AITS-5

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Space For Rough Work

IJSO STAGE-I _MOCK TEST-5_PAGE # 1

1. In the adjoining figure O is the centre of the circle.!AOD = 120. If the radius of the circle be rthen find

the sum of the areas of the quadrilateral AODP and OBQC :

(A) 2

3

r

2

(B) 3 3 r

2

(C)

2

r3 (D) None of these

2. In the given figureCD

BD=

4

3 and AE = 6BE, then

AF

CF=

(A) 2/9 (B) 4/6 (C) 3/8 (D) 5/9

3. The set of integers n for which n2+ 19n + 92 is a square

(A) 8, 11 (B) 9, 11 (C) 7, 11 (D) 7, 9

4. If a, b, c are in continued proportion, the expression22

22

cbcb

baba

""

""can be simplified to :

(A) ba

ca

"

"

(B) c

a

(C) a

c

(D) b

ca#

5. At a point, the angle of elevation of a tower is such that its tangent is12

5. On walking 240 m nearer the

tower, the tangent of the angle of elevation becomes4

3. Find the height of the tower..

(A) 225 m (B) 240 m (C) 465 m (D) None of these

6. If sin q + cos q = m and sec q + cosec q = n, then n (m21) is equal to :

(A) 2m (B) 2n (C) mn (D) None of these

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7. In the figure given, $ABC, is a right isosceles triangle with right angle at C. CD is a parallel to AB and

BD = BA. The degree measure of !DBC equals :

AB

CD

(A) 10 (B) 15 (C) 20 (D) 25

8. The sides of a triangle are in the ratio 4 : 6 : 11. Which of the following words best described the triangle ?(A) obtuse (B) isosceles (C) acute (D) impossible

9. The number of triangles with any three of the lengths 1, 4, 6 and 8 cm, are :

(A) 4 (B) 2 (C) 1 (D) 0

10. If x and y are natural numbers, find the number pairs (x, y) for which x2y2= 31

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

11. Ifa

1+

b

1+

c

1=

cba

1

"", then which one of the following is not true:

(A) na

1+ nb

1+ nc

1= nnn cba

1

"", n is odd integer

(B) 3a

1+ 3b

1+ 3c

1= 333 cba

1

"",

(C) 2a

1+ 2b

1+ 2c

1= 222 cba

1

""

(D) None of these

12. If, x + y

1

= 1 and y

z

1

= 1, then the value of xyz is -

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

13. If x +x

1= 3, then the value of x6+ 6x

1is :

(A) 927 (B) 114 (C) 364 (D) 322

14. If the centroid and circumcentre of a triangle are (3, 3) and (6, 2) respectively, then the orthocentre is :

(A) (3, 5) (B) (3, 1) (C) (3, 1) (D) (9, 5)

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15. If A (2, 2), B (4, 4), C( 5, 8) are the vertices of any triangle, the length of median passes through C will be :

(A) 65 (B) 117 (C) 85 (D) 113

16. A circle is inscribed in an equilateral triangle of side 'a' cm. The area (in cm2) of a square inscribed in the

circle is :

(A) a2/6 (B) a2/3 (C) 3a2/4 (D) a2/12

17. The side lengths of trapezium are 4 3 , 4 3 , 4 3 and 2 4 3 . Its area is the ratio of two relatively prime

positive integers, m and n. The value of (m + n) is equal to :

(A) 5 (B) 7 (C) 9 (D) 13

18. The measures of length of the sides of a triangle are integers and that of its area is also an integer. One

side is 21 and the perimeter is 48. Find the measure of the shortest side.

(A) 10 (B) 13 (C) 24 (D) none of these

19. Let a, b, c be the positive numbers. The following system of equations in x, y and z.

2

2

2

2

2

2

c

z

b

y

a

x#" = 1;

2

2

2

2

2

2

c

z

b

y

a

x"# = 1;

2

2

2

2

2

2

c

z

b

y

a

x""# = 1, has

(A) No solution (B) Unique solution(C) Infinitely many solutions (D) Finitely many solutions

20. If

2 2

2 2

a b ab

cdc d

"%

", then find the value of

a b

a b

"in terms of c & d only :

(A)c d

cd

"(B)

cd

c d"(C)

c d

c d"(D)

c d

c d

"

21. A wire of resistance 4& is stretched to twice its original length. The resistance of the wire now is :

(A) 16& (B) 4& (C) 2& (D) 1&

22. There is a steady water flow in a horizontal tube in which one part has cross sectional area A1

and the

other part has cross sectional area A2. Assume that water is incompressible.

If A1/A

2= 16, the ratio of the speed u

1in part 1 and the speed u

2in part 2, i.e. u

1/u

2is :

(A)16

1(B) 4 (C)

4

1(D) 1

23. If a body loses half of its velocity on penetrating 3 cm in a wooden block. How much will it penetrate

more before coming to rest :

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

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24. Light ray AB incidents on a plane mirror XY at an angle of 50. The second plane mirror is placed is such

a way that the reflected ray BC from the mirror XY retraces its path. Angle of inclination of two mirrors will

be :

(A) 25 (B) 50 (C) 75 (D) 90

25. An iron ball of radius 0.3 cm falls through a column of oil of density 0.94 g cm3. It is found to attain a

terminal velocity of 0.5 cm/s. Determine the viscosity of the oil. Given that density of iron is 7.8 g/cm3

(A) 268.91 Poise (B) 200.5 Poise (C) 350 Poise (D) 970 Poise

26. The acceleration due to gravity on the surface of the moon is one sixth that on the surface of earth and the

diameter of the moon is one fourth of that of earth. The ratio of escape velocity on moon and earth will be :

(A)24

1(B)

16

2(C)

3

2(D) 24

27. An 80 kg person is parachuting and experiencing a downward acceleration of 2.5 m/s2 . The mass of the

parachute is 5.0 kg. The upward force on the open parachute from the air is :

(A) 620 N (B) 740 N (C) 800 N (D) 920 N

28. The velocity of sound in a gas at temperature 27 C is V then in the same gas its velocity will be 2V at

temperature:

(A) 200C (B) 207C (C) 927C (D) 127C

29. 4th harmonic of an organ pipe has frequency 33 Hz lesser than 5th harmonic of same organ pipe. Finddifference of wavelength (in m) in the given two cases (Assume velocity of sound in air = 330 m/s).

Neglect end correction.

(A) 0.5m (B) 6 m (C) 7 m (D) 8 m

30. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two

forces. The angle between the two forces is :

(A) 120 (B) 60 (C) 90 (D) 150

31. The time of flight of a projectile is 10s and range is 500m. Maximum height attained by it is- [g = 10 m/s2]

(A) 25m (B) 50m (C) 82m (D) 125m

32. A ball is thrown at an angle of 30 to the horizontal .It falls on the ground at a distance of 90 m. If the ball is

thrown with the same initial speed at an angle 30 to the vertical, it will fall on the ground at a distance of -

(A) 120 m (B) 27 m (C) 90 m (D) 30 m

33. Which of the following curve represent variation of density of water with temperature best :

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

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34. Starting at rest, a 10 kg object is acted upon by only one force as indicated in figure. Then the total

work done by the fo rce is

0

30

force(N)

10

1 2 3Time

(A) 90 J (B) 125 J (C) 245 J (D) 490 J

35. A bullet is fired in horizontal direction with velocity 8 m/s. In first second :

(A) It will fall 5m (B) It will fall 10m

(C) It will fall less than 1m (D) none of these

36. A particle has a constant kinetic energy. Which of the following quantities must also be constant.

(A) Position (B) Speed (C) velocity (D) momentum

37. Kinetic energy of a particle moving in a straight line varies with time as K = 4t2. The force acting on

the particle.

(A) is constant (B) is increasing

(C) is decreasing (D) first increases and then decreases

38. A particle initially at rest starts moving from point A on the surface of a fixed smooth hemisphere of

radius r as shown. The particle looses its contact with hemisphere at point B. C is centre of the

hemisphere. The equation relating (and )is &

(A) 3 sin (= 2 cos ) (B) 2 sin (= 3 cos ) (C) 3 sin )= 2 cos ( (D) 2 sin )= 3 cos (

39. The weight of a body is 120 N on the earth. If it is taken to the moon, its weight and mass will be about

(Take ge= 10 m/s2) :

(A) 120 N, 120 kg (B) 60 N, 12 kg (C) 20 N, 12 kg (D) 720 N, 120 kg

40. Two solids X and Y float on water, X floats with half of its volume submerged while Y floats with one-third

of its volume out of water. The densities of X and Y are in the ratio of

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

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41. The types of bonds present in nitrogen pentoxide are -

(A) Only ionic (B) Only covalent

(C) Covalent and coordinate both (D) Covalent and ionic both

42. In which of the following arrangements, the order is not according to the property indicated against it ?

(A) Al3+< Mg2+< Na+< F - Increasing ionic size

(B) B < C < N < O - Increasing first ionisation energy

(C) *< Br < F < Cl - Increasing electron affinity

(D) Li < Na < K < Rb - Increasing metallic radius

43. CaCO3+ 2HCl+,CaCl

2+ H

2O + CO

2

The mass of calcium chloride formed when 2.5g of calcium carbonate are dissolved in excess of hydro-

chloric acid is -

(A) 1.39 g (B) 2.78 g (C) 5.18 g (D) 17.8 g

44. On analysis a certain compound was found to contain iodine and oxygen in the ratio 254 g of iodine and

80 g of oxygen. The atomic mass of iodine is 127 and that of oxygen is 16. Which is the formula of the

compound ?

(A) IO (B) I2O (C) I

5O

2(D) I

2O

5

45. 0.7 g of Na2CO

3. xH

2O were dissovled in water and the volume was made to 100 mL. 20 mL of this solution

required 19.8 mL of N/10 HCl for complete neutralisation. The value of x is :(A) 7 (B) 3 (C) 2 (D) 5

46. The mass of electron moving with velocity of light is :

(A) 2me

(B) 3me

(C) Infinite (D) Zero.

47. Two electrons A and B in an atom have the following set of quantum numbers :

A : 3, 2, 2, + 1/2.

B : 3, 0, 0, +1/2.

Which statement is correct for A and B.

(A) A and B have same energy. (B) A has more energy than B.

(C) B has more energy than A. (D) A and B represent same electron.

48. The equation -= h/mv was deduced by :

(A) Heisenberg (B) de Broglie (C) Einstein (D) Planck.

49. Choose the correct code regarding Roasting process.

(I) It is the process of heating ore in air to obtain the oxide.

(II) It is an exothermic process.

(III) It is used for hydrated oxide and oxysalt ore.

(IV) It is used after the concentration of ore.

(A) I, II and III (B) I, II and IV (C) I, III and IV (D) I, II, III and IV

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50. In the extraction of copper, metal is formed in the Bassemer converter due to reaction :

(A) Cu2S + 2Cu

2O ,6Cu + SO

2(B) Cu

2S ,2Cu + S

(C) Fe + Cu2O ,2Cu + FeO (D) 2Cu

2O,4Cu + O

2

51. Which of the following refining piocess does not make a correct match with teh curde metal ?

(A) Distillation : zinc and mercury (B) Liquation : tin

(C) Van Arkel : Zirconium (D) Mond process : lead

52. The decomposition of KCIO3to KCI and O

2on heating is an example of:

(A) Intermolecular redox change (B) Intramolecular redox change(C) Disproportionation or auto redox change (D) None of the above

53. Equal volumes of H2and Cl

2are mixed. How will the volume of the mixture change after the reaction ?

(A) Unchanged (B) Reduced to half (C) Increases two fold (D) None of these

54. Consider the reactions

(i) 2CO(g) + 2H2O (g) 2CO

2(g) + 2H

2(g); Eqm. Constant = K

1

(ii) CH4(g) + H

2O(g) CO(g) + 3H

2(g); Eqm constant = K

2

(iii) CH4(g) + 2H

2O(g) CO

2(g) + 4H

2(g) ; Eqm. Constant = K

3

(A) K3=

2

1

K

K(B) K

3= 2

2

2

1

K

K(C) K

3= K

1K

2(D) K

3= 21 K.K

55. Pair of similar radiations is :

(A) (- and .- rays (B) )- and X - rays (C) (- and )- rays (D) .- and X - rays

56. ;HePbPo 4220682

21084 ", Pb belongs to IVA, thus Po belongs:

(A) II A (B) IV B (C) VI B (D) VI A

57. Which is a major hurdle in finding ways to properly harness nuclear fusion energy on a commercial scale

in an effort to solve nuclear crisis ?(A) Purification of raw materials

(B) Finding safe ways to disposing off the waste products

(C) To maintain high temperature for the reaction

(D) Non-availability of skilled scientists

58. The pH of a solution is 6.0. To this solution sufficient acid is added to decrease the pH to 3.0. The

increase in hydrogen ion concentration is -

(A) 100 times (B) 10 times (C) 1000 times (D) 2.5 times

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59. When pure water is exposed to air containing (oxides CO2, SO

3etc.) pH of pure water will-

(A) increase (B) decrease

(C) not change (D) may increase or decrease

60. A person has as many as notes as number of oxygen atoms in 24.8 g Na2S

2O

3. 5H

2O (mol. wt. = 248.0).

A note counting machine counts 60 million notes per day. How many day would be taken to count these

notes?

(A) 1017 (B) 1010 (C) 1015 (D) 1012

61. Syngamy refers to

(A) fusion of one of the sperms with secondary nucleus(B) fusion of one sperm with the egg(C) fusion of one of the sperm with an egg and the other with secondary nucleus

(D) fusion of one of the sperm with synergids

62. In case of fungi, which type of asexual reproduction takes place

(A) Fission (B) Budding(C) Spore formation (D) None of these are correct

63. At the time of entering into an ovule, the pollen tube has

(A) one gamete nucleus (B) two male nuclei (C) three male nuclei (D) four male gamete

64. Composite fish culture increases the fish yield from a pond by growing a number of fish species in such

a way that they dont compete for(A) air. (B) food. (C) sunlight. (D) water

65. The chemical substance with water proof quality in desert plants is :

(A) cutin. (B) suberin. (C) lignin. (D) fat.

66. Cartilage makes up virtually the entire skeleton in

(A) chondrichthyes. (B) amphibia (C) aves. (D) mammalia.

67. The main inorganic component of bone is

(A) hydroxyapatite. (B) magnesium. (C) calcium chloride. (D) phosphate.

68. Which is true about excretion ?(A) 90% water and Na+of glomerular filtrate are absorbed

(B) Glucose is reabsorbed in proximal convoluted tubule

(C) Water is reabsorbed in proximal convoluted tubule

(D) 99% of water and glucose in the glomerular filtrate are reabsorbed

69. Which of the following parts of kidney contains lowest concentration of urea ?

(A) Loop of Henle (B) Branches of renal vein

(C) Bowmans capsule (D) Glomerulus

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70. Bats differ from birds in presence of :

(A) homeothermy. (B) four-chambered heart

(C) tracheae. (D) diaphragm.

71. Antibiotics help in treatment of diseases caused by

(A) viruses, by rendering them ineffective.

(B) protozoan, as they are able to survive in presence of antibiotics.

(C) bacteria, as the biochemical pathways important for them are blocked.

(D) worms, as they are present inside the body.

72. What will be the shape of a metacentric chromosome during anaphase ?(A) V-shape (B) L-shape (C) J-shape (D) *-shape

73. Chiasmata are formed during

(A) zygotene (B) pachytene (C) diplotene (D) leptotene

74. Chromosome number is restored by

(A) meiosis (B) mitosis (C) crossing over (D) interphase

75. The causative organism of sleeping sickness is

(A) Leishmania. (B) Trypanosoma. (C) Ascaris. (D) Staphylococci.

76. The correct order of evolutionary advancement among the plants is

(A) spirogyra,diatom hornwort,fern

(B) blue green alga,liverwort ,fern,seed bearing plant

(C) liverwort ,cyanobacterium ,moss,gymnosperm

(D) red alga ,fern,moss,liverwort

77. The graph below shows the relation between influence of light intensity and CO2concentration on the rate

of photosynthesis of Chlorella

High lightintensity

Low light

intensity

CO , Conc. (Volume % in air)2

rateo

fphotosynthesis

at25

C0

Which one of the following statements explains the diagram correctly ?

(A) At low light intensity, the light dependent reaction is rate limiting but at high light intensity CO2is rate

limiting

(B) The number of chlorophyll molecules limits the rate of photosynthesis

(C) Photosynthesis is independent of light intensity provided there is no total darkness

(D) Chlorophyll responds equally to light intensities and CO2concentrations thereby limiting the rate of

photosynthesis

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78. The important condition for the dark reaction of photosynthesis is

(A) absence of light (B) presence of chlorophyll

(C) presence of carbon dioxide (D) presence of O2

79. The combination of the following structures possessing a single set of genome is:

i. Ovary ii. Anther iii. Egg iv. Zygote

v. sepal vi. Petalvii. Pollen

(A) i,ii, iv, and vi (B) ii, iii, iv and vii (C) only iii and vii (D) only ii, iii and vii

80. Green fuel

means(A) fuel obtained from plant leaves (B) green coloured fuel

(C) chemicals used for the growth of plants (D) fuel obtained from plastic waste

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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: 5-10-2014 Max. Marks : 240

PCCP Head Office:

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

Contact. No. :+91-0744-2434727, 8824078330, Fax : 0744-2427146

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

ALL INDIA IJSO(STAGE-I) TEST SERIES

MOCK TEST PAPER # 5
http://www.pccp.resonance.ac.in/http://www.pccp.resonance.ac.in/mailto:[email protected]:[email protected]://www.pccp.resonance.ac.in/

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NSWER KEY

HINTS & SOLUTIONS

ALL INDIA IJSO(STAGE-I) TEST SERIES

MOCK TEST PAPER # 5

2. 3x 4x

M

B

5y

D

E

A

C

F

y

const : Draw BM || AE

so !BME ~ !CFD

or CF = 4BM/3

Now !AEF ~ !BEM

soAF

BM=

AE

BE

AF

BM=

y6

y

AF = BM "6

AF = BM "6 ....(ii)

AF

CF=

9

2equation (i) and (ii)

3. n2+ 19n + 92 = m2 m is non-negative

n2+ 19n + 92 m2= 0

n =2

1 #$

%&'( )*) 7m419 2

therefore 4m27 is a square

4m27 = p2

(2m + p) (2m p) = 7

by solving we get p +N

m = 2

n2+ 19n + 92 = 4

n2+ 19n + 88 = 0

(n + 8) (n + 11) = 0

n = 8, 11

4. a, b, c are in continued proportion.

,b

a=

c

b= k

a = bk, b = ck and a = ck2

22

22

cbcb

baba

----

=2222

2222

ckckc

bkbkb

--

--

=)1kk(c

)1kk(b22

22

--

--

= 2

2

c

b= k2 =

c

a.

5.

tan .=12

5, tan /=

4

3

Let the height of tower be h.

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

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

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

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

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

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

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

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

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In !ABC

tan /=x

h

x = /tanh

In !ABD

tan .=240xh

-

x + 240 =.tan

h

/tan

h+ 240 =

.tan

h

240 = h 001

2334

5

/). tan

1

tan

1

h = .)/./"

tantan

tantan240

h =

12

5

4

312

5

4

3240

)

""

[Substituting the value of tan .and tan /]

h =

12/4

75= 225 m

So, the height of tower = 225 m.

6. L.H.S. n(m21)

= (sec.+ cosec .)[(sin.+ cos.)2 1]

= 01

234

5.-. sin

1

cos

1(sin2.+ cos2.+ 2sin.cos.1)

= 012345 ..

.-.

cossin

sincos(1 + 2sin.cos.1)

=..

.-.

cossin

)sin(cos( 2sin.cos .)

= 2 (sin.+ cos.)= 2m

7.

A B

CD

E

Given in the following figure AB || DC

AB = BD & AC = CB

and 6ACB = 90now, draw DE 7AB and join BD

Let AC = BC = a

then AB = 2a = BD

now ar (!ADB) = ar(!ABC) (same base and

between same 11rt.)

82

1 AB DE =

2

1 AC ABAB

8 DE =2a

a2

8 DE =2

a

now in !DEB

sin(EBD) =BD

DE

sin.=2/a

2/a

8 sin.=2

1

8 sin.= sin 30

8 .= 30So, 6DBC = 45 30

6DBC = 15.

8. Sides of triangle are in the ratio 4 : 6 : 11.

But this type of triangle is impossible.

Because, 4 + 6 < 11.

Sum of two sides of triangle must be greater

than the third side.

9. Possible length of triangle are 4, 6, 8 so

required number of triangle is 1.

10. If x2

y2

= 31, then (x + y) (x

y) = 1 31Since x, y +N, 31 being prime, x + y = 31,

x y = 1 yielding x = 16 ; y = 15

12. x +y

1= 1

y z

1= 1

x = 1 y

1=

y

1y )

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y = 1 +z

1=

z

1z -

x =

z

1z

1z

1z

-

)-

=1z

1

-

xyz =1z

1

-"

z

1z -"z = 1

13.

2

x

1x 01

234

5- = 32

x2+ 2x

1+ 2 = 9

x2+ 2x

1= 7

3

2

2

x

1x 01

234

5- = x6+ 6x

1+ 3 0

1

234

5-

22

x

1x

73= x6+ 6x

1+ 3 (7)

343 21 = x6+ 6x

1

322

x = 140

14. Circumcentre O, Centriod G and orthocentre Oof

a triangle ABC are collinear such that G divides

OO in the ratio 2 : 1

O' O

(6, 2)

G

(x, y)

(3, 3)

2 1

,3 =3

x12- 8x = 3

And 3 =3

y4 -8 y = 5

So, orthocentre is (3, 5).

15.

D (Mid point of AB) = 01

234

5 ))

2

42,

2

42= (1,

1)

Length of Median CD = 22 )18()15( -)--

= 4936 - = 85

16. O

A

CDB

a

AD =2

3a

OD =3

1

2

3a

so diameter of circle = diagonal of square

= 2 "23

3

""a =

3

1a

Diagonal of square = 2 side of square

side of square =6

a

area of square =6

a2

17.

D CX

A

X

F X E B

X

X2

X2

DF = 22 AFAD

=4

xx

22

=2

x3

Area of trapezium =2

1(3x)

2

x3

=4

33

2

x2

=4

33: ;24 3 = 4

9

,m + n = 9 + 4 = 13.

8/10/2019 AITS-5

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18. Let a, b be the other two sides. then a + b = 27

s =2

cba -- = 24 ;

Area = )cs)(bs)(as(s )))

= )2124)(3a)(a24(24 ))) = )a24)(3a(72 ))

Now 72(a 3)(24 a) must be a perfect square.

If 'a' is the shortest side , then a < 13. Thus a

= 10 is the only possible value among the given

values satisfying the conditions

thus , of a = 10, area = 731424 """ = 84

which is an integer. The measure of the short-

est side is 10

20. 2

2

2

2

2

2

c

z

b

y

a

x)- = 1 ...(i)

2

2

2

2

2

2

c

z

b

y

a

x

-) = 1 ...(ii)

2

2

2

2

2

2

c

z

b

y

a

x--) = 1 ...(iii)

Adding Eq. (i), (ii) and (iii), we have

2

2

2

2

2

2

c

z

b

y

a

x-- = 3 ...(iv)

, 2

2

a

x= 1 8 x = * a

2

2

b

y= 1 8 y = * b

2

2

cz = 1 8 z = * c

Hence (D) is correct.

20.

2 2

2 2

a b ab

cdc d

-=-

ab2

ba 22 -=

cd2

dc 22 -[!By C & D]

ab2ba

ab2ba22

22

)-

--=

cd2dc

cd2dc22

22

)-

--

2

2

)ba(

)ba(

)-

= 2

2

)dc(

)dc(

--

ba

ba

)-

=dc

dc

)-

.

21. Given : Resistance, R = 4 >

Let "& A are the initial length and area of the

wire respectively. If ? is the specific resitance of

the wire then,

R =A

"?.........(i)

Let after stretching the length, the area and re-

sistance becomes, "@, A@and R@respectively.

R@ =@

@?

A

".........(ii)

We know that "@ = 2"

Also A " = A@"@

@AA

= 2

Divide equation (ii) by equation (i)

@"

@=

@

A

A

R

R

"

"= 2 2

8 R@= 4 2 2 = 16>

22. A1u

1= A

2u

28

16

1

A

A

u

u

1

2

2

1 ==

23. Suppose inital velocity is u

From third equation of motion

)03.0(a2u2

u 22

-=01

234

5

0.06a =2

22

2

u2

25

24.0

u3au

4

u)=)=8)

Final velocity of ball is zero

So, from third equation of motion

v2= u2+ 2ax

(0)2= u22(25/2) u2x

x =25

1m = 4 cm

So after 3 cm it will penetrate, 4 3 = 1 cm

24. 50

N

X40

A

B

C

50

Y

Ray BC retraces its path when A fall on second

mirror perpendicularly, so as per f igure L BYC

will be euqal to 50.

25. A= g)(v

r

9

2 2B)?

A=: ; : ;

5.09

98094.08.73.02 2

"")""

= 268.9 poise.

8/10/2019 AITS-5

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26. Given : ge= 6 g

m

Re= 4 R

m

On the surface of earth escape velocity,

Ve= eeRg2

Ve= mm R4g6.2 ""

Ve= mmRg224" 8 Ve= 24 Vm

(Vm= mmRg2 is the escape velocity at the

moon)

24

1

V

V

e

m =

27. Net mass = 80 + 5 = 85 kg

downword acceleration, a = 2.5 m/s2

So, 85 g f = 85 a

F = 85 (g a)

85g

F

aF = 85 (9.8 2.5)

F = 620 N

28. In a gas,

V =M

RTC8 V a T

8V2

V=

T

3008 T = 300 4 = 1200 K

= 927C

29."2

v4=

"2

v533

"2

v= 33

2"= 10

"= 5m.

34. Change in velocity = mass

graphTFunderarea

=10

)10(60-= 5 m/s

WF= !K.E. =

2

1(10) 52 = 125 J

35. Sy= u

yt +

2

1gt2

at t = 0, uy= 0

Sy= 0 +

2

1 10 12

, Sy= 5 m

36. K.E. =2

1mv2 where V is the speed of the

particle.

37.22 t.4mv

2

1= 8

dt

dvv2m

2

1 = 4 2t

8m.dt

dv=

v

t8= m8

m

t8

t8

2=

38. Let v be the speed of particle at B, just when

it is about to loose contact.

From application of Newton's second law to

the particle normal to the spherical surface.

r

mv 2= mg sin D

.......... (1)

Applying conservation of energy as the block

moves from A to B..

2

1mv2= mg (r cos Er sin D)

.......... (2)

Solving 1 and 2 we get

3 sin D= 2 cos E

39. Weight depends on the acceleration due to

gravity,

! gm= g

e/6

so, weight of body on the moon will be =6

120 =

20 N

Mass of body does not depends on value of g

so, m =eg

F=

10

120= 12 kg

Its value remains same on the surface of moon. ]

8/10/2019 AITS-5

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40. If V and D are the volume and density of solid X

respectively. Let V@ and D@ are the volume and

density of solid Y respectively

By law of floatation,

Weight of solid X = Weight of water displaced

Vdg =2

1V 1g

D =2

1g/cc

Weight of solid Y = Weight of water dispalced

V@ D@g = 01

234

5)

3

11 V 1g

D@=3

2g/cc

4

3

3/2

2/1

YofDensity

XofDensity==

8 3 : 4

41. Nitrogen pentoxide contains both covalent and

co-ordinate bonds.The structure of nitrogen pen-

toxide is -

O = N O N = O

O O

42. Correct order of increasing first I.E. of B, C, N

and O is - B < C < O < N.

43. CaCO3+ 2HClFGCaCl

2+ H

2O + CO

2

100 g 111 g

111 g of CaCl2is obtained from = 100 g of CaCO

3

2.5 g of CaCl2is obtained from =

111

100 2.5 of CaCO

3

=111

250= 2.78 g

44. g atom of I2= 2

127

254=

g atom of oxygen =16

80= 5

, Compound is I2O5.

45. Meq. of Na2CO

3. x H

2O in 20mL = 19.8

10

1

, Meq. of Na2CO3.xH2O in 100 mL = 19.8

10

1 5

, 1000E

w" = 19.8

10

1 5

or2/M

7.0 1000 =

2

8.19

, M = 141.41

, 23 2 + 12 + 3 16 + 18 x = 141.41

, x = 2

46. me=

2

e

c

v1

m

01

234

5)

47. For A, (n + H) = 5 Thus, larger is value of (n+H)

For B, (n + H) = 3 more is energy level.

48. Follow de Broglie equation.

52. 2KCIO3

FGF 2KCI + 3O2

. An intramolecular

redox change is one in which one element of a

compound is oxidised (O2to O20) and one ele-

ment is reduced (CI5+to CI1).

53. H2+ Cl

2 FGF 2HCl; Moles before and after

the reaction are same.

55. Both are electromagnetic waves.

56.. Emission of an E-particle changes parent

elements position two places to the left of it.

57. Nuclear fusion occurs at 1.2 107K tempera-

ture.

58. Initial pH of the solution = 6

,Initial [H+] of the solution = 1 10-6

On diluting the solution three times [H+] be-

comes = 1 10-3

,Final pH of the solution

=3

6

-3

10101

101=

"

")

60. No. of notes =248

8.2410023.6 23

""

= 6.023 1022

Days for counting = 6

22

1060

10023.6

"

"= 1015

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