÃ yÓTT‘·Ô+ |üs¡ ekÕHê\qT sêj·T+&ç.

ôdø£åHé ` II



5. 15 Cot A = 8 nsTTq#√ sin A eT]j·TT sec A \qT ø£qT>=q+&ç.

6. ˇø£ ‘·s¡>∑‹˝À >∑\ q\T>∑Ts¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 72, eTT>∑TZs¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 78

eT]j·TT Ç<ä›s¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 80. nsTTq Ä ‘·s¡>∑‹ jÓTTø£ÿ dü>∑≥T e÷s¡Tÿ m+‘· ?

21

7. Á|üø£ÿ |ü≥+ qT+&ç Á‹uÛÑT»eTT ABC eT]j·TT Á‹uÛÑT»eTT CPQ \T

@$<Ûä+>± düs¡÷bÕ˝À $e]+#·+&ç. x $\TeqT ø£qT>=q+&ç?

8. düeTdü+uÛÑe |òüT≥q\T nq>±H$T ? ˇø£ ñ<ëVü≤s¡D Çe«+&ç.

9. ˇø£ >∑&çj·÷s¡+ ì$TcÕ\ eTTfió¢ bı&Ée⁄ 14 ôd+.MT. ˇø£ 1

2 >∑+ˆˆ˝À Ä eTTfió¢ ‹]π> ÁbÕ+‘· yÓ’XÊ\´+

ø£qT>=q+&ç.

ôdø£åHé ` III


2. Á|ür Á|üXï˝À n+‘·s¡Z‘·+>± a Ò<ë b m+|æø£ #düTø=qe#·TÃ.


10 (a) _+<äTe⁄\T (1, − 1), ( − 4, 6) eT]j·TT ( − 3, 5) \T osê¸\T>± >∑\ Á‹uÛÑT»eTT uÛÑTC≤\ eT<Ûä

_+<äTe⁄\qT ø£\T|ü>± @s¡Œ&ÉT Á‹uÛÑT» yÓ’XÊ\´+qT ø£qT>=qTeTT. Ä Á‹uÛÑT» yÓ’XÊ\´+, <ä‘·Ô Á‹uÛÑT»

yÓ’XÊ˝≤´\ ìwüŒ‹Ô ø£qT>=qTeTT.

( Ò<ë)

(b) ˇø£ ≥esY n&ÉT>∑TuÛ≤>∑+ qT+&ç uÛÑeq+ ô|’uÛ≤>∑+ 30+ }s¡ú«ø√D+ #düTÔ+~. uÛÑeq+ n&ÉT>∑TuÛ≤>∑+

qT+&ç ≥esY ô|’uÛ≤>∑+ 60+ }s¡ú«ø√D+ #düTÔ+~. ≥esY m‘·TÔ 30 MT≥s¡T¢ nsTTq uÛÑeq+ m‘·TÔ

ø£qT>=qTeTT.

11 (a) ˇø£ ø£sêà>±s¡+˝Àì 50 eT+~ ø±]à≈£î\ ~qdü] uÛÑ‘· eTT áÁøÏ+~ bÂq'|ü⁄q´ $uÛ≤»ø£ |ü{Ïºø£ À

Çe«ã&çq~.

‘·>∑T |ü<äΔ‹ì m+#·Tø=ì Ä ø£sêà>±s¡+˝Àì ø±]à≈£î\ dü>∑≥T uÛÑ‘· eTT\qT ø£qTø√ÿ+&ç.

C

P Q

A B5

3

3

70)

~qdü] uÛÑ‘· + (r) 200`250 250`300 300`350 350`400 400`450

ø±]à≈£î\ dü+K´ 12 14 8 6 10

22

( Ò<ë)

(b) ˇø£ ô|f…ºq+<äT 1 qT+&ç 90 es¡≈£î Áyêj·Tã&çñqï 90 |òü\ø±\T ñHêïsTT. yê{ÏqT+&ç j·÷<äè∫Ã¤ø£+>±

ˇø£ |òü\ø±ìï mqTïø=+fÒ <ëìô|’ ÁøÏ+~ dü+K´\T ñ+&ÉT≥≈£î dü+uÛ≤e´‘· m+‘Ó+‘· ?

(i) ¬s+&É+¬ø\ dü+K´, (ii) K∫Ã‘· es¡Zdü+K´, (iii) Á|ü<Ûëq dü+K´, (iv) 10# uÛ≤>∑+|üã&ÉT dü+K´.

12 (a) ˇø£ \+ãø√D Á‹uÛÑT»eTT˝À ø£s¡íeTT MT~ es¡ZeTT, $T–*q ¬s+&ÉT uÛÑTC≤\ esêZ\ yÓTT‘êÔìøÏ

düe÷q+ nì ìs¡÷|æ+#·+&ç.

( Ò<ë)

(b) Cosec θ cot θ = a nsTT‘ sec θ = 2

2

1

1

a

a

+−

nì #·÷|ü+&ç.

13 (a) Ç∫Ãq Á‹uÛÑT»eTT ABC øÏ düs¡÷|ü+>± ñ+≥÷, <ëì uÛÑTC≤\≈£î 4

3 ¬s≥T¢ ñ+& nqTs¡÷|üuÛÑTC≤\T

ø£*–q Á‹uÛÑTC≤ìï ì]à+#·+&ç. ìsêàDÁø£eTeTT Áyêj·T+&ç.

( Ò<ë)

(b) 3 ôd+.MT. yê´kÕs¡ú+‘√ ˇø£ eè‘êÔìï ^j·T+&ç. πø+Á<äeTT qT+&ç 5 ôd+.MT. <ä÷s¡+˝À >∑\ _+<äTe⁄

qT+&ç ˇø£ »‘· düŒs¡ÙπsK\qT ^∫ yê{Ï bı&Ée⁄\T ø=\e+&ç. ìsêàDÁø£eTeTT Áyêj·T+&ç.

23


10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT









ôdø£åHé ` IV



1/2 R 10 e÷s¡Tÿ\T

14. _+<äTe⁄\T A( − 4, 3) eT]j·TT B(2, 8) \qT ø£*ù| πsU≤K+&É+ô|’ _+<äTe⁄ P(m, 6) ( )

nsTT‘ m $\Te m+‘· ?

A) 1

2B)

3

2C)

2

5

−D)

1

3

15. ΔABC ˝À DE � BC, AD = 6 ôd+.MT., BD = 9 ôd+.MT., ( )

AE = 8 ôd+.MT. nsTTq AC bı&Ée⁄ m+‘· ?

A) 20 ôd+.MT. B) 12 ôd+.MT.

C) 15 ôd+.MT. D) 18 ôd+.MT.

16. |ü≥+˝À Bs¡È#·‘·Ts¡Ádü+ bı&Ée⁄ 20 ôd+.MT. n+‘·]¢œ‘· eè‘êÔ\T ( )

düs¡«düe÷Hê\T. nsTTq ùw&é #j·Tã&çq ÁbÕ+‘· yÓ’XÊ\´+

A) 40 cm2 B) 43 cm2

C) 25 cm2 D) 33 cm2

C

D E

A B

9 cm

6 cm 8 cm

20 ôd+.MT.

24

17. sin2 10o + sin2 15o + sin2 75o + sin2 80o $\Te ( )

A) 0 B) 1 C) 2 D) 3

18.1

2,

2

3,

3

4,

1

6 eT]j·TT

7

12 \ eT<ä >∑‘·eTT m+‘·? ( )

A) 3

4B)

7

12C)

2

3D)

1

6

19. ¬s+&ÉT bÕ∫ø£\qT πøkÕ] $dæ]q|ü⁄&ÉT bÕ∫ø£\ eTTU≤\ô|’ >∑\ n+¬ø\ yÓTT‘·Ô+ 14 ( )

njT´ dü+uÛ≤e´‘·

A) 1

2B) 1 C) 0 D)

2

3

20. ÁøÏ+~ yêì˝À ndü‘· Á|üe#·Hêìï >∑T]Ô+#·+&ç. ( )

A) ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\T>± 1, 1 eT]j·TT 2 \T ñ+&Ée#·TÃ.

B) 1, 2, 3 \T ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\ bı&Ée⁄\T.

C) 4:1 ìwüŒ‹Ô À yÓ’XÊ˝≤´\T >∑\ ¬s+&ÉT #·‘·Ts¡ÁkÕ\ nqTs¡÷|ü uÛÑTC≤\ ìwüŒ‹Ô 2:1

D) 17, 8 eT]j·TT 15 \T ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\ bı&Ée⁄\T ne⁄‘êsTT.

21. x > 0, y < 0 nsTTq (x, − y) ñ+&ÉT bÕ<äeTT ( )

A) Q1

B) Q2

C) Q3

D) Q4

22. ªθμ jÓTTø£ÿ @ $\Te≈£î tan θ = cot θ dü‘· eT>∑TqT. (θ∈Q1) ( )

A) 60+ B) 45+ C) 90+ D) 0+

23. ªzJyé eÁø£eTTμ qT+&ç @ πø+ÁBj·T kÕúq$\TeqT ø£qT>=+{≤s¡T ? ( )

A) n+ø£eT<ä eT+ B) eT<ä >∑‘·+ C) u≤VüQfiø£+ D) yê´|æÔ

24. R eT]j·TT r yê´kÕsêú\T>± >∑\ @ø£πø+Á<ä eè‘êÔ\ eT<Ûä @s¡Œ&ÉT ÁbÕ+‘· yÓ’XÊ\´+ ( )

A) π (R − r)2 B) π (R2 − r2) C) π (R + r)(R − r) D) π R2 r2

25. ΔABC ˝À ∠B = 90o. θ n\Œø√DeTT. Sin θ = AB

AC nsTTq

AC

BC @ Á‹ø√D$Trj·T

ìwüŒ‹Ôì dü÷∫+#·TqT. ( )

A) cos θ B) tan θ C) sec θ D) cosec θ

25

26. _+<äTe⁄\T A(2a, 4a), B(2a, 6a) eT]j·TT C(2a + 3 a, 5a) \# @s¡Œ&ÉT Á‹uÛÑT»eTT ˇø£ ( )

A) \+ãø√D Á‹uÛÑT»eTT B) düeT~«u≤VüQ Á‹uÛÑT»eTT

C) düeTu≤VüQ Á‹uÛÑT»eTT D) n\Œø√D Á‹uÛÑT»eTT

27. ˇø£ dü+e‘·‡s¡+ »qe] HÓ\˝À X+ø£sY 165 bò Héø± Ÿ‡ #ôdqT. Ä dü+e‘·‡s¡+ »qe] ( )

1e ‘~ XóÁø£yês¡+. Ä HÓ\˝À Ä~yês¡+Hê&ÉT dü>∑≥Tq 7 f…*bò Héø± Ÿ‡ #XÊ&ÉT. $T–*q

s√E\˝À dü>∑≥Tq mìï bò Héø± Ÿ‡ #ôdqT ?

A) 165

31B) 5 C) 7 D)

137

27

28. ˇø£ ãT≥º À >∑\ e÷$T&ç|ü+&É¢ À 90% eT+∫$. j·÷<äè∫Ã¤ø£+>± Ä ãT≥ºqT+&ç ˇø£ ( )

e÷$T&ç|ü+&ÉTqT mqTïø=+fÒ n~ bÕ&Ó’b˛sTTq e÷$T&ç|ü+&ÉT njT´ dü+uÛ≤e´‘·

A) 9

100B)

1

100C)

9

10D)

1

10

29. 30 ôd+.MT. >∑\ eè‘·Ô|ü]~Û À, 4 #·.ôd+.MT. ÁbÕ+‘· yÓ’XÊ\´+ ÄÁø£$T+# yÓTTø£ÿ\qT ( )

mìï Hê≥e#·TÃ ?

A) 18 B) 750 C) 24 D) 120

30. Á|üø£ÿ |ü≥+˝À ùw&é #j·Tã&çq ÁbÕ+‘·eTT <ìì ÁbÕ‹ì<ä |üs¡TÃqT ( )

A) n~Ûø£ eè‘·ÔK+&ÉeTT B) n~Ûø£ Á‹C≤´+‘·s¡eTT

C) n\Œ eè‘·ÔK+&ÉeTT D) n\Œ Á‹C≤´+‘·s¡eTT

31. nes√Vü≤D zJyé eÁø£eTT ì]à+#·T≥≈£î x`nø£å+ô|’ rdüTø=H$ ( )

A) ~>∑Te Vü≤<äT›\T B) m>∑Te Vü≤<äT›\T C) eT<ä $\Te\T D) bÂq'|ü⁄qéTT

32. |ü≥+˝À #·÷|æq _+<äTe⁄ P(a, b) eT÷\_+<äTe⁄ qT+&ç >∑\ <ä÷s¡eTT ( )

A) 1

2ab B) 2 2a b+

C) a2 + b2 D) 2 2a b−

33. ΔABC ˝À BD ⊥ AC eT]j·TT ∠B = 90o qT ÁbÕ‹ì<ä |ü]# |ü≥eTT ( )

A) B) C) D)

A Bx

o

x

y

o

B D C

A A

B C B C

D E

A DB

C

A

Documents

NON - LANGUAGESpvsap.weebly.com/uploads/8/2/5/0/8250405/non_languages.1-114.pdf · Trigonometry Similar Triangles Statistics Trigonometry Tangents and Secants of Circles Co-ordinate