Sample Paper for One Year Course

7/30/2019 Sample Paper for One Year Course

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Sample Paper For One Year Course(+1 Studying Students Moving To +2)GENERAL APTITUDE (I.Q.)

1. Find the missing number

(A) 24 (B) 25 (C) 23 (D) 31

2. A person spends 40% of his salary on food items and 1/3rd

of the remaining on transport. After spending

on food items and transport, he spends 50% of the balance on other items and saves Rs. 450/- per month

His monthly salary is

(A) Rs.1125/- (B) Rs.1575/- (C) Rs.2250/- (D) Rs.4500/-

3. 60% of the students in a school are boys. If the number of girl students in the school is 300, then the

number of boys is :

(A) 300 (B) 450 (C) 500 (D) 750

4. If ENGLAND is written as 1234526 and FRANCE is written as 785291, how is GREECE coded ?

(A) 381171 (B) 381191 (C) 832252 (D) 835545

Directions for Q.5 Q.7

A, B, C, D, E and F are a group of friends. There are two housewives, one professor, one engineer, one

accountant and one lawyer in the group. The lawyer is married to D, who is a housewife. No woman in the

group is either an engineer or an accountant C, the accountant, is married to F, who is a professor. A is married

to a housewife. E is not a housewife.

5. How many members of the group are males ?

(A) 2 (B) 3 (C) 4 (D) Cannot be determined

6. What is Es profession ?

(A) Engineer (B) Lawyer (C) Professor (D) Accountant

36

2649

64

25

9

2181

25

16

25

?64

144

36


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7. Which of the following is one of the married couples ?

(A) A & B (B) B & E (C) D & E (D) A & D

Directions (Q.8 & Q.9) : Sometimes we are given figures showing the same die in various positions. After

observing these figures, we have to find the number opposite a given number on the die. The procedure to be

adopted for solving such problems, will be clear from the following examples :

Example: A die is thrown four times and its four different positions are given below. Find the number on the

face opposite the face showing 2.

(A) 3 (B) 4 (C) 5 (D) 6

Solution :

Here, the number 2 appears in three dice, namely (i), (ii) and (iv). In these dice, we observe that the numbers 2,

4, 1 and 6 appear adjacent to 3. So, none of these numbers can be present opposite 2. The only number left is 5.

The answer is (c)

8.

What number is opposite 4 ?

(A) 1 (B) 2 (C) 5 (D) 6

9.

Which number is opposite 3 ?

(A) 1 (B) 2 (C) 4 (D) 6


3/15

Directions (Q.10 & Q.11) : Find the missing character in each of the following questions :

10.

(A) 72

(B) 70

(C) 68

(D) 66

11.

(A) 10

(B) 11

(C) 12

(D) 13

12. The expression 2 +22

1

22

12

equals :

(A) 2 (B) 2 2 (C) 2 + 2 (D) 2 2

Directions (Q.13 & Q.14) : Question 13 & 14 are based on the following figure.

13. How many squares are there in adjoining figure ?

(A) 13 (B) 15 (C) 16 (D) 17

14. How many minimum colours are required if the figure is to be coloured such that no two adjacent sides

have the same colour ?

(A) 2 (B) 3 (C) 4 (D) 5

15. If 2 < x < 4 and 1 < y < 3, then find the ratio of the upper limit for x + y and the lower limit of xy.

(A) 6 (B) 7 (C) 8 (D) None of these

?

7

16

34142

286

13

8

5?

1

2

3

4


4/15

16. The simplest form of 1

a1

a1

1

is

(A) a if a 0 (B) 1 (C) a if a 1 (D) none of these

17. If 102y = 25, then 10

y equals :

(A) 51 (B)

6251 (C)

501 (D)

51

18. In our number system the base is ten. If the base were changed to four you would count as follows :

1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, . The twentieth number would be :

(A) 20 (B) 38 (C) 44 (D) none of these

19. Raj starts from his office facing west and walks 100 metres straight then takes a right turn and walks 100

metres. Further he takes a left turn and walks 50 metres. In which direction is Raj now form the starting

point ?

(A) NorthEast (B) SouthWest (C) North (D) NorthWest

20. The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is

subtracted form the denominator, it becomes 2/3, the fraction is

(A) 5/6 (B) 6/5 (C) 3/8 (D) 8/3

PHYSICS

21. A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a

moving train A records a frequency 5.5 kHz while the train approaches the siren. During his return

journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The

ratio of the velocity of train B to that of train A is

(A)256

242(B) 2 (C)

6

5(D)

6

11

22. Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a

frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in thedirection of the lighter block. The velocity of the centre of mass is

(A) 30 m/s (B) 20 m/s (C) 10 m/s (D) 5 m/s

23. A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time

period of a spy satellite orbiting a few hundred kilometers above the earths surface (Rearth = 6400 km)

will approximately be

(A) 1/2 hr (B) 1 hr (C) 2 hr (D) 4 hr


5/15

24. An ideal spring with spring constant k is hung form the ceiling and a block of mass M is attached to its

lower end. The mass is released with the spring initially unstretched. Then the maximum extension in

the spring is

(A)k

Mg4(B)

k

Mg2(C)

k

Mg(D)

k2

Mg

25. An ideal gas is taken through the cycle A B C A, as shown in the figure. If the net heat is

supplied to the gas in the cycle is 5 J, the work done by the gas in theprocess C A is(A) 5 J (B) 10 J

(C) 15 J (D) 20 J

26. Which of the following graphs correctly represents the variation of =

V

)dP/dV(with P for an ideal gas at constant temperature ?

(A) (B)

(C) (D)

27. A wooden block, with a coin placed on its top, floats in water as shown in figure. The distances l and hare shown there. After some time the coin falls into the water. Then

(A) l decreases and h increases

(B) l increases and h decreases

(C) both l and h increase

(D) both l and h decrease

28. A simple pendulum is oscillating without damping. When the displacement of the bob is less than

maximum, its acceleration vector a

is correctly shown in

(A) (B)

(C) (D)


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29. A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping

throughout these motions). The directions of the frictional force acting on the cylinder are :

(A) up the incline while ascending and down the incline while descending

(B) up the incline while ascending as well as descending

(C) down the incline while ascending and up the incline while descending

(D) down the incline while ascending as well as descending

30. When a block of iron floats in mercury at 0C, a fraction k1 of its volume submerged, while at the temp

60C, a fraction k2 is seen to be submerged, the coeff. of volume expansion of iron is VFe & that of

mercury is VHg then the ratio k1/ k2 can be expressed as :

(A)Hg

Fe

601

601

(B)

Hg

Fe

601

601

(C)

Hg

Fe

601

601

(D)

Fe

Hg

601

601

31. Three rods made of same material and having same crosssection have been joined as shown in fig

Each rod is of same length. The temp. of the function will be

(A) 45C (B) 60C (C) 30C (D) 20C

32. A small block is shot into each of the four tracks as shown below. Each of the track rises to the same

height. The speed with which the block enters the track is the same in all cases. At the highest point of

the track, the normal reaction is maximum in :

(A) (B)

(C) (D)

33. A simple pendulum has a time period T1 when on earths surface and T2 when taken to a height R above

the earths surface, where R is the radius of earth. The value of T2/T1 is

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

34. Two particles of masses m1 and m2 in projectile motion have velocities 1v and 2v respectively at time

t = 0. They collide at time t0. Their velocities become

1v and

2v at time 2t0 while still moving in air

The value of | (m1

1v + m2

2v )(m1

1v + m2

2v ) | is :

(A) Zero (B) (m1 + m2) gt0 (C) 2(m1 + m2)gt0 (D)2

1(m1 + m2)gt0


7/15

35. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to

rotate about a line perpendicular to its plane and passing through the center of the original disc. Its

moment of inertia about the axis of rotation is :

(A) 1/2 MR2

(B) 1/4 MR2

(C) 1/8 MR2

(D) 2 MR2

36. The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the

displacement of the wire is y1 =A sin (x/L) sin t and energy is E1 and in another experiment its

displacement is y2 = sin (2x/L) sin 2t and energy is E2. Then :

(A) E2 = E1 (B) E2 = 2E1 (C) E2 = 4E1 (D) E2 = 16E1

37. Two pulses in a stretched string, whose centres are initially 8 cm apart, are moving towards each other as

shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds the total energy of the pulses will be :

(A) zero (B) purely kinetic

(C) purely potential (D) partly kinetic and partly potential

38. An insect crawls up a hemispherical surface very slowly (see fig.). The coefficient of friction between

the insect and surface is 1/3. If the line joining the center of the hemispherical surface to the insect

makes an angle with the vertical, the maximum possible value of is given by :

(A) cot = 3 (B) tan = 3 (C) sec = 3 (D) cosec = 3

39. A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as

shown in figure. The force on the pulley by the clamp is given by

(A) 2 Mg (B) 2 mg (C) gm)mM( 22 (D) gM)mM( 22


8/15

40. An aluminium rod (length l1 and coefficient of linear expansion A) and a steel rod (length l2 and

coefficient of linear expansion B) are joined together. If the length of each rod increases by the same

amount when their temperatures are raised by tC, then21

1

ll

l

is

(A)s

A

(B)

A

s

(C)

AA

s

(D)

As

A

41. A particle is performing an uniform circular motion on a horizontal place. Its angular momentum is

constant about

(A) origin at centre of circle (B) point on circumference of circle

(C) point outside the circle (D) point inside the circle

42. A rod of negligible mass of length l connected with two identical masses at both ends, placed on

horizontal surface (frictionless). A sudden impulse of Mv is given (as shown in figure) calculate the

angular velocity of rod.

(A) 4v/l (B) v/l (C) 2v/l (D) 3v/l

43. The adjacent graph shows the extension (l) of a wire of length I m suspended form the top of a roof at one

end and with a load W connected to the other end. Area of cross section of wire is 106 m2. find Y is SI units

(A) 2 106 N/m2 (B) 5 106 N/m2 (C) 2 1011 N/m2 (D) 5 1011

44. For a particle executing simple harmonic motion the displacement x is given by x = A sin t. Identify

the graph which represents the variation of potential energy (PE) as a function of time t and

displacement x.

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


9/15

45. The graph, shown in the diagram, represents the variation of temperature (T) of the bodies, x and y

having same surface area, with time (t) due to the emission of radiation. Find the correct relation

between the emissivity and absorptivity power of the two bodies. :

(A) Ex > Ey and ax < ay (B) Ex < Ey and ax > ay

(C) Ex > Ey and ax > ay (D) Ex < Ey and ax < ay

CHEMISTRY

46. If the nitrogen atom had electronic configuration 1s7, it would have energy lower than that of the normal

ground state configuration 1s

2

, 2s

2

2p

3

because the electrons would be closer to the nucleus. Yet 1s

7

isnot observed. It violates :

(A) Heisenberg uncertainty principle (B) Hunds rule

(C) Paulis exclusion principle (D) Bohr postulate of stationary orbits

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

(A) I < Br < F < Cl (increasing electron gain enthalpy with negative sign)

(B) Li < Na < K < Rb (increasing metallic radius)

(C) Al+ 3

< Mg+ 2

< Na+

< F

(increasing ionic size)

(D) B < C < N < O (increasing first I.E.)

48. The molecular shapes of SF4, CF4 and XeF4 are :

(A) different with 0, 1 and 2 lone pairs of electrons on central atom respectively

(B) different with 1, 0 and 2 lone pair of electrons on central atom

(C) same with 2, 0 and 1 lone pairs (D) same with 1 lone pair in each case

49. Specify the Coordination geometry around and hybridization of N and B atoms in a 1 : 1 complex of

BF3 and NH3 :

(A) N : Tetrahedral, sp3

; B : Tetrahedral, sp3

(B) N : Pyramidal, sp3

; B : Pyramidal, sp3

(C) N : Pyramidal, sp3 ; B : Planar, sp2 (D) N : Pyramidal, sp3 ; B : Tetrahedral, sp3

50. Van der Waals equation for n moles of a gas is :

(A)

2v

anP (vnb) = RT (B)

2

2

v

anP (vnb) = nRT

(C)

2

2

v

anP (vb) = nRT (D)

2v

aP (vb) = nRT


10/15

51. NH3 and HCl gas are introduced simultaneously from the two ends of a long tube. A white ring of

NH4Cl appears first :

(A) Through out the tube (B) Nearer the NH3 end

(C) Nearer the HCl end (D) At the centre of the tube

52. Two moles of an ideal gas expand isothermally and reversibly from 1 litre to 10 litre at 300 K.

The enthalpy change (in kJ) for the process is :

(A) 11.4 kJ (B) 11.4 kJ (C) 0 kJ (D) 4.8 kJ

53. Consider the equilibrium state of the following reaction carried out in a closed container :

N2O4 (g) 2 NO2 (g)

At constant temperature, the volume of the reaction vessel is halved. For this change, which of the

following statements is correct about equilibrium constant (Kp) and degree of dissociation () :

(A) Neither Kp nor changes (B) Kp and both one changed

(C) Kp changes but does not change (D) Kp does not change but changes

54. A schematic plot of ln Keq versus inverse of temperature for a reactions is shown below :

The reaction must be :

(A) one with negligible enthalpy change

(B) highly spontaneous at ordinary temperature

(C) exothermic

(D) endothermic

55. The solubility of A2X3 is y mol dm3

. It solubility product is :

(A) 6y4 (B) 64y4 (C) 36y5 (D) 108y5

56. The correct sequence in order of increasing pH of 0.1 M solution of NaCl (I), NH4Cl (II), NaCN (III)

and HCl (IV) will be :

(A) I < II < III < IV (B) III < II < I < IV

(C) IV < II < I < III (D) IV < I < II < III

57. The volume strength of 1.5 N H2O2 :

(A) 4.8 (B) 8.4 (C) 3.0 (D) 8.0

58. In a compound, C, H and N atoms are present in 9 : 1 : 3.5 by weight. If the molecular weight of the

compound is 108, then the molecular formula of the compound is :

(A) C9H12N3 (B) C3H4N (C) C2H6N2 (D) C6H8N2


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59. [A]Catalyst

s'Lindlar CH3C CH33NH.liq

inNa [B]. [A] and [B] are respectively :

(A) cis, trans2Butene (B) both trans2Butene

(C) trans, cis2Butene (D) both cis2butene

60. An alkene having molecular formula C9H18 on ozonolysis gives 2,2dimethylpropanal and 2butanone

The alkene is :

(A) 2,2,4Trimethyl3hexane (B) 2,2,6Trimethyl3hexane

(C) 2,3,4Trimethyl2hexane (D) 2,3,4Trimethyl2hexene

61. PhC CCH3 H/2Hg A, A is :

(A)

H3C

Ph

O

(B)

H3C

Ph

O (C)

H3C

Ph

OH

(D)

H3C

Ph

OH

62. Which of the following compounds is not aromatic ?

(A)

+

(B)

(C)

+

(D)

N

63. The number of isomers for the compound with molecular formula C 2BrClFI is :

(A) 3 (B) 4 (C) 5 (D) 6

64. Identify the correct order of reactivity in electrophilic substitution reactions of the following compounds

1 2

CH 3

3

Cl

4

NO 2

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

65. Propyne and propene can be distinguished by :

(A) conc. H2SO4 (B) Br2 in CCl4 (C) dil. H2SO4 (D) AgNO3 in ammonia

66. The intermediate during the addition of HCl to propene in the presence of peroxide is :

(A) CH3CH ClHC 2 (B) CH3 3HCHC

(C) CH3CH2 2HC

(D) CH3CH2 2HC

67. Lithium is strongest reducing agent among alkali metals due to which of the following factor ?

(A) Ionization energy (B) Electron affinity

(C) Hydration energy (D) Lattice energy


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68. Which has lowest thermal stability ?

(A) Li2CO3 (B) Na2CO3 (C) K2CO3 (D) Rb2CO3

69. To neutralize completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H 3PO3), the volume of

0.1 M aqueous KOH solution required is :

(A) 60 mL (B) 20 mL (C) 40 mL (D) 10 mL

70. If a molecule MX3 has zero dipole moment the sigma bonding orbitals used by M (at. no. < 21) is :

(A) Pure p (B) sphybrid (C) sp2hybrid (D) sp

3hybrid

MATHEMATICS

71. Which of the following is correct ?

(A) 2 + 3i > 1 + 4i (B) 6 + 2i > 3 + 3i (C) 2 + 8i > 5 + 7i (D) none of these

72. If z =3

2

i, then z

69is equal to

(A) i (B) i (C) 1 (D) 1

73.20

15

)i1(

)3i1(

+

20

15

)i1(

)3i1(

is equal to

(A) 32 (B) 64 (C) 64 (D) None of these

74. If x +

x

1= 1, then x2000 +

2000

x

1is equal to

(A) 1 (B) 1 (C) 0 (D) none of these

75. If x2

+ x + 1 = 0 then the numerical value of ;

2

x

1x

+

2

2

2

x

1x

+

2

3

3

x

1x

+

2

44

x

1x

+ .+

2

27

27

x

1x

=

(A) 54 (B) 36 (C) 27 (D) 18

76. The number of real solution of the equation x23|x| + 2 = 0 is

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

77. If the equation (a5) x2

+ 2 (a10) x + a + 10 = 0 has roots of the opposite sign, then

(A) a > 10 (B) 15 < a < 5 (C) 10 < a < 5 (D) none of these

78. The number of positive integral solutions of65

432

)7x2()5x(

)2x()4x3(x

0 is :

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


13/15

79. For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

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

80. A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms

occupying odd places, the common ratio will be

(A) 2 (B) 3 (C) 4 (D) 5

81. If a1, a2, a3,is an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225 then a1 + a2 + a3 + + a24 =

(A) 75 (B) 750 (C) 900 (D) 909

82. If ax3 + bx2 + cx + d is divisible by ax2 + c, then a, b, c, d are in

(A) AP (B) GP (C) HP (D) none of these

83. The number of common terms to the two sequences 17, 21, 25, ., 417 and 16, 21, 26, 466 is

(A) 21 (B) 19 (C) 20 (D) 91

84. If sin x + sin2 x = 1, then the value of cos 12x + 3 cos 10x + 3 cos 8x + cos 6x1 is equal to

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

85. Given A = sin2 + cos4 , then for all real ,

(A) 1 A 2 (B)4

3 A 1 (C)

16

13 A 1 (D)

4

3 A

16

13

86. The expression [x (x3 1)1/2]5 + [x (x3 1)1/2]5 is a polynomial of degree

(A) 5 (B) 6 (C) 7 (D) 8

87. The coefficient of x53 in the expansion

100

0mm100 C (x3)100m . 2m is

(A) 100C47 (B)100C53 (C)

100C53 (D) 100C100

88. The number of permutations that can be formed by arranging all the letters of word NINETEEN in

which no two Es occur together is

(A)!3!3

8(B)

26c!3

!5

(C)

!3

!5 6c3 (D)

!5

!8 6c3

89. Everybody in a room shakes hand with everybody else. The total number of hand shakes is equal to 153.

The total number of persons in the room is equal to

(A) 18 (B) 19 (C) 17 (D) 16

90. The incentre of the triangle with vertices (1, 3 ), (0, 0) and (2, 0) is

(A)

2

3,1 (B)

3

1,

3

2(C)

2

3,

3

2(D)

3

1,1


14/15

91. Let 0 < < /2 be a fixed angle.

If P = (cos , sin ) and Q = (cos (), sin ()), then Q is obtained from P by

(A) clockwise rotation around origin thro an angle

(B) anticlockwise rotation around origin thro an angle

(C) reflection in the line through origin with slope tan (D) reflection in the line through origin with slope /2

92. If the abcissae and ordinates of two points P and Q are the roots of the equations x2 + 2axb

2 = 0 and

x2 + 2pxq2 = 0, respectively then the equation of the circle with PQ as diameter is

(A) x2 + y2 + 2ax + 2pyb2q

2 = 0 (B) x2 + y22ax2py + b2 + q2 = 0

(C) x2

+ y22ax2pyb

2q

2= 0 (D) x

2+ y

2+ 2ax + 2py + b

2+ q

2= 0

93. The angle between the two tangents from the origin to the circle (x 7)2

+ (y + 1)2

= 25 equals

(A)/4 (B)

/3 (C)

/2 (D) none

94. The lines 2x3y = 5 and 3x4y = 7 passes through the center of the circle whose area is 154 sq. units,

then equation is of circle is

(A) x2

+ y22x + 2y = 47 (B) x

2+ y

2+ 2x2y = 31

(C) x2

+ y22x2y = 47 (D) x

2+ y

22x2y = 31

95. The least distance from origin to the circle (x 6)2 + (y8)

2 = 92 is

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

96. The two ends of latus rectum of a parabola are the points (3, 6) and (5, 6). The focus is

(A) (1, 6) (B) (1, 6) (C) (1,6) (D) (1,6)

97. The length of the latus rectum of the parabola 169 {(x 1)2

+ (y3)2} = (5x12y + 17)

2is

(A) 12/13 (B) 14/13 (C) 28/13 (D) none

98. If the latus rectum of an ellipse is equal to half the minor axes then its eccentricity is equal to

(A)2

1(B)

2

3(C)

4

1(D)

4

3

99. An ellipse has OB as a semiminor axis, F, F as its foci and the angle FBF is a right angle. Then, the

eccentricity of the ellipse is

(A)2

1 (B)21 (C)

23 (D) none of these

100. For the hyperbola2

2

cos

x

2

2

sin

y= 1 which of the following remains constant with change in

(A) abscissae of vertices (B) abscissae of foci

(C) eccentricity (D) directrix


15/15

Answer key

1. (D)

2. (C)

3. (B)

4. (B)

5. (B)

6. (A)

7. (D)

8. (A)

9. (C)

10. (B)

11. (C)

12. (A)

13. (D)

14. (B)

15. (B)16. (D)

17. (A)

18. (D)

19. (B)

20. (C)

21. (D)

22. (C)

23. (C)

24. (A)

25. (A)

26. (A)

27. (C)

28. (B)

29. (B)

30. (A)

31. (B)

32. (A)

33. (D)

34. (C)

35. (A)

36. (C)

37. (B)

38. (A)

39. (D)

40. (D)41. (A)

42. (B)

43. (C)

44. (A)

45. (D)

46. (C)

47. (D)

48. (B)

49. (A)

50. (B)

51. (C)

52. (C)

53. (D)

54. (C)

55. (D)

56. (C)

57. (B)

58. (D)

59. (A)

60. (A)

61. (A)

62. (C)

63. (D)

64. (C)

65. (D)66. (B)

67. (C)

68. (A)

69. (C)

70. (C)

71. (D)

72. (A)

73. (C)

74. (B)

75. (A)

76. (D)

77. (C)

78. (B)

79. (C)

80. (C)

81. (C)

82. (B)

83. (C)

84. (A)

85. (B)

86. (C)

87. (C)

88. (C)

89. (A)

90. (D)91. (D)

92. (A)

93. (C)

94. (A)

95. (D)

96. (B)

97. (C)

98. (B)

99. (A)

100. (B)

Documents

Sample Paper for One Year Course