I want the answer key/ Solutions of Class XII SB / SX Stream - Stage I of Kishore Vaigyanik Protsahan Yojana" (KVPY) 2015-16 so can you provide me?

The Class XII SB / SX Stream - Stage I of Kishore Vaigyanik Protsahan Yojana" (KVPY) 2015-16 on 1st November 2015.

KVPY2015-16 Class XII SB / SX Stream - Stage I answer key

Q. No Key Q. No Key Q. No. Key
1 D 31 C 81 A
2 A 32 A 82 D
3 C 33 D 83 C
4 * 34 B 84 D
5 B 35 C 85 D
6 B 36 B 86 D
7 C 37 D 87 B
8 B 38 A 88 A
9 A 39 D 89 C
10 A 40 A 90 D
11 D 41 C 91 C
12 D 42 B 92 A
13 D 43 B 93 C
14 A 44 D 94 C
15 B 45 C 95 A
16 D 46 B 96 A
17 B 47 B 97 A
18 B 48 A 98 A
19 C 49 B 99 A
20 D 50 D 100 A
21 A 51 B 101 **
22 * 52 A 102 A
23 C 53 B 103 C
24 B 54 A 104 A
25 D 55 C 105 C
26 B 56 D 106 B
27 A 57 C 107 C
28 B 58 A 108 A
29 A 59 C 109 A
30 A 60 A or B 110 B

*Candidates who have attempted this section will be awarded One mark.

**Candidates who have attempted this section will be awarded Two mark.

KVPY2015-16 Class XII SB / SX Stream - Stage I question paper
1. The number of ordered pairs(x, y) of real numbers that satisfy the simultaneous equations
2 2 x y x y 12 
(A) 0 (B) 1
(C) 2 (D) 4
2. If z is a complex number satisfying|z3 + z-3| 2, then the maximum possible value of |z + z–1|
is
(A) 2 (B) 3 2
(C) 2 2 (D) 1
3. The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + …. + 23 –13 is
(A) 12 (B) 22
(C) 10072 (D) 20142
4. Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the
parabola y = x2. Then C must lie on the curve
(A) y = x2 + 2 (B) y = 2x2 + 1
(C) y = –x2 + 2 (D) y = -2x2 + 1
5. Circle C1 and C2 of radii r and R respectively, touch each other as shown in figure. The line
, which is parallel to the line joining the centres of C1 and C2 is tangent to C1 at P and
intersects C2 at A, B. If R2 = 2r2, then AOB equals
(A)
o 1
22
2
(B) 45o
(C) 60o (D)
o 1
67
2
6. The shortest distance from the origin to a variable point on the sphere (x - 2)2 + (y - 3)2 + (z -
6)2 = 1 is
(A) 5 (B) 6
(C) 7 (D) 8
7. The number of real numbers for which the equality
sin cos
1
sin cos



Holds for all real which are not integral multiples of /2 is
(A) 1 (B) 2
(C) 3 (D) Infinite
8. Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the
vertices A, B, C, D, E, F are concylic the radius of the circle passing through them is
(A)
5
2
(B)
7
3
(C)
11
5
(D) 2
9. Let p(x) be a polynomial such that p(x) – p’(x) = xn, where n is a positive integer. Then p(0)
equals
(A) n! (B) (n – 1)!
(C)
1
n!
(D)

1
n 1 ! 
10. The value of the limit
2 6/x
x 0
x
lim
sinx 



is
(A) e (B) e–1
(C) e-1/6 (D) e6
11. Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle
at the centre of this sector(i.e. the angle between the bounding radii) is
(A)
3

(B)
3
2
(C) 3 (D) 2
12. Define a function f: by
f(x) = max {|x|, |x -1|, ….|x – 2n|},
where n is a fixed natural number, Then 
2n
0
f x dx is
(A) n (B) n2
(C) 3n (D) 3n2
13. If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2 and p(-1) = 4, then 
1
1
p x dx is


(A) 2 (B) 3
(C) 4 (D) 5
14. Let x > 0 be a fixed real number. Then the integral t
0
e | x t |

dt is equal to
(A) x + 2e-x – 1 (B) x – 2e-x + 1
(C) x + 2e-x + 1 (D) – x – 2e-x + 1
15. An urn contains marbles of four colours: red, white, blue and green. When four marbles are
drawn without replacement, the following events are equally likely
(1) the selection of four red marbles
(2) the selection of one white and three red marbles
(3) the selection of one white, one blue and two red marbles
(4) the selection of one marble of each colour
The smallest total number of marbles satisfying the given condition is
(A) 19 (B) 21
(C) 46 (D) 69
16. There are 6 boxes labeled B1, B2, ….., B6. In each trial, two fair dice D1, D2 are thrown. If D1
shows j and D2 shows k, then j balls are put into the box Bk. After n trials, what is the
probability that B1 contains atmost one ball?
(A)
n 1 n
n 1 n
5 5 1
6 6 6





(B)
n n 1
n n 1
5 5 1
6 6 6





(C)
n n 1
n n 1
5 5 1
n
6 6 6





(D)
n n 1
n n 1 2
5 5 1
n
6 6 6





17. Let a 6i 3j 6k and d i j k . Suppose that a b c where b is parallel to d and c is
perpendicular to d. Then c is
(A) 5i 4j k (B) 7i 2j 5k 
(C) 4i 5j k (D) 3i 6j 9k 
18. If 2
2
3x 1 9x 6x 1
log x 2 log 2x 10x 2 , 
then x equals
(A) 9 15 (B) 3 15 
(C) 2 5 (D) 6 5 
19. Suppose a, b, c are positive integers such that a b c 2 4 8 328 . Then
a 2b 3c
abc

is equal
to
(A)
1
2
(B)
5
8
(C)
17
24
(D)
5
6
20. The sides of a right – angled triangle are integers. The length of one of the sides is 12. The
largest possible radius of the incircle of such a triangle is
(A) 2 (B) 3
(C) 4 (D) 5
PHYSICS
21. A small box resting on one edge of the table is stuck in such a way that it slides off the other
edge, 1 m away, after 2 seconds. The coefficient of kinetic friction between the box and the
table
(A) must be less than 0.05 (B) must be exactly zero
(C) must be more than 0.05 (D) must be exactly 0.05
22. Carbon – 11 decays to boron – 11 according to the following formula.
11 11
6 5 e C B e V 0.96 MeV 
Assume that positrons eproduced in the decay combine with free electrons in the
atmosphere and annihilate each other almost immediately. Also assume that the neutrinos
e V are massless and do not interact with the environment. At t = 0 we have 1 g of 12
6 C. If
the half – life of the decay process is 0 t , then net energy produced between time t = 0 and
0 t 2t will be nearly
(A) 18 8 10 MeV (B) 16 8 10 MeV 
(C) 8 4 10 MeV (D) 16 4 10 MeV 
23. Two uniform plates of the same thickness and area but of different materials, one shaped
like an isosceles triangle and the other shaped like a rectangle are joined together to form a
composite body as shown in the figure. If the centre of mass of the composite body is
located at the mid point of their common side, the ratio between masses of the triangle to
that of the rectangle is
(A) 1 : 1 (B) 4 : 3
(C) 3 : 4 (D) 2 : 1
24. Two spherical objects each of radii R and masses m1 and m2 are suspended using two
strings of equal length L as shown in the figure R L . The angle, which mass m2
makes with the vertical is approximately
(A)

1
1 2
mR
m m L 
(B)

1
1 2
2mR
m m L 
(C)

2
1 2
2m R
m m L 
(D)

2
1 2
m R
m m L 
25. A horizontal disk of moment of inertia 4.25 kg – m2 with respect to its axis of symmetry is
spinning counter clockwise at 15 revolutions per seconds about its axis, as viewed from
above. A second disk of moment of inertia 1.80 kg – m2 with respect to its axis of symmetry
is spinning clockwise at 25 revolutions per second as viewed from above about the same
axis and is dropped on top of the first disk. The two disks stick together and rotate as one
about their axis of symmetry. The new angular velocity of the system as viewed from above
is close to
(A) 18 revolutions/second and clockwise
(B) 18 revolutions/second and counter clockwise
(C) 3 revolutions/second and clockwise.
(D) 3 revolutions/second and counter clockwise
26. A boy is standing on top of a tower of height 85 m and throws a ball in the vertically upward
direction with a certain speed. If 5.25 seconds later he hears the ball hitting the ground, then
the speed with which the boy threw the ball is (take g = 10 m/s2, speed of sound in air = 340
m/s)
(A) 6 m/s (B) 8 m/s
(C) 10 m/s (D) 12 m/s
27. For a diode connected in parallel with a resistor, which is the most likely current(I)
– voltage(V) characteristic?
(A)
(B)
(C)
(D)
28. A beam of monoenergetic electrons, which have been accelerated from rest by a potential U.
is used to form an interference pattern in a Young’s Double Slit experiment. The electrons
are now accelerated by potential 4 U. Then the fringe width
(A) remains the same
(B) is half the original fringe width.
(C) is twice the original fringe width.
(D) is one-fourth the original fringe width.
29. A point charge Q (= 3 × 10–12 C) rotates uniformly in a vertical circle of radius R = 1 mm. the
axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular
speed , the effective magnetic field at the center of the circle will be reduced to zero?
(Horizontal component of Earth’s magnetic field is 30 micro Tesla)
(A) 1011 rad/s (B) 109 rad/s
(C) 1013 rad/s (D) 107 rad/s
30. A closed bottle containing water at 30°C is open on the surface of the moon. Then
(A) the water will boil
(B) the water will come out as a spherical ball.
(C) the water will freeze
(D) the water will decompose into hydrogen and oxygen
31. A simple pendulum of length  is made to oscillate with an amplitude of 45 degrees. The
acceleration due to gravity is g. Let T0 = 2 / g . The time period of oscillation of this
pendulum will be
(A) T0 irrespective of the amplitude
(B) slightly less than T0
(C) slightly more than T0
(D) dependent on whether it swings in a plane aligned with the north-south or east-west
directions.
32. An ac voltmeter connected between points A and B in the circuit below reads 36 V. If it is
connected between A and C, the reading is 39 V. The reading when it is connected between
B and D is 25 V. What will the voltmeter read when it is connected between A and D?
(Assume that the voltmeter reads true rms voltage values and that the source generates a
pure ac)
(A) 481 V (B) 31 V
(C) 61 V (D) 3361 V
33. A donor atom in a semiconductor has a loosely bound electron. The orbit of this electron is
considerably affected by the semiconductor material but behaves in many ways like an
electron orbiting a hydrogen nucleus. Given that the electron has an effective mass of
0.07 me, (where me is mass of the free electron) and the space in which it moves has a
permittivity 130, then the radius of the electron’s lowermost energy orbit will be close to (The
Bohr radius of the hydrogen atom is 0.53 Å)
(A) 0.53 Å (B) 243 Å
(C) 10 Å (D) 100 Å
34. The state of an ideal gas was changed isobarically. The graph depicts three such isobaric
lines. Which of the following is true about the pressures of the gas?
(A) P1 = P2 = P3 (B) P1 > P2 > P3
(C) P1 < P2 < P3 (D) P1/P2 = P3/P1
35. A metallic ring of radius a and resistance R is held fixed with its axis along a spatially uniform
magnetic field whose magnitude is B0 sin(t). Neglect gravity. Then,
(A) the current in the ring oscillates with a frequency of 2.
(B) the Joule hating loss in the ring is proportional to a2
(C) the force per unit length on the ring will be proportional to 2
0 B .
(D) the net force on the ring is non-zero.
36. The dimensions of the area A of a black hole can be written in terms of the universal
gravitational constant G, its mass M and the speed of light C as A = GMc. Here
(A) = –2, = –2, and = 4 (B) = 2, = 2, and = –4
(C) = 3, = 3, and = –2 (D) = –3, = –3, and = 2
37. A 160 watt infrared source is radiating light of wavelength 50000 Å uniformly in all directions.
The photon flux at a distance of 1.8 m is of the order of
(A) 10 m–2 s–1 (B) 1010 m–2 s–1
(C) 1015 m–2 s–1 (D) 1020 m–2 s–1
38. A wire bent in the shape of a regular n – polygonal loop carries a steady current I. Let I be
the perpendicular distance of a given segment and R be the distance of a vertex both from
the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given
by
(A) 0 n I
sin / n
2 I



(B) 0 n I
sin / n
2 R



(C) 0 n I
cos / n
2 I



(D) 0 n I
cos / n
2 R



39. The intensity of sound during the festival season increased by 100 times. This could imply a
decibel level rise from
(A) 20 to 120 dB (B) 70 to 72 dB
(C) 100 to 10000 dB (D) 80 to 100 dB
40. One end of a slack wire (Young’s modulus Y, length L and cross – sectional area A) is
clamped to a rigid wall and the other end to a block (mass m) which rests on a smooth
horizontal plane. The bock is set in motion with a speed v. What is the maximum distance
the block will travel after the wire becomes taut?
(A)
mL
v
Ay
(B)
2mL
v
AY
(C)
mL
v
2AY
(D)
mv
L
AY

For question paper here is the attachment;

Attached Files

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