Mathmatics Question Type Odisha Board Exam

7/29/2019 Mathmatics Question Type Odisha Board Exam

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SAMP

LE

Roll No. of the Candidate

2013AH

Grand Total Marks Grand Total

in words .......................................................................................................

[No. of Qns. : 14] Time : 2 Hours]

[No.of Printed Pages: 24 ] [Full Marks : 100

Signature of Examiner &

Regd. No.

Signature of the Scrutiniser

& Regd. No.Signature of the Chief Evaluator &

Regd. No.

Signature of the Deputy Chief &

Regd. No.

Date............................

Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Marks

REGULAR SET : A

AR 15

_el[u c iP^ :

K. _g_Z ifM Ce LZU _Aa _e Gj C_e c\Z [a _g iL I _ iL_g_Z ifM Ce LZe _ZK_e _g iL I _ iL ijZ ckA @ G[eiU iKZ _Z _e VK bae fL jAQ ^ ^jc ckA @

L. ~\ KQ ZU _eflZ jG, Za ZU~q _g_Z ifM Ce LZU _el Mj \dZe[a ^elKu `eA @C MUG VK _g_Z cM @

FOR USE AT THE EVALUATION CENTRE

(Varified and found correct)

Full signature of the Invigilator

MTH

MATHEMATICS

QUESTION - CUM - ANSWER BOOKLET


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: i]eY iP^ :: GENERAL INSTRUCTIONS :

l Gj _g_Z ifM CeLZe Cbd \NI il CeckK, Ga a^ _g ej@Q The question-cum-Answer Booklet consists of objective and subjective types of questions.

l _ZK a^ _g c Ce fLa _A ce eZ i^ \@~AQ _el[c^ iji e Ce fLa @agK Required space has been provided against each objective type question. The candidate has

to choose the correct choice and write the complete answer along with its bit number in the

space provided.

l \NCeckK _g c ce Ce fLa c eZ i^ \@~AQ _el[c^ iji^ ce Ce fLa @agK For subjective type questions required space for each question has been provided. The

candidate has to answer the questions in the space provided.

l ^g @ ~d _ZK _ge Ce \a @agK Follow the instructions given against both the objective and subjective types of questions.

l Ce Kk Ga ^k af _G _^e fLa @agK Candidate should write the answer with blue / black ball point pen only .

l a^ _gMWKe Cee KYi KUKU K fbA Ce fLf Zje cfu^ Ke~a^j In case of Multiple Choice, Fill in the blanks and Matching questions, scratching / rewriting /

marking /over writing is not permitted, thereby rendering to disqualification for evaluation.

l _g_Z ifM Ce LZe [a _g _Xa c _el[c^u15 c U@]K icd \@~a Extra 15 minutes shall be given for reading the question paper.

l _g_Z ifM Ce LZe ghe ifM [a Lf _, bf Ke[a ~KYi _ge Ce fLa^c aaje Ke~a Extra two rulling pages given at the end of this booklet may be utilised for writing the wrong

answers or extra answers if necessary.

: INSTRUCTIONS TO THE CANDIDATES :A : Check up the number of questions and number of printed pages mentioned on the top left-

hand and right-hand corner of this page with the number of questions and number of printed

pages of this question paper soon after the receipt of the question paper. Verify whether the

Set Symbol in this page is printed in all other pages and write this Set Symbol on the space

provided for writing the Set Symbol on the cover page of the answer paper.

B : In case of discrepancy, collect a fresh correct question paper in exchange of the defective

one from the invigilator of your hall / room after receipt of the question paper.


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x~ Q{ AB$# QSL Z Dd >

The figures in the right-hand margin indicate marks.

D A >Answerallquestions.

aRMYZ / Algebra1. _ZK^ _Yke ic]^ Ke : 5

Solve by the method of substitution

2x + 3y 2 = 0

10x 6y 3 = 0

L/ (OR)

_aMe _eYZ Ke ic]^ Ke :Solve by completing the squares :

2x2 9x + 4 = 0_________________________________________________________________

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2. a = 2

1

3 2

1

3

jf, _cY Ke ~ 2a3 + 6a = 3 5

If a = 2

1

3 2

1

3

, then prove that 2a3 + 6a = 3

L/ (OR)

^c ieYe \@~A[a Z[ake cc^ ^d Ke :

Find the mean of the data given in the following table :

ibM 0-10 10-20 20-30 30-40 40-50Class Interval

aeeZFrequency 3 8 25 35 19

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3. DABC icKY ZbRe mB = 900, a = 4 i.c. I c = 3 i.c. Gje Ke \NI lZ`k ^e_Y Kea _A GK _aj PZ _Z Ke 5

In the right angled tri angle, DABC, mB = 900, a = 4 cm and c = 3 cm. Preparea flow-chart to find the length of its hypotenuse and area.

L/ (OR)

RY aq GK _Ke95 Uu@ 10% KZK @g 98 Uu aK cfe KY i[ecU190 Uu ahK @d Kf Za i KZ Uu a^~M Ke[f, ^d Ke

A man, purchasing some 95 rupees 10% share selling at market value of Rs.

98.00 earned Rs. 190.00 per annum. Find the amount of money he invested.

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4. ^cfLZ _gc^u ce ~ KYi PeUe Ce \@ 4 x 4Answer any four of the following questions :

(i) _Zu adie \AMY I _Ze adi cg 90 cZ _Zu adi I _Z adie \AMY cg60 _Z I _Zue adi ^d Ke Sum of the twice fathr's age and son's age is 90. But the sum of father's age and

twice the son's age is 60. Find father's and son's age.

(ii) ax2 + bx + c = 0 icKeYe MUG ck @_eUe Z^MY jf, _cY Ke ~3b2 = 16ac (a 0)If one of the roots of the equation, ax2 + bx + c = 0 is three times that of hte

other, then prove that 3b2 = 16ac.

(iii) iek Ke :

Simplify :

3 loga2 + 2 log

a3 + log

a5 log

a9 (a > 0, a 1)

(iv) ^c ieYe \@~A[a Z[ake cc ^d Ke :Find the median of the data given in the following table :

fu 15 16 17 18 19 20ScoresaeeZFrequency 5 9 15 20 14 2


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(v) (x)2

K \K e_e _eYZ Ke Give the value of (x)

2in binary form.

(1101)2 + (x)2 = (11101)2 + (11)2

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5. ic _ge Ce \@ : 2 x 6Answer all questions :

(i) px 4y = 0 I 16x py = 0 ijicKeY\de @iL ic]^ [f, p ec^ ^d Ke


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If the simultaneous equations, px 4y = 0 and 16x py = 0 have infinite

number of solutions, then find the value of p.

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(ii) 2x2 + 5x c = 0 icKeYe MUG ck 2 jf, c e c ^d Ke If one of the rootsof the equation, 2x2 + 5x c = 0 is 2, then find the

value of c._________________________________________________________________

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(iii) log 0.01986 e KeUeK I ci ^d Ke Find the characteristic and mantesa of log 0.01986

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(iv) 15 U fa]ue cc^ 52.5 I ic^ue cc 53.2 jf, ic^ue MeK^d Ke

The mean of 15 scores is 52.5 and their median is 53.2. Find their mode.

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(v) (64)10

K \K e_e _Kg Ke :Express (64)

10in binary form.

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(vi) ic]^ Ke :

Solve :

1

61 2 x = 216

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6. ^cfLZ _gc^ue Kak Ce fL : 1 x 5Write the answer only of the following questions.

(i)x y

3 40+ = I

y x

4 30 = icKeY \de ic]^ KZ ?

What is the solution of the two equations,x y

3 40+ = and

y x

4 30 = ?

Ans : _________________________________________________________

(ii) 3x2 + 9x = 2 icKeYe ck\de MY`k KZ ?What is product of the roots of the equation, 3x2 + 9x = 2 ?

Ans : _________________________________________________________

(iii) 161

1

2

e c^ KZ ?

What is he value of 161

1

2 ?

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(iv)log 8

log 1

2

2 6e iekKZ c^ KZ ?

What is he simplified value oflog 8

log 1

2

2 6?

Ans : _________________________________________________________

(v) _aj PZe Z[_ag _A aajZ iKZe MUG PZ Ke Draw the figure of the symobol used for "Impute" in a flow-chart.

Ans : _________________________________________________________


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RcZ I ZKYcZGeometry and Trigonometry

= 227d i

7. _cYKe ~, MUG ae K Ve ic\ea R c^ue \N ic^ 5Prove that chords of a circle equidistant from the centre are of equal length.

L/ (OR)

_cY Ke ~ ae GK aji aP c \A MUG Q\K aKA I B ae Q\Kf Ga PT ae GK gKL jf, PA . PB = PT2

Prove that if a secant to a circle passing through an external point P meets the

cirlce at A and B and PT is a tangent segment then PA . PB = PT2

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8. A I B K ag \AU a _eeKP I Q ae Q\ Ke P c \A AB ijice iek eL a \dK ~[Kc M I N ae Q\ Ke

_cY Ke ~ MN = 2AB 5Two circles having centres at A and B intersect each other at points P and Q.

A straight line through P parallel to AB meets the circles at points M and N

respectively. Prove that MN = 2AB

L/ (OR)

GK ae ai MN M Ve @uZ gK C_e A I B G_e \AU a ~_e

A M B Ga AN I BN aK ~[Kc P I Q ae Q\ Ke _cY Ke ~PN

BN

QN

AN=

MN is the diameter of a circle. A and B are points on the tangent drawn at M

such that A M B. AN and BN meet the circle at P and Q respectively.

prove thatPN

BN

QN

AN=

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9. (A + B + C) = 1800 jf, _cY Ke ~tan A + tan B + tan C = tanA . tan B . tan C 5

If (A + B + C) = 1800, then Provl that

tan A + tan B + tan C = tanA . tan B . tan C

L/ (OR)

i~e KYK C^Z 600 e450 K ji _Aae GK e QA 24 cUe a _Af eCyZ d Ke ( 3 = 1.732)

When the sun's angle of elevation decreased from 600 to 450, the shadow of a

pillar increased by 24 metres. Find the height of the pillar. ( 3 = 1.732)

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10. D ABC e AB = 7 i.c., m C = 600 I CX cc = 5 i.c.

ZbRU @u^ Ke 5

In D ABC, AB = 7 cm, m C = 600 and median CX = 5 cm. Construct the

triangle.

L/ (OR)

ABCD @dZ PZe BC = 6 i.c., I AB = 5 i.c. @dZ PZU @u^ Ke Gje _ea@u^ Ke In rectangle ABCD, BC = 6 cm and AB = 5 cm. Construct the rectangle and

then construct its circum-circle.

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11. 4.5 i.c. ai ag GK a @u^ Ke Gj ce GK ic\aj ZbR

@fL^ Ke ~je bc = 7 i.c. 2Construct a circle of radius 4.5 cm and inscribe in it an isosceles triangle whose

base is 7 cm.

L/ (OR)

4.5 i.c. ai ag GK a @u^ Ke Gj C_e P GK a @ P Ve a_Z GK gK @u^ Ke Construct a circle of radius 4.5 cm. Take a point P on it. At P construct a

tangent to the circle.

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12. ^cfLZ _gc^u ce ~KYi Z^Ue Ce \@ : 4 x 3

Answer any three of the following questions.

(i) MUG @aKe lZe Pe_U aW \ae cUeK1

3Uu jiae 288 Uu Ly

jf @ _e]e \N ^d Ke

Rs. 288.00 was spent for fencing around a semi-circular field at the rate of

Rs.1

3per metre. Find the length of the semi circumference.

(ii) \AU ae aie @^_Z 3:5 _[c ae lZ`k 198 a.i.c. jf, \Zd aelZ`k ^d Ke The ratio of the diameters of two circles is 3:5. If the area of the first circle is 198

sq.cm. then find the area of the second circle.


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(iii) MUG _Rce bc GK icaj ZbR I CyZ 11 i.c. Gje @dZ^ 44 3 Nî.c. jf, Gje _g_Zke lZ`k d Ke

The base of a prism is an equilateral triangle and its height is 11 cm. If its volume

is 44 3 cubic cm. then find its lateral surface area.

(iv) 33 i.c. CyZ ag GK ifee aK_Zke lZ`k 11 i.c. \N ag MUGicNê icM _Zke lZ`k ic^ ifee bce ai ^d Ke

The curved surface area of a cylinder of height 33 cm is equal to the whole

surface area of a cube of side 11 cm. Find the diameter of the base of the

cylinder.

(v) MUG @dZNê @dZ^ 2430 N^cUe Gje \\, _i I CyZe @^_Z 6:5:3jf, Gje _g_Zke lZ`k ^d Ke

The volume of a cuboid is 2430 cubic meter and its length, breadth and height

are in the ratio 6:5:3. Find its lateral surface area.

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13. ic _ge Ce \@ : 2 x 7 = 14Answer all questions :

(i) \ ae AB CDII _cY Ke ~ AC = BD

In the given fiture, AB CDII . Prove that AC = BD

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(ii) \ PZe O, ae K

_cY Ke ~ mOBC = 900 mBACIn the given figure, O is the centre of the circle.

C

B

D

A

O

C

A

B


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Prove that mOBC = 900 mBAC

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(iii) MUG aeK O Ga P GK aji a PQ I PR \AU gK L _cY Ke ~ DOPQ DOPR

O is the centre of a circle and P is an external point. PQ and PR are two

tangent-segments. Prove that DOPQ DOPR

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(iv) MUG a C_eiP ae @uZ gK RS R ij ice jf, _cY Ke ~ PaMc aiRPS K ic\L Ke

P is a point on a circle. At P a tangent is drawn parallel to the chord RS . Provethat the radius through P bisects RPS.

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(v) PQ MUG ae R P I Q Ve Cq R _Z f\d ~[Kc aKR I S aeQ\ Ke _cY Ke ~ PR = QS

PQ is a chord of a circle. At P and Q perpendiculars drawn to PQR meet the

cirlce at R and S respectively. Prove that PR = QS._________________________________________________________________

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(vi) \ PZe PT gK L Q\K m AX T = 700I

m BY T = 1500

jf APTe _ecY ^d Ke In the given figure, PT is a tangent segment.

If m AX T = 700 and m BYA = 1500

then find the measure ofAPT._________________________________________________________________

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OA

TP

BY

X

Q


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(vii) _cY Ke :

Prove : cos (450 + q) =1

2

(sin q cos q)

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14. a^ ce \@~A [a ia Cec^u ce _ZK _g _A VK CeU aQ ZcCe LZe fL 1 x 4Choose the correct answer from the possible answers given in the bracket below

each question and write it in your answer book.

(i) \ ae m AXB : m BY C : m C ZA : : 2:3:4 jf,

ACB e _ecY KZ ?

If in the given circle, m AX B : m BY C : m C ZA : : 2 : 3 : 4, thenwhat is the measure ofACB ? (400, 600, 800, 1000)

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(ii) GK ae 8 i.c. \N ag GK R KVe6 i.c. \ee @aiZ aeai KZ i.c.

In a circle a chord of length 8 cm is at a distance of 6 cm from the

centre. What is the length of the radius in cm ? (10, 12, 14, 16)

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B

A

C

X Z

Y


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(iii) MUG ae Ga R Ke 900KY C_^ Ke Re \N 7 i.c.

jf, ai KZ i.c. ?In a circle a chord subtends an angle of 900 at the centre. If the length

of the chord is 7 cm, then what is the length of the radius in cm ?

2

77 2 2 7

7

2, , ,

FHG

IKJ

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(iv) tan 1350e c^ KZ ?

What is the value of tan 1350 (1, 0, 1, 3 )

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Mathmatics Question Type Odisha Board Exam