AITS-6

8/10/2019 AITS-6

1/21

GENER L INSTRUCTIONS

1. In addition to this question paper, you are given a separate answer sheet.

2. Fill up all the entries carefully in the space provided on the OMR sheet ONLY IN BLOCK CAPITALS.

Incomplete/incorrect/carelessly filled information may disqualify your candidature.

3. A student has to write his/her answers in the OMR sheet by darkening the appropriate bubble with the

help of HB Pencil as the correct answer(s) of the question attempted.

4. Paper carries 80 questions each of 3 marks.

5. Any rough work should be done only on the blank space provided at the end of question paper.

6. Foreach correct answer gets 3 marks, each wrong answer gets a penalty of 1 mark.

7. Blank papers, clip boards, log tables, slide rule, calculators, mobiles or any other electronic gadgets in

any form is "NOT PERMISSIBLE".

Time : 2 Hr. Date : 12-10-2014 Max. Marks : 240

PCCP Head Office:Address :J-2, Jawahar Nagar, Main Road, Kota (Rajasthan)-324005

Contact. No. :+91-0744-2434727, 8824078330

Website :www.pccp.resonance.ac.in E-mail :[email protected]

ALL INDIA IJSO(STAGE-I) TEST SERIES

MOCK TEST PAPER # 6
mailto:[email protected]://www.pccp.resonance.ac.in/

8/10/2019 AITS-6

2/21

IJSO STAGE-I _MOCK TEST-4_PAGE # 2

Space For Rough Work

1. If ! "#2 2a b is a prime number then ! "#2 2a b =..........

(A) ! "#a b (B) ! "$a b (C) 1 (D) 0

2. )38( nn # is always divisible by

(A) 8 (B) 3 (C) 5 (D) 2

3. If ! "#4x y is a multiple of 3, then )274( 22 yxyx #$ is divisible by

(A) 3 (B) 7 (C) 6 (D) 9

4. The highest power of 3 contained in (1000 factorial) is

(A) 490 (B) 492 (C) 498 (D) 500

5. The values of ! "%n n Z for which ! "$ $2 19 92n n is a square are

(A) ! "8,11 (B) ! "#8,11 (C) ! "#8, 11 (D) ! "# #8, 11

6. The pairs of positive integers (m, n) for which $2 3m nis a perfect square is

(A) ! "1,2 (B) ! "4,2 (C) ! "3,1 (D) ! "6,3

7. The remainder when ! "5555

2222 is divided by 7 is

(A) 4 (B) 5 (C) 6 (D) 0

8. The rational roots of # # $ &3 22 3 11 6 0x x x are

(A)' () *+ ,

1,1,2

2(B)

' (#) *+ ,

1, 2,3

2(C)

' (# #) *+ ,

1, 1,2

2(D)

' (# #) *+ ,

1, 2, 3

2

9. If # $ # $ &5 3 24 25 125 625 3125 0p qp rp sp t then the roots of the equations

tsxrxqxpxx $$$$$ 2345 are

(A) A.P. (B) G.P. (C) H.P. (D) A.G.P.

IJSO TEST P PER

8/10/2019 AITS-6

3/21



10. The condition that the roots of # $ # &3 2 0x px qx r be in G.P. is

(A) # &2 2 0p r q (B) # &3 3 0p r q (C) # &4 2 3 0p r q (D) # &3 2 0p r q

11. Roots of the equation # $ # $ &4 3 210 26 10 1 0x x x x are

(A) (+3, +2) (B) ! "- -3 2 2,2 3 (C) ! "- -3, 2 (D) ! "- -1 2,2 3

12. Solution of the system of equations

$ $ &

$ $ &

$ $ &

2 4 4

3 9 9

4 16 16

log log log 2

log log log 2

log log log 2

x y z

y z x

z x y

(A) & & &1 34 26

; ;3 3 7

x y z (B)3

32z;

8

27y;

3

2x &&&

(C) & # & &2 27 32

; ;3 8 3

x y z (D) & & # & #2 34 32

; ;3 3 3

x y z

13. Real (x, y) that satisfy $ & $ $ $ $ &3 3 2 27 & 4x y x y x y xy are

(A) ! " ! "# #2, 1 , 1,2 (B) ! " ! "# # # #2, 1 , 1, 2 (C) ! " ! "#2,1 , 1,2 (D) ! " ! "#2,1 , 1, 2

14. If a, b, c are +ve real numbers representing the sides of a triangle then which of the following is

correct.

(A) )(3)()(2 2

cabcabcbacabcab $$.$$.$$(B) ! " ! " ! "$ $ . $ $ . $ $

23 4ab bc ca a b c ab bc ca

(C) ! " ! " ! "$ $ . $ $ . $ $2

2ab bc ca a b c ab bc ca

(D) none of these

15. In a /ABC, the incircle touches the sides BC, CA and AB respectively at D, E and F. If the radius of

the incircle is 4 units and if BD, CE and AF are consecutive integers, the sides of /ABC

(A) ! "12,13,14 (B) ! "13,15,14 (C) )11,10,9( (D) ! "12,14,15

8/10/2019 AITS-6

4/21



16. A circle passes through the vertex C of a rectangle ABCD and touches its sides AB and AD at M and

N. If the distance from C to the line segment MN is equal to 5 units, find the area of the rectangle

ABCD

O

A DN

M

B C

(A) 20 (B) 36 (C) 25 (D) 15

17. In an acute angled triangle there are points D, E, F are points on BC, CA, AB such that 0AD BC ;

AE = EC and CF bisects 1Cinternally. Suppose CF meets AD and DE in M and N respectively. IfFM = 2; MN = 1; NC = 3, the perimeter of /ABCis

A

F

B D C

E

M N

(A) 6 3 (B) 18 3 (C) 12 3 (D) 24 3

18. If a transversal cuts the sides BC, CA, AB of a /ABCat X, Y, Z then . .BX CY AZ

XC YA ZB equals

(A) 1 (B) 2 (C) 3 (D) -1

8/10/2019 AITS-6

5/21



19. In a /ABC, D is the mid-point of BC. If 1 & 45ADB and 1 & 30ACD ; the value of 1BADis

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

20. ABCD is a cyclic quadrilateral with AC 0 DB and AC meets BD at E. Then $ $ $2 2 2 2EA EB EC ED isC

B

A

D

O

E

(A) R2 (B) 3R2 (C) 4R2 (D) 2R2

Where R is the radius of circumscribed circle]

21. A boy leaves his house at 9:30 a.m. for his school. The school is 2 km away and classes start at 10:00 a.m.

If he walks at a speed of 3 km/h for the first kilometre, at what speed should he walk the second kilometre to

reach just in time ?

(A) 6 km/h (B) 8 km/h (C) 9 km/h (D) 12 km/h

22. A cylinder of mass 10 g weighs 7 g in water. If its area of cross-section is 0.75 cm2, its length will be

(A) 4 cm (B)3

40cm

(C)3

28(D) known only in terms of its density

23. A bullet in motion hits and gets embedded in a solid resting on a frictionless table. What is conserved :

(A) Momentum and K.E. (B) Momentum only(C) K.E. alone (D) None of these

24. The statement for a given pair of forces (in figure) can be written as :

W= mg

Rn

(A) It is not an action-reaction pair (B) It is an action-reaction pair

(C) Depends on situation (D) None of these

8/10/2019 AITS-6

6/21



25. An object of mass m is dropped from a height h, it penetrates in sand upto a depth x. Find the average

resistance (force) exerted by the sand :

(A) mgx

h(B) mg (1 +

x

h) (C) mgh (D) none of these

26. What is the relation between FAand F

B. F

Aand F

Bare the magnitudes of magnetic field at A and B?

(A) FA= F

B(B) F

A> F

B(C) F

A< F

B(D) Nothing can be said

27. A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive

index of water is 4/3 and the fish is 12 cm below the surface, the radius of the circle is :

(A) 12 3 5 cm (B) 12 3 7 cm (C) 12 2/5 cm (D) 12 7

3cm

28. A step down transformer reduces 220V to 11V. The primary coil draws 5 A current and secondary coil

supplies 90A. Efficiency of the transformer will be :

(A) 4.4% (B) 20% (C) 33% (D) 90%

29. Which of the following correctly depicts the graphical variation in case of a spherical mirror ?

(A)

v-1

u-1

y

xO

(B)

v-1

u-1

y

xO

(C)

u

-1

v-1

y

xO

(D)

u

-1

y

xO

v-1

8/10/2019 AITS-6

7/21



30. A body is moving on a circular path if its velocity (linear velocity) is incresed by 10% and angular velocity

is increased by 20%, then what will be the percent change in centripetal accleration ?

(A) 10% (B) 20% (C) 30% (D) 32%

31. The result of mixing equal masses of ice at 10C and water at 60C (the specific heat of ice = 0.5 cal g1c1) :

(A) temperature 0C,16

11of total mass of ice melts

(B) temperature 0C,11

16of total mass of Ice melts

(C) temperature 10C,16

11of total mass of ice melts

(D) data given are not sufficient

32. Water falls from a height of 100 m. Find the change in temperature of water at the bottom :

(A) 2.4C (B) 0.24C (C) 24C (D) 0C

33. A wire 88 cm long bent into a circular loop is placed perpendicular to the magnetic field of flux density2.5 Wb m2. Within 0.5 s, the loop is changed into a square and flux density is increased to 3.0 Wb m2.

The value of e.m.f. induced is :

(A) 0.018V (B) 0.016V (C) 0.020V (D) 0.012V

34. A pebble is dropped into a well of depth h. The splash is heard after time t. If cbe the velocity of sound,

then :

(A) t=h2

gc(B) t = c + gh (C) t = c v (D) t=

g

h2+

c

h

35. An infinite wire bent in the form of L carries current 2. What is the magnetic field at the point O ?

(A) zero (B)d4

0 234

5(C)

d240 234

5(D)

d

2

40 234

5

8/10/2019 AITS-6

8/21



36. The focal length of a concave mirror is 20 cm. Determine where an object must be placed to form an

image magnified two times when the image is real-

(A) 30cm from the mirror (B) 10cm from the mirror(C) 20cm from the mirror (D) 15cm from the mirror

37. An oscillator crosses the mean possition at t = 0. Its displacement at the end of 3s is twice that after 1s.

The period of the oscillation is :

(A) 4 second (B) 12 second (C) 4

12

second (D) 4

6

second

38. Light incident on a rotating mirror M is reflected to a fixed mirror N placed 22.5 km away from M. The fixed

mirror reflects it back to M (along the same path) which in turn reflects the light again along a direction

that makes an angle of 27 with the incident direction. The speed of rotation of the mirror is:

(A) 250 revolutions s1 (B) 500 revolutions s1

(C) 1000 revolutions s1 (D) 125 revolutions s1

39. A real inverted image in a concave mirror is represented by (u, v, f are coordinates)

(A) (B) (C) (D)

40. According to the quantum theory, a photon of electromagnetic radiation of frequency v has energy

E = hv where h is known as plancks constant. According to the theory of relativity, a particle of mass m

has equivalent energy E = mc2, where c is speed of light. Thus a photon can be treated as a particle

having effective mass m = 2C

hv. If a flash of light is sent horizonatally in earths gravitational field, then

photons while traveling a horizontal distance d would fall through a distance given by -

(A) 2

2

c2gd (B)

mch (C)

hmcd

2

(D) zero

41. Which set of quantum number is not consistent with the theory? :

(A) n = 2, != 1, m = 0, s = 1/2 (B) n = 4, != 3, m = 2 s = 1/2

(C) n = 3, != 2, m = 3, s = + 1/2 (D) n = 4, != 3, m = 3, s= + 1/2

42. Match column (A) with column (B) and select the correct option.

Column (A) Column (B)

(a) Resistant to corrosion (i) Galena

(b) Pig iron (ii) Galvanised iron

(c) Fe2O

3(iii) Impure iron

(d) PbS (iv) Haematite

(A) a(iii), b(ii),c(iv), d(i) (B) a(ii), b(iii), c(iv), d(i)(C) a(iv), b(i), c(iii), d(ii) (D) a(i), b(iv), c(ii), d(iii)

8/10/2019 AITS-6

9/21



43. Elements upto atomic number 103 have been synthesized and studied. if a newly discovered element is

found to have an atomic number 106. Its electronc configuration will be :

(A) [Rn] 5 f14, 6d4, 7s2 (B) [Rn] 5 f14, 6d1, 7s2,,7p3

(C) [Rn] 5 f

14, 6d6, 7s0 (D) [Rn] 5 f

14, 6d5, 7s1

44. The quantum levels upto n = 3 has :

(A) s- and p-levels (B) s, p, d, f-levels

(C) s, p, dlevels (D) slevels

45. Aluminium is not extracted by carbon reduction process. This is due to the following reason :

(A) At the temperature of the furnace, Al is oxidised by CO2

(B) Melting point at Al is very high

(C) Melting point at Al is very low

(D) Al reacts with carbon

46. Cu2S + 2Cu

2O 787 6Cu + SO

2

In which process of metallurgy of copper, above equation is involved ?

(A) Roasting (B) Reduction (C) Bessemerisation (D) Purification

47. The electron identified by quantum numbers n and !, (i) n = 4, !=1 (ii) n = 4, != 0 (iii) n = 3, != 2 (iv) n

= 3, != 1 can be placed in order of increasing energy from the lowest to highest :

(A) (iv) < (ii) < (iii) < (i) (B) (ii) < (iv) < (i) < (iii)

(C) (i) < (iii) < (ii) < (iv) (D) (iii) < (i) < (iv) < (ii)

48. In the reaction, H2O

2+ NaCO

3 787 Na

2O

2+ O

2+ H

2O, the substance underrgoing oxidation is

(A) H2O

2(B) Na

2CO

3(C) Na

2O

2(D) None of these

49. In the above question, the velocity acquired by the electron will be :

(A) ! "m/V (B) ! "m/eV (C) ! "m/eV2 (D) None of these.

50. Iodine has highest oxidation number in the compound :

(A) KIO4

(B) IF5

(C) KI2

(D) KI

51. Which is a redox reaction?

(A) 2CuI2 787 2CuI + I

2(B) NaCI + AgNO

3 787 AgCI + NaNO

3

(C) NH4CI + NaOH 787 NH

3+ NaCI + H

2O (D) Cr

2(SO

4)

3+ 6KOH 787 2Cr (OH)

3+ 3K

2SO

4

8/10/2019 AITS-6

10/21



52. 171 g of can sugar (mol.wt. = 342) are dissovled in 1000 g of water at 30C. If the density of solution is 1.1

g/mL, then :

(A) Molarity < Molality (B) Molarity = Molality (C) Molality < Molarity (D) None of these

53. The empirical formula of a compound is CH2O. If its VD is 30, its molecular formula is :

(A) CH2O (B) C

2H

4O

2(C) C

3H

6O

3(D) CH

3OH

54. An aqueous solution of urea containing 18 g urea in 1500 cm3of solution has a density of 1.052 g/cm3. If

the molecular weight of urea is 60, then the molality of solution is :

(A) 0.2 (B) 0.192 (C) 0.064 (D) 1.2

55. Equal volumes of 0.1 M AgNO3and 0.2 M NaCl are mixed. The concentration of NO

3ions in the mixture

will be :

(A) 0.1 M (B) 0.05 M (C) 0.2 M (D) 0.15 M

56. The species having octahedral shape is :

(A) SF6 (B)#3BF (C) PCI5 (D)

#33BO

57. How many 4- bond are there in the nitrogen molecule :

(A) One (B) Three (C) Two (D) None of these

58. The type of bonds present in CuSO4.5H

2O are.......only . :

(A) Electrovalent and covalent (B) Electrovalent and co-ordinate

(C) Electrovalent , covlent and co-ordinate (D) Covalent and co-ordinate

59. In nuclear fission and fusion:

(A) Fission refers to the absorption of a neutron by the nucleus and the emission of an alpha particle

(B) Fusion reactions be illustrated by the reaction, He2LiH42

73

11 8$ + energy

(C) The critical mass for nuclear fission depends on the temperature and pressure of the system

(D) Fusion occurs at lower temperatures than fission

60. The temperature of an ideal gas is increased from 140 K to 650 K. If at 140 K the root mean square

velocity of the gas molecules is V, at 560 K it becomes :

(A) 5V (B) 2V (C) V/2 (D) V/4

61. The organelles that contain their own genetic material are:

(A) Mitochondria, Vacuoles (B) Plastids, Golgi complex

(C) Mitochondria, Plastids (D) Ribosomes, Nucleolus

8/10/2019 AITS-6

11/21



62. The enclosures in which heat is trapped to maintain higher temperature, are called

(A) white houses. (B) warm houses. (C) blue houses. (D) green houses

63. The stage in which separation of sister chromatids occurs is

(A) anaphase. (B) telophase. (C) metaphase. (D) prophase.

64. Haversian canals occur in

(A) humerus. (B) pubis (C) scapula. (D) clavicle.

65. Bone marrow is absent in the bones of

(A) fish. (B) bird. (C) reptile (D) frog.

66. A fern commonly used as biofertiliser is

(A) Lycopodium. (B) Marsilea. (C) Azolla. (D) Adiantum.

67. Camel is best adapted to desert habitat as

(A) it can drink 50 litres of water at a time which is evenly distributed in all its tissues.

(B) it excretes very small amount of water during urination

(C) it can regulate its body temperature at a wider range

(D) all are correct

68. Aerenchyma is found in which plants ?

(A) sciophytes (B) hydrophytes (C) mesophytes (D) epiphytes

69. In the lunch, you ate boiled green vegetables, a piece of cooked meat, one boiled egg and a sugar candy.

Which one of these foods may have been digested first ?

(A) Boiled green vegetables (B) The piece of cooked meat

(C) Boiled egg (D) Sugar candy

70. In the given food chain 'Plants Sheep Man', 5 J of energy is available to man. The energy that

was available at producer level is

(A) 50 J. (B) 500 J. (C) 5 J. (D) 0.5 J.

71. Producers prepare their own food like

(A) blue green algae. (B) amoeba. (C) rhizopus. (D) yeast.

72. Which one does not produce any digestive enzyme ?

(A) Pancreas (B) Liver (C) Stomach (D) Duodenum

73. Tunica albuginea is the covering of

(A) lungs (B) testis (C) kidneys (D) heart

74. An organism with two identical alleles of a gene in a cell is called

(A) homozygous (B) dominant (C) heterozygous (D) hybrid

8/10/2019 AITS-6

12/21



75. Mendels law do not explain principle which is :

(A) Segregation of genes (B) Dominance

(C) Linkage (D) Independent assortment

76. Role of isolation in evolution is

(A) magnification (B) maintenance of species

(C) evolutionary divergence (D) extermination of species

77. Soil is composed of

(A) mineral + water + air

(B) mineral + organic matter + air

(C) mineral + organic matter + air + water

(D) organic matter + water

78. The link between krebs cycle and glycolysis is

(A) citric acid (B) acetyl - co - A (C) Succinic acid (D) Fumaric acid

79. Compensation point refers to the intensity of light at which

(A) Rate of respiration = Rate of photosynthesis

(B) Rate of respiration > Rate of photosynthesis

(C) Rate of respiration < Rate of photosynthesis (D) None of the above.

80. Prevention of a disease is more desirable than its cure because

(A) some of the body functions may be damaged during the effect of the disease.

(B) the person suffering from the disease will not be bedridden.

(C) the disease can not be communicated to others during the course of treatment.

(D) body does not look good during this condition.

IJSO Questionmaths : 1 to 20Phy : 21 to 40Che : 41 to 60Bio: 61 to 80

8/10/2019 AITS-6

13/21

SOL. IJSO STAGE-I _MOCK TEST-4_PAGE # 1

NSWER KEY

HINTS & SOLUTIONS

1. a2b2= (a b) (a + b) ..(i)

!a2b2 a prime equation= 1

!(a b) = 1 [!(a b) < (a + b)]!The only adivisor of a prime equation are 1 and itself!Equation (i) becomes (a2b2) = 1(a + b)or a2b2 = (a + b)eg. 3222= 5 (which coprime)32

22= 3 + 2, 3, 2 "N

2. 8n3n= (83) (8n1+ 8n23 + 3n1)

!(893n) is divisible by 5If n is either even or oddxnyn= (x y) (xn1+ xn2+ ... + yn1)If n is oddxn

+ yn= (x + y) (xn1xn2+ xn3y2....+ yn1)

3. !(4x y) is a multiple of 3!(4x y) = 3m!y = (4x 3m)

on putting value of y in (4x2+ 7xy

2y2)4x2+ 7xy 2y2= 4x2+ 7x(4x 3m) 2(4x 3m)2

= 4x2+28x221mx 32x 18m2+ 48mx= 27mx18m2

= 9m (3x 2m)

!4x2+ 7xy 2y2

is divisible by 9

ALL INDIA IJSO(STAGE-I) TEST SERIES

MOCK TEST PAPER # 4

DATE : 28-09-2014

Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Ans. B C D C D B B B A B B B A B B C C D C C

Ques. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Ans. A A B A B B D D C D A B A D A A B A A A

Ques. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ans. C B D C D C A D C A A A B B B A C C B B

Ques. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Ans. C D A A B C D B D B A B B A C C C B A A

4. !if p is a prim number and the longestexponent of p such that pe divides n! then

8/10/2019 AITS-6

14/21


e = #$

%&

'()

*10

1ipi

n

[x] is the largest integer + xIn this case p = 3, n = 1000

%

&

'(

)

*

p

n= %

&

'(

)

*3

1000= 333

%%&

'

(()

*2p

n= %

&

'()

*23

1000= 11111

%%&

'

(()

*3p

n= %

&

'()

*33

1000= 37

%%&

'

(()

*4p

n= %

&

'()

*43

1000= 12

%%&'

(()* 5p

n = %&'(

)* 531000 = 4

%%&

'

(()

*6p

n= %

&

'()

*63

1000= 1

%%&

'

(()

*7p

n= %

&

'()

*73

1000= 0

!Highest power of 3 contained in 1000!= 333 + 111 + 37 + 12 + 4 + 1 + 0 = 498

5. n2+ 19n + 92 = m2: n is a non negative integer. Thenn2+ 19n + 92 m2= 0

solving for n =2

)7m419( 2 ,-,

!(4m27) is a square ie 4m27 = p2 when p " N!(2m p) (2m + p) = 7!(2m + p) being positive is 7 and (2mp)= 1 ; 4m = 8 .m = 2Thus we have n2+ 19n + 92 = 4n2+ 19n + 88 = 0(n + 8) (n + 11) = 0

.n = 8 or n = 116. Let 2m+ 3n= k2

since (1)m/2m/ k2/ 1 (med3) [!31k]m is , say 2pnow (k2p) (k + 2p) = 3n

.k 2p= 1 andk + 2p= 3n;

.k 2p= 3n

.2p+1+ 1 = 3n

since (1)n/ 3n(mod4)= 2p+1+ 1n is even, say 2qNow (3q1) (3q+1) = 2p+1

.3q1 = 2

.3q= 3.q = 1 and hence p = 12

so we have only one solution (4, 2)

8/10/2019 AITS-6

15/21


7. 2222 /3 mod7(2222)3/27 mod 7and 27 / 1!(2222)3=1 mod 7.(2222)5553=1 mod 7(2222)2= 9 mod 7

.(2222)5555=9 mod 7But 9 / 5 mod 7 ; !(2222)5555/ 5 mod 7

8. Let the runs be if the form2

p(where (p q) = 1 and q > 0)

since q/2, q must be 2 or 1and p/6

.*1, - 2, - 3, - 6

f 01

234

52

1= f(2) = f(3) = 0

Hence root are2

1,2 and 3

9. Let the root bea 2d, a

d, a, a + d, a + 2d

sum of roots = 5a = p

!a =5

p,

But a is a root of the given equation hence

5

5

p01

234

5,+ p

4

5

p01

234

5,+ q

3

3

p01

234

5,+ r

2

5

p01

234

5,+ t = 0

or 4p525ap2+ 125 rp2625p + 3125 t = 0

10. Let the root of the given equation be ap, a, pa

!# 678 = 678 = ap :a : pa

= r

a3= r ; a = r1/3

But a is root of the given equation

!(r1/3) p(82/3) + qr1/3r = 0!pr2/3= qr1/3

.p2r2= q2r

.p3rq3= 0 is required condition

11.Dividing throughtout by x

2

01

234

5;

2

2

x

1x 10 0

1

234

5;

x

1x + 26 = 0

Let x +x

1= 9

!(y22) 10y + 26 = 0y2 10y + 24 = 0(y6) (y 4) = 0y = 6 OR y = 4

x +

x

1= 6 , x3 6x + 1 = 0

8/10/2019 AITS-6

16/21


x =2

326-= 3 - 22

and x +x

1= 4 ; x2 4x + 1 = 0

x =

2

124-= 2 - 3

12. Log2x + log

4y + log

4z = 2

log3y + log

9z + log

9x

=

2

log4z + log

16y + log

16z = 2

.(log4x) log

24 + log

6y + log

4z = 2

x2yz = 16 (i)similarly the other equation riduce to(ii) y2zx = 81 andz2xy = 256 ...(iii)solvingdivide (i) by (iii)

yx =

8116 ; x =

81y16

Dividing (ii) by (iii)

z

y=

256

81; z =

81

256y

! 2

2

)81(

)16(y2. y.

81

256y = 16

y4= 3

3

)16(

)81(, y =

8

27;

x =818

2716

::

=3

2; z =

3

32

13. Let x + y = 6, xy = 7and hence x2+ y2= 6227x2+ y3= (x + y) (x2xy + y2)

6(6237) = 7, 633a7= 7and x2+ y2+ x + y + xy = 4

62 27+ 6+ 7 = 4 = 627+ 6= 47 = 62 + 64!623636+ 12 6= 7262362126+ 7 = 0

f(1) = 262

+ 362

126+ 7 = 0hence (61) (factor of f(6))f(6) = (61)(2a2+ 5a7)f(6) = (61) (2a + 7a 2a7)f(6) = (61) {a(2d + 7) 1 (2a + 7)}f(6) = (61) (a 1) (2a + 7)6= 1 OR 6= 7/2when 6= 1, 7=2. thenx + y = 1 and xy = 2Hence xy are roots oft2 t 2 = 0 ; t = 2 or t = 1x = 2; x = 1 .y = 1, y = 2

If we take d =27 and f =

419 then

8/10/2019 AITS-6

17/21


x,y are root of 4t + 14t + 19 = 0whose discriminent < 0. Hence no real roots.hence solution are (2,1) and (1, 2)

14.2

ba 22 ; > ab ,

2

cb 22 ;> bc

and2

ac 22 ;> ca [A.M. > G.M.]

a2+ b2> 2ab ; b2+ c2> 2bc ; c2+ a2> 2ca ;

.a2+ b2+ b2+ c2+ c2+ a2> 2 (ab + bc + ca)

.a2+ b2+ c2> ab + bc + caab + bc + ca < a2+ b2+ c2 ..(i)In

8/10/2019 AITS-6

18/21


x2+ 8x 6x 48 = 0x(x + 8) 6(x + 8) = 0(x + 8) (x 6) = 0x = 6; hence a = 13, b = 15, c = 14

16. Let O be the centre of the circle and P be the root of the perpendicular from C to MN.Then OM is perpendicular to AB , ON is perpendicular to AD. Hence OM = ON = radius of the circle.so AMON is a square

=MNC =2

1=MON = 45

=CMP + =CNP = 135 = =CMP + =CMB= =CNP + =CNDHence=CNP ==CMB and =CMP ==CNDHence in

8/10/2019 AITS-6

19/21


18.

A

Qz

B C x

YR

P

h2

h1

h3

Let h1, h

2, h

3be the length of 1sAP, BQ, CR respectively from A, B, C on the transersal

8/10/2019 AITS-6

20/21

8/10/2019 AITS-6

21/21

SOL IJSOSTAGE I MOCKTEST 4 PAGE# 9

52.

d1000

)1711000(342

171m

:;

:$ = 0.429 1.4 = 0.47

m =1342

171

:= 0.5

! M = 0.1853. Mol. wt. of (CH2O)n= 30 2 = 60

! n = 230

60$

Empirical formula wt. (CH2O) = 30

54. m =)18052.11500(60

100018

,:::

= 0.19

55. mM of AgNO3= 0.1 V

mM of NaCl = 0.2 V! mM of NO3

= 0.1 V and total V = 2V

! [NO3] =

V2

V1.0 := 0.05

56. S atom in SF6in sp3d2-hybridized state and shows octahedral shape

57. N /N or N2has 1Aand 2B-bonds.

59. Fusion involves joining of two lighter nuclei.

60. urms

=M

RT3=

M

140R3 :at 140 K

uCrms

=M

560R3 :at 560 K

uCrms

= 2 urms

.

Documents

AITS-6