RT (Main)
RT (Main)
RT (Main)
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4. The Test Booklet consists of 90 questions. The maximum marks are 360.
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having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct
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PART –A (PHYSICS)
1. A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to
the radius of the earth. The minimum energy required- is
(A) mgR/4 (B) 2mgR
(C) mgR/2 (D) 3mgR/4
2. A satellite S is moving in an “elliptical” orbit around the earth. The mass of the satellite is very small
compared to the mass of the earth
(A) the acceleration of S is always directed towards the centre of the earth
(B) the angular momentum of S about the centre of the earth changes in direction, but its magnitude
remains constant
(C) the total mechanical energy of S varies periodically with time
(D) the linear momentum of S remains constant in magnitude
3. A point particle of mass 0.1kg (attached to a horizontal spring) is executing SHM with amplitude of
–3
0.1m. When the particle passes through the mean position, its K.E. is 8×10 J. What is the value of
spring constant k?
(A) 1.6 N/m (B) 0.4 N/m
(C) 3.2 N/m (D) 4 N/m
S1 4m D
4. In the figure the intensity of waves arriving at D from two
coherent sources S1 and S2 is I0. The wave length of the wave is
= 4m. Resultant intensity at D will be 3m
(A) 4I0 (B) I0
(C) 2I0 (D) zero
S2
5. Two pendulums of length 121 cm and 100cm start vibrating. At some instant the two are in the mean
position in the same phase. After how many vibration of the short pendulum the two will be in phase in
the mean position?
(A) 10 (B) 11
(C) 20 (D) 21
T
6. 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 y
emission of radiation. Find the correct relation between the emissivity and x
absorptivity power of the two bodies
t
(A) Ex Ey and ax ay (B) Ex Ey and ax ay
(C) Ex Ey and ax ay (D) Ex Ey and ax ay
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7. A person carrying a whistle emitting continuously a note of 272 Hz is running towards a reflecting
surface with a speed 18 km/ hr. The speed of sound in air is 345 m/s. The number of beats heard by
him is
(A) 4 (B) 6
(C) 8 (D) 3
8. A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas
in two parts respectively are (P, 5V) and (10P,V). If now the piston is left free and the system
undergoes isothermal process, then the volume of the gas in two parts respectively are
(A) 2V, 4V (B) 3V, 3V
(C) 5V, V (D) 4V, 2V
9. Two bodies of mass M1 and M2 are initially at rest and a distance R apart. They the move directly
towards one another under the influence of their mutual gravitational attraction. What is the ratio of
distance travelled by M1 to distance travelled by M2?
M1 M2
(A) (B)
M2 M1
1
(C) 1 (D)
2
11. A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped
vertically in water so that half of it is in water. The fundamental frequency of the air column is now
(A) f/2 (B) 3f/4
(C) f (D) 2f
12. A wave represented by the equation y = acos(kx - t) is superposed with another wave to form a
stationary wave such that the point x = 0 is a node. The equation for other wave is
(A) a sin (kx + t) (B) – a cos (kx - t)
(C) – a cos(kx + t) (D) – a sin (kx - t)
13. Which of the following process does not occur through convection?
(A) Boiling of water (B) Land breeze and Sea breeze
(C) Circulation of air around furnace (D) Heating of glass bulb through filament
Space for rough work
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O
15. If a tunnel is dug along the diameter of the earth and a body is dropped into it, them the time taken by
it to cross the tunnel once is (R = radius of earth)
R R
(A) 2 (B)
g g
g g
(C) 2 (D)
R R
P
16. P–V plots for two gases during adiabatic processes are shown in the
figure. Plots 1 and 2 should correspond respectively to
(A) He and O2 (B) O2 and He 1
2
(C) He and Ar (D) O2 and N2
V
17. A block of ice at –10°C is slowly heated and converted to steam at 100°C. Which of the following
curves represent the phenomenon qualitatively?
Temperature
Temperature
(A) (B)
Temperature
(C) (D)
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19. Two SHM’s are represented by y1 = 10 sin 3t / 4 and y2 = 5 sin(3 t) + 53 cos(3t), the ratio of
their amplitudes is
(A) 1 : 2 (B) 5 : 7
(C) 2 : 1 (D) 1:1
20. A rocket is fired form the earth to the moon. The distance between the earth and the moon is r and the
mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero,
when its distance from the moon is
r r
(A) (B)
20 15
r r
(C) (D)
10 5
21. In a resonance tube experiment, the first resonance is observed when the length of the air column is
14.2 cm and the second resonance when the length of the air column is 46.2 cm. Which of the
following is correct choice? (Velocity of sound = 320 m/s)
(A) The wavelength of the vibration set up in the air column is 64 cm.
(B) The diameter of the tube is 3 cm.
(C) The frequency of the tuning fork with which the air column is in resonance is 400 Hz.
(D) The tube will be again in resonance when the length of the air column is 78.6 cm.
22. Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of
7T0
Nitrogen at temperature T 0. While box B contains one mole of helium at temperature . The boxes
3
are then put into thermal contact with each other and heat flows between them until the gases reach a
common final temperature. (Ignore the heat capacity of boxes). Then the final temperature of the
gases in terms of T0 is:
5T0 3T0
(A) (B)
2 7
7T0 3T0
(C) (D)
3 2
23. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is
acceleration due to gravity at surface then orbital speed is
gR
(A) gx (B)
Rx
1
gR2 gR2 2
(C) (D)
Rx Rx
24. One mole of a gas expands with temperature according to the relation V = KT 2/3. What is the work
done when the temperature changes by 300C?
(A) 10 R (B) 20 R
(C) 30 R (D) 40 R
Space for rough work
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25. A liquid takes 5 minutes to cool from 600C to 500C, when temperature of surrounding is 300C. How
long will it take to cool from 500C to 400C? (nearly)
(A) 5 minute (B) 4 minute
(C) 9 minute (D) 10 minute
26. At t = 0, a transverse wave pulse in a wire is described by the function y = 6/(x² – 3) where x and y are
in metres. The function y(x, t) that describes this wave equation if it is travelling in the positive x
direction with a speed of 4.5 m/s.
6 6
(A) y (B) y
x 4.5t x 4.5t
2 2
3 3
6 6
(C) y (D) y
x 4.5t x 4.5t
2 2
3 3
27. A simple pendulum has time period T1. The point of suspension is now moved upward according to the
relation. y = Kt2. (K = 1m/s2) where y is vertical displacement. The time period now become T 2. The
T12
ratio of is (g = 10 m/s2)
T22
(A) 6/5 (B) 5/6
(C) 1 (D) 4/5
4
28. Pressure versus temperature graph of an ideal gas to equal
number of moles of different volumes are plotted as shown in
figure. Choose the correct alternative P 2
(A) V1 V2 V3 V4
(B) V4 V3 V2 V1
3
(C) V1 V2 ;V3 V4 and V2 V3 1
(D) V1 V2 ,V3 V4 and V2 V3
T
29. The slope of a graph plotted between T 2 and r 3 for a planet, will be
(A) zero (B) 4 GM
(C) GM /4 (D) 4 /GM
2 2
30. The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an
acceleration of g/3. The time period of pendulum will be
T
(A) 2T (B)
2
3 T
(C) T (D)
2 3
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PART –B (CHEMISTRY)
1. CH 3CH 2CHCH 2Cl
CH3
Which of the following electronic effect is observed in the above molecule?
(A) +R effect (B) –R effect (C) +I and – I effect (D) Hyperconjugation
(C) (D)
(A)
Cl2 /h
HCl
CH3 CH3
Cl
(B)
Cl2 /Fe
CH3 CCl 3
(C)
Cl2
Heat
CH3 CHCl 2
(D)
Cl2 /h
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6. Which of the following compound is most acidic in nature?
(A) CH3CH2COOH (B) ClCH2CH2COOH
(C) - O- (D) O
-C-O-
9. The electrophile formed when a mixture of conc. H2SO4 and conc.HNO3 are heated is
(A) SO3 (B) NO2
(C) NO+ (D) N2
11. Which of the following compound has the highest value of Ka?
OH
CH 2OH
(A) (B)
CH3
(C) (D)
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12. Which of the following compound shows geometrical as well as optical isomerism?
(A) CH2 CH CH2 CH CH2 CH3
CH3
(B) CH3 – CH = CH – CH = CH – CH3
14. Which of the following compound is most reactive towards Friedel Craft methylation reaction?
Cl CH3
(A) (B)
CCl 3 CH 2OH
(C) (D)
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17. Which of the following substance is most basic in non-polar solvent?
(A) CH3NH2 (B) CH3NHCH3
(C) CH3 (D) CH3
N CH 3 - N - CH 3
H3C CH3
CH3
(C) (D)
19. CH3
CH 3 - C - CH 2 - CH 3
CH3
How many monochloro product(s) is/are formed by the above compound?
(Do not consider stereoisomers)
(A) 1 (B) 2
(C) 3 (D) 4
20. Which of the following compound will produce maximum heat, when reacts with H 2 in presence of Ni
as catalyst?
(A) CH3 – CH = CH2 (B) CH2 = CH2
(C) CH3CH = CHCH3 (D) CH3CH2CH = CH2
21. HCl
CH3 CH CH CH2 Products
CH3
The major product of above reaction is:
(A) CH3 CH CH2 CH2Cl (B) CH3 CH CH CH3
CH3 CH3 Cl
(C) Cl (D) CH3 CH CH2 CH3
CH3 C CH2 CH3 CH 2Cl
CH3
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22. CH3 – CH = CH – CH3 and CH3 – CH2 – C CH can be distinguished by using
(A) Br2/H2O (B) H2/Ni
(C) AgNO3/NH4OH (D) HCl
23. CH3
NO 2
4
3 1
2
Above compound will be favourably attacked by electrophiles at positions
(A) 1 and 2 (B) 2 and 3
(C) 3 and 4 (D) 2 and 4
24. The most stable free radical out of the following is:
(A) (B)
(C) (D)
25. Which of the following reaction intermediate is not an electron deficient species?
(A) Carbocation (B) Carbanion
(C) Free radical (D) Carbene
26. Which of the following compound has the highest melting point?
(A) (B)
(C) (D)
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27. Addition of which of the following substance to an unsymmetrical alkene does not follow
Markownikoff’s rule?
(A) Cl2/CCl4 (B) Br2/H2O
(C) HCl (D) NO2Cl
28. CH3CH = CH2 will produce only a secondary alcohol when treated with
Hg OCOCH3 2 ,H2O
(A) H2O/H+ (B)
NaBH4
B2H6 ,THF
(C) (D) Cl2/H2O
NaOH,H2O2
29. OH
BrCl
Product
OH
Cl
(C) (D)
Cl
30. CH3 – CH = CH2 will produce a racemic mixture when reacts with
(A) HCl (B) Cl2/CCl4
(C) H2O/H+ (D) H2/Ni
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PART–C (MATHEMATICS)
1 iz
1. For the complex number z , if 1 , then
z i
(A) z lies on the imaginary axis (B) z lies on the real axis
(C) z lies on the unit circle (D) None of these
2. The number of diagonals that can be drawn by joining the vertices of an octagon is
(A) 28 (B) 48
(C) 20 (D) None of these
3. O(0, 0) , A (z) and B (22 , 0) are the vertices of a right angle triangle at A . If |z| = 1 + 3 , then arg(z)
is
(A) /12 (B) /6
(C) /3 (D) /2
5. A point ‘z’ moves on the curve |z – 4 – 3i| = 2 in an argand plane. The maximum & minimum value of
|z| are
(A) 2, 1 (B) 6, 5
(C) 4, 3 (D) 7, 3
7. The number of triangles which can be formed from 12 points out of which 7 are collinear is
(A) 105 (B) 210
(C) 175 (D) 185
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10. If arg z1 = arg(z2), then
(A) z2 = k z1–1 (k > 0) (B) z2 = kz1 (k > 0)
(C) |z2| = | z 1| (D) none of these
11. The general solution of the equation tan2 + 23 tan = 1 is given by
1
(A) (B) n
2 2
n
(C) n (D)
12 12
12. If |z1| =|z2|=|z3| = 1 and z1 z2 z3 are represented by the vertex of an equilateral triangle, then which of
the following is NOT true.
(A) z1 + z2 + z3 = 0 (B) z1 z2 z3 = 1
(C) z1 z2 + z2 z3 + z3 z1 = 0 (D) z1z2 z3 = 0
13. Four different persons have got four different rooms in a hotel. Number of ways that no- one will go to
his own room.
(A) 9 (B) 12
(C) 16 (D) 4
15.
If cos2 x
1
1 tan2 2y 3 sin 3z 4 , then
cos2 x
(A) x may be a multiple of (B) x can not be an even multiple of
(C) z can be a multiple of (D) None of these
16 The number of ways of distributing 10 different books among 4 students (S 1, … S4) such that S1 and
S2 gets 2 books each and S3 and S4 get 3 books each is
(A) 12600 (B) 25200
10 !
(C) 10C4 (D)
2 ! 2 ! 3 ! 3 !
2n 1
17. Integral part of 5 5 11 is
(A) even (B) odd
(C) neither (D) can’t Say
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9
1
18. The coefficient of x in the expansion of x 2 is
x
(A) 1 (B) 1
(C) 48 (D) 0
19. If the data given to construct a triangle ABC is a = 5, b = 7, sin A = 3/4, then it is possible to construct
(A) only one triangle (B) two triangles
(C) infinitely many triangles (D) no triangle
21. The number of terms which are free from radicals in the expansion of (a 1/5 + b1/10)55.
(A) 6 (B) 7
(C) 5 (D) 4
22. The number of triangles whose vertices are at the vertices of an octagon but none of whose sides
happen to come from the sides of the octagon is
(A) 24 (B) 52
(C) 48 (D) 16
23. The complex number z, the least in the absolute value, which satisfies the condition z 4 4i 2 is
(A) z 3 3i (B) z 5 5i
(C) z 3 3i (D) z 1 i
25. Number of ways in which four letter of the word ‘DEGREE’ can be selected is
(A) 7 (B) 6
6!
(C) (D) none of these.
3!
26. The number of ways in which a mixed double game can be arranged amongst 9 married couples if no
husband and wife play in the same game is
(A) 756 (B) 1512
(C) 3024 (D) none of these.
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27. The number of ways of selecting 10 balls out of an unlimited number of white, red, blue and green
balls is
(A) 270 (B) 84
(C) 286 (D) 86
6
2k 2k
28. The value of sin
k 1 7
icos
7
is
(A) 1 (B) 0
(C) i (D) i
29. The values of satisfying sin7 + sin = sin4 and 0 < < /2 are
(A) , (B) ,
9 4 3 9
(C) , (D) ,
6 9 3 4
30. The number of 5-digit numbers in which no two consecutive digits are identical, is
(A) 92 83 (B) 9 84
(C) 95 (D) none of these.
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