India's No. 1 Institute For JEE/PMT

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India’s No. 1 Institute For JEE/PMT

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PHYSICS SECTION-I

Straight Objective Type This section contains 7 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking scheme- for each correct answer +3 marks will be awarded and for each wrong answer -1 mark will be awarded 1. A positron e+ and a proton of the same momentum enter a region of uniform magnetic field

perpendicular to the plane of paper as shown below. Then the shape of the correct trajectory is nearest to

2. Consider the barometer shown in figure. Density of mercury is ρ. A small hole is

made at point S as shown. The mercury comes out from this hole speed v equal to (a) 2gh (b) 2gH (c) 2g(H h)− (d) none of these 3. A boat is inside a swimming pool and contains light thermocole bricks. If bricks are thrown in the water,

the level of water in pool will, (density of bricks is less than that of water) (a) rises (b) decreases (c) remains same (d) none

4. A solid sphere has linear velocity v0 = 4 m/s and angular velocity ωo = 9 rad /s as shown. Ground on which it is moving is smooth. It collides elastically with a rough wall of coefficient of frictionμ. Radius of the sphere is 1m and mass is 2 kg.

If the sphere after colliding with the wall rolls without slipping in opposite direction, then coefficient of friction μ is

(a) 12

(b) 23

(c) 13

(d) 14

5. A disc of circumference S stands vertically on a horizontal surface. A

horizontal force P acts on the centre of disc. Half of the circumference (ABC) is rough and the friction is sufficient to prevent slipping when the disc rolls along xy. The other half of the circumference (ADC) is smooth. The disc starts from the rest when P begins to act and the point C is at the bottom. The distance moved by the disc along xy when it completes one rotation

e +

(a)

p R

(b)

p + R e +

(c)

p

e +

(d)

pe +

S

Mercury

Hh



India’s No. 1 Institute For JEE/PMT (a) 15 s

12 (b) 13 s

8

(c) 19 s16

(d) None

6. A semicircular panel of radius r is attached with hinges to a circular plate of

radius r and initially held in the vertically position as shown. The plate and the panel are made of the same material and have the same thickness. Knowing that the entire assembly is rotating freely with an initial angular velocity ωo, determine the angular velocity of the assembly after the panel has been released and comes to rest against the plate.

(a) 5ω0/6 (b) 2ω0/5 (c) 3ω0/5 (d) None 7. A 3 kg collar can slide without friction on a vertical rod and is held so it just

touches an un-deformed spring. The maximum deflection of the spring if the collar is suddenly released.(given K=2.5 kN/m)

(a) 2.4cm (b) 3.2cm (c) 4.2cm (d) None 8. A particle of mass m is transferred from the centre of the base of a uniform

solid hemisphere of mass M and radius R to infinity. The work performed in the process by the gravitational force exerted on the particle by the hemisphere is

(a) GMmR

− (b) 1 GMm2 R

−

(c) 3 GMm2 R

− (d) None

9. A hemispherical bowl is rotating with angular velocity ω about a

vertical axis. The radius of the rim of the bowl is r. The minimum coefficient of static friction between the bowl and the insect so that it may come out of it is

(a) g/ω2r (b) 2g / rω

(c) ω2 r/g (d) 2r / gω 10. A sonometer wire resonates with a tuning fork forming standing waves

with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by M, the wire resonates with the same tuning fork forming three antinodes for the same position of bridges. The values of M is

(a) 25 kg (b) 5 kg

(c) 12.5 kg (d) 1 kg25



India’s No. 1 Institute For JEE/PMT 11. A conical block, floats on water with 90% height immersed in it. Height h of the block is equal to diameter

i.e. cm. The mass to be kept on the block, so that the block just floats at the surface of water, is (ρ water =1 g / cc )

(a) 568 g (b) 980 g (c) 112 g (d) 196 g

12. A particle moved from position 1r 3 i 2 j 6 k→ → → →

= + − to position 2r 14 i 13 J 9 k→ → →

= + + under the action of a

force 4 i j 3k→ → →⎛ ⎞+ +⎜ ⎟

⎝ ⎠ Newton. Find the work done.

(a) 10 J (b) 100 J (c) 0.01 J (d) 1 J 13. A ball is thrown vertically upwards. It was observed at a height h twice with a time interval Δt.

The initial velocity of the ball is

(a) 2 28gh g ( t)+ Δ (b) 2g t8gh

2Δ⎛ ⎞+⎜ ⎟

⎝ ⎠

(c) 2 21 8gh g ( t)2

+ Δ (d) 2 28gh 4g ( t)+ Δ

14. A solid metallic sphere has a charge + 3Q. Concentric with this

sphere is a conducting spherical shell having charge −Q. The radius of the sphere is a and th at of the spherical shell is b. (b < a). What is the electric field at a distance R (a< R < b) from the centre?

(a) 20

Q2 Rπ∈

(b)0

3Q2 Rπ∈

(c) 20

3Q4 Rπ∈

(d) 20

4Q2 Rπ∈

15. A shot is fired with a velocity u at an angle (α +θ) with the horizon from the foot of an incline plane of

angle α through the point of projection .if it hits the plane horizontally then

(a) tan θ = 2

tanα1+ 2tan α

(b) tan θ =2 tan α

(c) tanθ = 2

2 tanα1+ 2tan α

(d) tan θ = 2

sinαcosα1- sin α

16. Two blocks each of mass M are connected to the ends of a light frame as

shown in fig. The frame is rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds T0. Find the maximum frequency with which the frame may be rotated without breaking with rod. (Neglecting the effect of gravity)

(a)1/2

0T1f2 M

⎡ ⎤= ⎢ ⎥π ⎣ ⎦l

(b) 0T1f2 M

⎡ ⎤= ⎢ ⎥π ⎣ ⎦l

(c)1/2

0T1fM⎡ ⎤

= ⎢ ⎥π ⎣ ⎦l (c) None

M

l

M



India’s No. 1 Institute For JEE/PMT 17. A plane loop shown in fig. is shaped in the form of two squares with sides a = 0.5 m and b = 0.3 m, and

is introduced into a uniform magnetic field at with right angles to the loop’s plane. The magnetic induction varies with time as B = B0 sin ω t, where B0 = 20 m T and ω = 100 rad/s, the amplitude of the current induced in the loop if its resistance per unit length is equal to r = 50 mΩ/metre.(The induction of the loop is negligible).

(a) 2 amp (b) 4 amp (c) 3 amp (d) None 18. A freely moving piston divides a vertical cylinder, closed at both ends, into two parts each containing one

mole of gas. In equilibrium, at temperature T, the volume of upper part is n1 times greater than the lower part. At what temperature the ratio of the volumes (upper is to lower) is equal to n2?

(a) 2

2 22

1 1

n n 1T

n n 1⎛ ⎞−⎜ ⎟

−⎝ ⎠ (b)

21 1

22 2

n n 1T

n n 1⎛ ⎞−⎜ ⎟

−⎝ ⎠

(c) 2

2 12

1 2

n n 1T

n n 1⎛ ⎞−⎜ ⎟

−⎝ ⎠ (d) none

19. What is the mass of a vertical column of air (M = 29) of height H, assuming that up to this height there is no change in temperature and acceleration due to gravity? The temperature at the earth’s surface is T and pressure p0, the area of cross-section of the column is A.

(a)MgH

0 RTAp1 e

g⎡ ⎤+⎢ ⎥

⎣ ⎦ (b)

MgH0 RTAp

1 eg

−⎡ ⎤+⎢ ⎥

⎣ ⎦

(c) MgH

0 RTAp1 e

g⎡ ⎤−⎢ ⎥

⎣ ⎦ (d)

MgH0 RTAp

1 eg

−⎡ ⎤−⎢ ⎥

⎣ ⎦

20. Neglecting friction, the angle β of line AB for equilibrium in terms of α1, α2, W1, W2

(a) β = tan−1 (W2/ tan α1−W1/ tan α2) / W1 + W2 (b) β = tan−1 (W2/ tan α1+W1/ tan α2) / W1 - W2 (c) β = 2tan−1 (W2/ tan α1+W1/ tan α2) / W1 + W2 (d) None 21. In the figure, the potentiometer wire AB of length L and resistance 9r

is joined to the cell D of emf ε and internal resistance r. The cell C emf is ε/2 and its internal resistance 2r. The galvanometer G will show no deflection when the length AJ is

(a) 4L9

(b) 5L9

(c) 7L18

(d) 11L18




22. Successive wave fronts propagating in a material medium are shown in the figure. The refractive index of the medium

(a) increases as Y increase (b) increases as X increase (c) decreases as Y increases (d) Velocity of light and wavelength of the wave decreases with Y 23. Half the space between two concentric electrodes of a spherical

capacitor is filled, as shown in Fig. with uniform isotropic dielectric with permittivity ε. The charge of the capacitor is q. Find the magnitude of the electric field strength between the electrodes as a function of distance r from the curvature centre of the electrodes

(a) 20

q2 ( 1)rπε ε +

(b) 20

2q2 ( 1)rπε ε +

(c) 20

q4 ( 1)rπε ε +

(d) 20

q( 1)rπε ε +

24. A converging lens of focal length 20 cm and diameter 5 cm is cut along the line AB. The part of the lens

shown shaded in the diagram is now used to form an image of a point object P placed 30 cm away from it on line XY, which is perpendicular to the plane of the lens. The image of P will be formed.

(a) on XY (b) 1 cm below XY (c) 1.5 cm below XY (d) 0.5 cm above XY

25. A ray of light ab passing through air, enters a liquid of refractive index μ1, at the boundary XY. In the liquid, the ray is shown as bc. The angle between ab and bc is δ (angle of deviation). The ray then passes through a rectangular slab ABCD of refractive index μ2 ( μ2 > μ1 ), and emerges from the slab as ray de. The angle between XY and AB is θ. The angle between ab and de is

(a) δ (b) δ +θ

(c) δ + sin-1 1

2

⎛ ⎞μ⎜ ⎟μ⎝ ⎠

(d) δ +θ 1

2

⎛ ⎞μ−⎜ ⎟μ⎝ ⎠



India’s No. 1 Institute For JEE/PMT 26. The effective refractive index of two immiscible liquids of equal thickness & individual refractive indices

n1 and n2 is equal to

(a) 1 2n n (b) 1 2n n2+

(c) 1 2

1 2

2n nn n+

(d) 2 21 2n n+

27. Consider a windmill with blades of cross-sectional area A as shown. Assume that mill is facing directly into the wind. If the wind speed is υ, then the kinetic energy of the air that passes through the blades in time Δt is

(a) 12ρ Aυ3Δt (b) 1

2ρ A υ2 Δt

(c) ρ υ3Δt (d) ρ Aυ2 Δt

28. Two rods of different materials having coefficient of thermal expansion α1 , α2 and Young’s

modulii Y1, Y2 respectively are fixed between two rigid walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α1 : α2 =2:3, the thermal stresses developed in the two rods are equal provided Y1: Y2 is equal to

(a) 2:3 (b) 1:1 (c) 3:2 (d) none

29. A train of length 200 m has its headlight switched on as soon as it starts from rest with an acceleration of

0.5 ms-2. After 20 s, the tail-light of train is switched on. A person in an inertial frame moving parallel to the railway track observes the two events occurring at the same place. The inertial frame has velocity of

(a) 5 ms-1 in the direction of motion of train (b) 5 ms-1 opposite of the direction of motion of train (c) 10 ms-1 in the direction of motion of train. (d) 10 ms-1 opposite to the direction of motion of train. 30. A block of mass 200 kg is set into motion on a frictionless

horizontal surface with the help of frictionless pulley and rope system as shown in fig.The horizontal force that should be applied on block to produce an acceleration of 1 m/s2 in it is

(a) 100 N (b) 200 N (c) 300 N (d) 400 N 31. A mass of 0.5 kg moving with a sped of 1.5 m/s on a horizontal

smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be;

(a) 0.12 m (b) 0.5 m (c) 0.5 m (d) 0.15 m 32. A metal plate is placed 5 metres from a monochromatic light source whose power output is 10–3 W.

Consider that a given ejected photoelectron may collect its energy from a circular area of the plate as large as ten atomic diameters (10 – 9 m) in radius. The energy required to remove an electron through the metal surface is about 5.0eV. Assuming light to be a wave how long would it take for such a ‘target’ to soak up this much energy from such a light source.

(a) 20 hrs (b) 25 hrs (c) 39 hrs (d) None



India’s No. 1 Institute For JEE/PMT 33. A “double star” is composite system of two stars rotating about their center of mass under their mutual gravitational attraction. Let us consider such a “double star” which has two stars of masses m and 2m at

separation l . If T is the time period of rotation about their center of mass then,

(a) 3lT 2

mG= π (b)

3lT 22mG

= π

(c) 3lT 2

3mG= π (d)

3lT 24mG

= π

34. A particle free to move along the x-axis has potential energy given by U(x) = k[ 1- exp(-x2)] for

x ,−∞ < < +∞ where k is a positive constant of appropriate dimensions. Then, (a) At point away from the origin, the particle is in unstable equilibrium. (b) For any finite non-zero value of x, there is a force directed away from the origin.

(c) If its total mechanical energy is k ,2

it has its minimum kinetic energy at the origin.

(d) For small displacements from x = 0, the motion is simple harmonic. 35. A thin dielectric rod of length l lies along the x axis with one end at the origin and the other end at the

point (l, 0). It is charged uniformly along its length with a total charge Q. The potential at a point (x,0) when x >l is

(a) 0

Q4 lπε

(b) 0

Q4 lπε

logexl

⎛ ⎞⎜ ⎟⎝ ⎠

(c) 0

Q4 lπε

logex

x-1⎛ ⎞⎜ ⎟⎝ ⎠

(d) 0

Q4 lπε

logex - lx

⎛ ⎞⎜ ⎟⎝ ⎠

36. In an n-p-n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the

collector then the (a) emitter current will be 9 mA (b) emitter current will be 11 mA (c) base current will be 2 mA (d) base current will be –1 mA. 37. The work done in splitting a drop of water of 1 mm radius into 106 droplets is (S.T. of Water = 72×10-3J/m2) (a) 9.98×10-5Joule (b) 8.95×10-5Joule (c) 5.89×10-5Joule (d) 5.98×10-5Joule 38. A cord of mass m, length L, area of cross-section A and Young’s modulus Y is hanging from a ceiling

with the help of a rigid support. The elongation developed in the wire due to its own weight is

(a) Zero (b) mgLAY

(c) mgL2AY

(d) 2mgLAY

39. A railway compartment is 16 m long, 2.4 m wide and 3.2 m high. It is

moving with a velocity v. A particle moving horizontally with a speed u, perpendicular to the direction of v, enters through a hole at an upper corner A and strikes the diagonally opposite corner B. Assume g = 10 m/s2.

(a) v = 20 m/s (b) u = 6 m/s (c) To an observer inside the compartment, the path of the particle is a parabola. (d) To a stationary observer outside the compartment, the path of the particle is a circle.



India’s No. 1 Institute For JEE/PMT 40. Two particles instantaneously at A and B respectively 4.5 metres apart are moving with uniform

velocities, the former towards B at 1.5 m/sec and the latter perpendicular to AB at 1.125 m/sec. The instant when they are nearest. (a) 2 sec (b) 3 sec

(c) 4 sec (d) 231 sec25

SECTION-II More Than One

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which MORE THAN ONE may be correct. Marking scheme:- for each correct answer +4 will be awarded, for each wrong answer 0 will be awarded.

41. A 60 mm-radius drum is rightly attached to a 100 mm radius drum as

shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that end E of the cord is pulled to the left with a velocity of 120 mm/s. (a) The angular velocity of the drums 3rad/s (b) the velocity of the center of the drums 300 mm/s (c) The length of the cord wound or unwound per second wound 180 mm/s

(d) None

42. A fish, F in the pond is at a depth of 0.8 m from water surface and is moving vertically upwards with velocity 2 ms-1. At the same instant a bird B is at a height of 6 m from water surface and is moving downwards with velocity 3 ms-1. At this instant both are on the same vertical line as shown in Fig. Which of the following statements is/are correct?

(a) Height of B, observed by F (from itself) is equal to 5.30 m.

(b) Depth of F, observed by B (from itself) is equal to 6.60 m. (c) Height of B, observed by F (from itself) is equal to 8.80 m. (d) None of these 43. An aeroplane is flying horizontally with constant velocity v0 at a height h from the ground. at an instant, it

is vertically above a cannon (on the ground). At the same instant, a shell is fired to hit the aeroplane with muzzle velocity u.

(a) Angle of projection must be equal to cos-1 0vu

⎛ ⎞⎜ ⎟⎝ ⎠

.

(b) Muzzle velocity should not be less than 202gh v+ .

(c) Angle of projection cannot be less than cos-1 0

20

v

v 2gh+.

44. State which of the following statement(s) is / are correct for a particle projected at an angle of projection α up an incline plane of inclination β

(a) If it strikes the plane normally then tan α = cot β + 2 tan β (b) If it strikes the plane horizontally then tan α = 2 tan β (c) If it rebounds and retraces its path then tan α tan β = 1 +2 tan2 β (d) None



India’s No. 1 Institute For JEE/PMT 45. A ball is shot form the ground into the air. At a height of 9.1 m, its velocity is observed to be

ˆ ˆv 7.6i 6.1j→

= + in metres per second ( ˆ ˆi horizontal, j upward) (a) the ball rises to a maximum height 17.2 m

(b) total horizontal distance traveled by the ball is 23 m (c) the ball hits the ground with a velocity 17 m/s

(d) the direction of the ball’s velocity just before it hits the ground is tan−1(2) 46. A compound microscope has an objective of focal length 1 cm and an eyepiece of focal length 2.5 cm.

An object has to be placed at a distance of 1.2 cm away from the objective for normal adjustment. (a) The angular magnification is -50. (b) The length of the microscope tube is 8.5cm. (c) The angular magnification is -60. (d) The length of the microscope tube is 6.5cm. 47. A bar of mass m is pulled by means of a thread up an inclined plane

forming an angle θ with the horizontal as shown in fig. The coefficient of friction is μ.

(a) min 2m gsin mgcosT

(1 )θ + μ θ

=+μ

(b) for min . tension T α = tan−1 (μ)

(c) min 2m gsin mgcosT

(1 )θ − μ θ

=+μ

(d) None of the above is correct

48. A container holds 1026 molecule/m3, each of mass 3 x 10-27 kg. Assume that 16

of the molecules move

with velocity 2000 ms-1 directly toward one wall of the container while the remaining 56

of the molecules

move either away from the wall or in perpendicular direction, and all collisions of the molecules with the wall are elastic:

(a) Number of molecules hitting 1 m2 of the wall every second is 1/3× 1029 (b) Number of molecules hitting 1 m2 of the wall every second is 2× 1029 (c) Pressure exerted on the wall by molecules is 24 x 105 Nm-2. (d) Pressure exerted on the wall by molecules is 4 x 105 Nm- 49. Two different coils have self inductances L1 = 8 mH and L2 = 2 mH. The current in one coil is increased

at a constant rate. The current in the second coil is also increases at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time, the current the induced voltage and the energy stored in the first coil ad i1, V1 and W1 respectively. Corresponding values for the second coil at the same instant are i2, V2 and W2 respectively. Then

(a) 1

2

i 1i 4= (b) 1

2

i 4i=

(c) 2

1

W 1W 4

= (d) 2

1

V 4V

=

50. An isotropic point source emits light with wavelengthλ. The radiation power of the source is P. Then

(a) the photon flux at a distance r is. 2P / 4 chrλ π (b) the distance between the source and the point at which the mean concentration of photons is equal to n is r = 2P / 4 hncλ π (c) the photon flux at a distance r is 2 2P / 8 chrλ π

(d) None




CHEMISTRY This section contains 50 multiple choice questions. Each question has 4 choices (a),

(b), (c) and (d) out of which ONLY ONE is correct. Marking scheme: for each correct answer +3 marks will be awarded and for each wrong answer -1 mark will be awarded.

1. The oxidation number of carbon in CH2O is: (a) – 2 (b) +2 (c) zero (d) + 4 2. The compound with the highest boiling point is (a) n-Hexane (b) n-Pentane (c) 2,2-Dimethylpropene (d) 2-Methylbutane 3. The compound with no dipole moment is (a) Methyl chloride (b) Carbon tetrachloride (c) Methylene chloride (d) Chloroform 4. The compound that can be most readily sulphonated is (a) Benzene (b) Nitrobenzene (c) Toluene (d) Chlorobenzene 5. A compound that can be most gives a positive iodoform test is (a) 1-Pentanol (b) 2-Pentanone (c) 3-Pentanone (d) Pentanal 6. The maximum number of isomers for an alkene with the molecular formula C4H8 is: (a) 2 (b) 3 (c) 4 (d) 5 7. In the nitration of benzene with a mixture of con. HNO3 and conc. H2SO4 the active species involved is (a) Nitrite ion (b) Nitrate ion (c) Nitronium ion (d) NO2 8. The compound 1,2-butadien has (a) only sp-hybridised carbon atoms (b) only sp2-hybridised carbon atoms (c) both sp and sp2-hybridised carbon atoms (d) sp, sp2 and sp3, hybridized carbon atoms 9. The rate constant of a reaction depends on: (a) Temperature (b) initial concentration of reactant (c) time of reaction (d)extent of reaction 10. At 90oC, pure water has 6

3H O 10+ −⎡ ⎤ =⎣ ⎦ mole litre−1. What is the value of Kw at 900C

(a) 10−6 (b) 10−12 (c) 10−14 (d) 10−8 11. The ratio of root mean square speed to average speed of a gas molecule at a particular temperature is (a) 1.086 : 1 (b) 1 : 1.086 (c) 2 : 1.086 (d) 1.086 :2 12. The standard reduction potentials at 298 K for the following half cell reactions are given as: 2 oZn (aq) 2e Zn(s)E 0.762V+ + = − ; 3 oCr (aq) 3e Cr(g) E 0.740 V+ + = −

o22H (aq) 2e H (g) E 0.000+ + = − gas; 3 2Fe (aq) e Fe (aq) E 0.770+ ++ = −



India’s No. 1 Institute For JEE/PMT The strongest reducing agent is (a) Zn(s) (b) Cr(s) (c) H2(g) (d) Fe2+(aq) 13. Which of the following statement about anhydrous aluminium chloride is correct: (a) it exists as AlCl3 molecules (b) it is not easily hydrolyzed (c) it sublimes at 100oC under vacuum (d) it is strong Lewis base 14. Sodium thisulphate is used in photography because of its: (a) Reducing behaviour (b) Oxidising behaviour (c) Complex forming behaviour (d) reaction with light 15. If a molecule MX3 has zero dipole moment, the sigma bonding orbitals used by M. (atomic no. < 21) are: (a) Orbitals (b) sp hybrid (c) sp2 hybrid (d) sp3 hybrid 16. The bond order of individual carbon-carbon bonds in benzene is (a) one (b) two (c) between one and two (d) None 17. Molecule in which the distance between the two adjacent carbon atoms is largest: (a) Ethane (b) Ethene (c) Ethyne (d) Benzene 18. The compound which reacts fastest with Lucas reagent at room temperature is (a) Butan-1-ol (b) Butan-2-ol (c) 2-Methyl propanol-1- (d) 2-Methyl propan-2-ol 19. The compound which on reaction with aqueous nitrous acid at law temperature produces on oily

nitrosoamine is (a) Methylamine (b) Ethylamine (c) Diethylamine (d) Triethylamine 20. The reagent with which both acetaldehyde and acetone reacts easily (a) Fehling’s reagent (b) Grignard reagent (c) Schiff’s reagent (d) Tollen’s reagent 21. The compound which is not isomeric with diethyl ether is (a) n-Propyl methyl ether (b) Butan-1-ol (c) 2-Methyl propan-2-ol (d) Butanone 22. The angle between two covalent bond is maximum in: (a) CH4 (b) H2O (c) C2H4 (d) CO2 23. The weakest hydrogen halogen acid is (a) HF (b) HCl (c) HBr (d) HI 24. Pair of molecules which form strongest intermolecular H-atoms is (a) SiH4, SiF4 (b)CH3COCH3, CHCl3 (c) HCOOH, CH3COOH (d) CH3Cl, CH3Br 25. Among the given cations the most stable cation is (a) Sec. Butyl carbocation (b) Ter. butyl carbocation (c) n-Butyl carbocation (d) All of same strength



India’s No. 1 Institute For JEE/PMT 26. The most acidic among the following is: (a) C2H6 (b) C2H4 (c) C2H2 (d) All of same strength 27. The compound having both sp and sp2 hybridised carbon atoms is (a) Propene (b) Propane (c) Butane (d) Propadiene 28. The most strained ring is in (a) Cyclopropane (b) Cyclobutane (c) Cyclopentane (d) All 29. Mn2+ can be oxidized to MnO4

− by (a) SnO2 (b) PbO (c) BaO2 (d) ZnO 30. Which of the following is strongest base: (a) Toluene (b) Aniline (c) Phenol (d) Nitrobenzene 31. Which compound will exhibit cis-trans isomerism: (a) 2-Butene (b) 2-Butyne (c) 2-Butanol (d) Butanal 32. Any p-orbital can accommodate upto: (a) Four electrons (b) Two electrons with parallel spins (c) Six electrons (d) Two electrons with opposite spins 33. Carbon tetrachloride has net dipole moment zero because of: (a) Its planar structure (b) its regular tetrahedral structure (c) Similar sizes of carbon and chlorine (d) Similar electron affinities of carbon and chlorine 34. Which does not have the hydrogen bond: (a) Phenol (b) Liquid NH3 (c) Water (d) Liquid HCl 35. The types of bonds present in CuSO4. 5H2O are only: (a) electrovalent and covalent (b) electrovalent and co-ordinate (c) electrovalent, Covalent and co-ordinate (d) none of these 36. Diethyl ether on heating with conc. HI gives two moles of : (a) Ethanol (b) ethyl iodide (c) Iodoform (d) Methyl iodide 37. When acetaldehyde is heated with Fehling’s solution it gives a precipitate of (a) Cu (b) CuO (c) Cu2O (d) Cu + Cu2O + CuO 38. The principal quantum number of an atom is related to the (a) size of the orbitals (b) spin angular momentum (c) orbital angular momentum (d) orientation of the orbital in space



India’s No. 1 Institute For JEE/PMT 39. Rutherford’s scattering experiment is related to the size of the (a) Nucleus (b) Atom (c) Electron (d) Neutron 40. When propyn is treated with aqueous H2SO4 in presence of HgSO4 the major product is (a) Propanol (b) Acetone (c) Propyl hydrogen sulphate (d) Propanal 41. The cannizzaro reaction is not given by (a) Trimethyl acetaldehyde (b) Acetaldehyde (c) Benzaldehyde (d) Formaldehyde 42. Acetamide is treated separately with the following reagents. Which one of the these would give

methylamine: (a) PCl5 (b) Sodalime

(c) NaOH + Br2 (d) None 43. Which of the following compounds does not dissolve in conc. H2SO4 even on warming: (a) Ethylene (b) Benzene (c) Hexane (d) Aniline 44. The specific rate constant of a first order reaction depends on the (a) concentration of reactant (b) concentration of product (c) time (d) temperature 45. A catalyst is a substance which (a) increases the equilibrium concentration of products (b) change the equilibrium constant of the reaction (c) shortens the time to reach equilibrium (d) supplies energy to the reaction 46. Heavy water is (a) H2

18 O (b) D2O (c) water obtained by repeated distillation (d) Water at 4oC 47. Chlorine acts as a bleaching agent only in presence of (a) dry air (b) moisture (c) sunlight (d) A solder 48. In the aluminothermite process, aluminium acts as (a) an oxidant (b) a flux (c) a reducing agent (d) a solder 49. Faraday’s laws of electrolysis are related to (a) atomic number of the cation (b) atomic number of the anion (c) Equivalent weight of electrolyte (d) speed of cation 50. The radiations from a turaly occurring radioactive substance as seen after deflection by a magnitude

field in one direction are: (a) Definitely α- rays (b) Definitely β-rays (c) Both α and β rays (d) either α or β rays




MATHEMATICS SECTION–I

Straight Objective Type This section contains 50 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking scheme– for each correct answer +3 marks will be awarded and for each wrong answer –1 mark will be awarded

1. If f(x) is a continuous function and f(0) = 0 then

x

0

x 0

f(t)dtlim

x→

∫ is:

(a) zero (b) one (c) two (d) three 2. Two points A and B move on the x–axis and the y–axis respectively such that the distance between the

two points is always the same. The locus of the middle point of AB is: (a) a straight line (b) a pair of straight lines (c) a circle (d) none of these

3. The line λx + μy =1 is a normal to the circle 2x2 + 2y2 −5x + 6y −1 =0 if: (a) 5λ − 6μ = 2 (b) 4 + 5μ = 6λ (c) 4 + 6μ = 5λ (d) none of these

4. Two distinct chords drawn from the point (p, q) on the circle x2 + y2 = px + qy, where pq ≠0, are bisected by the x–axis. Then:

(a) | p | = | q | (b) p2 = 8q2 (c) p2 < 8q2 (d) p2 > 8q2

5. If 3a + 2b + 6c =0, the family of straight lines ax + by + c = 0 passes through a fixed point whose co–

ordinates are given by:

(a) 1 1,2 3

⎛ ⎞⎜ ⎟⎝ ⎠

(b) (2, 3)

(c) (3, 2) (d) 1 1, .3 2

⎛ ⎞⎜ ⎟⎝ ⎠

6. The value of C0 + 3 C1 + 5 C2 + 7 C3 …+ (2 n + 1) Cn is equal to (a) 2n (b) 2n + n ⋅ 2n–1 (c) 2n ⋅ (n +1) (d) none of these 7. In the expansion of (1+x)50, the sum of the coefficients of odd powers of x is (a) 0 (b) 249 (c) 250 (d) 251 8. If (6 6 + 14)2n+1 = m and if f is the fractional part of m, then fm is equal to (a) 15n+1 (b) 202n+1 (c) 25n (d) none of these

9. If α, β, γ are the cube roots of p, p < 0, then for any x,y and z the values of x y zx y zα + β + γβ+ γ + α

are

(a) w, w2 (b) –w, – w2 (c) 1, –1 (d) none of these 10. Line x + 2y – 8 = 0 is the perpendicular bisector of AB. If B = (3, 5), then coordinates of A are (a) (2, 1) (b) (1, 2)



India’s No. 1 Institute For JEE/PMT (c) (2, 2) (d) (1, 1)

11. The ellipse 2 2

2 2

x ya b

+ = 1 and the straight line y = mx + c intersect in real points only if

(a) a2m2 < c2 – b2 (b) a2m2 > c2 – b2 (c) a2m2 ≥ c2 – b2 (d) c ≥ b 12. If z2 – z + 1 = 0 then zn – z− n; where n is a multiple of 3, is (a) 2(–1)n (b) 0 (c) (–1)n+1 (d) none of these 13. The number of real roots of the equation ( )x x3 7

5 5 2+ = (a) form a null set (b) is only one (c) is more than one (d) none of these 14. The number of real solution of the equation sin ex = 5x + 5− x is (a) 0 (b) 1 (c) 2 (d) ∞ 15. Solution set of the equation [ x +[x + [x]]] = 6 is (a) [ 2, 3) (b) [2, 3) ∪ ( 3, ∞) (c) (–∞, ∞) (d) none of these 16. The equation 1 + 3x/2 = 2x has (a) three solutions (b) two solutions (c) a unique solution (d) none of these

17. The value of n ∈ I for which the function f (x) = ( )x

n

sinnxsin

has 4π as its period; is

(a) 2 (b) 3 (c) 5 (d) 4 18. Fundamental period of the function f (x) = sin4x + cos4x is (a) π (b) 2π (c) π/2 (d) none 19. The locus of the mid points of the chords of the circle x2 + y2 + 4x – 6y – 12 = 0 which subtend an

angle of π/3 radians at its circumference is (a) (x + 2)2 + ( y–3)2 = 6.25 (b) (x–2)2 + (y + 3)2 = 6.25 (c) (x + 2)2 + ( y– 3)2 = 18.75 (d) (x +2)2 + (y + 3)2 = 18.75 20. Let f be a function satisfying f (x+ y) = f (x)+ f (y) and f (x) = x2 g (x) for all x and y, where g (x) is a

continuous function then f ′ (x) is equal to (a) g′ (x) (b) g (0) (c) g (0) + g′ (x) (d) 0

21. The integral1

2tan X

2

1 x xe1 x

− ⎛ ⎞+ +⎜ ⎟+⎝ ⎠

∫ dx is equal to

(a) 1tan

2

e x1 x

−

++ C (b) x .

1tan xe C−

+

(c) 1tan

2

xe x1 x

−

++C (d) none of these



India’s No. 1 Institute For JEE/PMT 22. The least integral value of k for which (k –2) x2 +8x +k + 4 > 0; ∀ x ∈R, is (a) 5 (b) 4 (c) 3 (d) none of these

23. The inequality 2

2

x |x| 2 22|x| x 2

− −>

− −holds only if

(a) –1 < x <– 2/3 (b) only for 2/3 < x < 1 (c) –1 < x < 1 (d) –1< x < –2/3 or 2/3 < x < 1

24. The solution set of the inequality |x| 111 |x| 2

− ≥+

is

(a) x ∈ [ –2, 2] (b) x ∈ (– ∞ ,∞) (c) (–1, 0) ∪ (0, 1) (d) none of these 25. If z be a complex number satisfying z4 + z3 + 2z2 + z +1 = 0 then | Z | is equal to (a) 1/2 (b) 3/4 (c) 1 (d) none of these 26. If | z | ≤ 1 and |ω| ≤ 1 then expression {|z – ω|2 – [(|z | – |ω|)2 + (arg z – arg ω)2]} is (a) > 0 (b) < 0 (c) ≤ 0 (d) can not say anything

27. The value of integral 3

dxx 1 x−∫ is given by

(a) 3

3

1 x 11 log C3 1 x 1

− ++

− − (b)

3

3

1 x 11 log C3 1 x 1

− −+

− −

(c) 3

2 1log C3 1 x

+−

(d) 31 log 1 x C3

− +

28. If 1

2

2

x tan x dx 1 x1 x

−

= ++

∫ f (x) + k log (x + 2x 1)+ + C then

(a) f(x) = tan–1 x, k = –1 (b) f (x) = tan–1 x, k = 1 (c) f (x) = 2 tan–1 x, k = –1 (d) f (x) =2 tan–1 x, k = 1

29. The integral cos4x 1cot x tanx

−−∫ is equal to

(a) −12

cos 4x + C (b) − 14

cos 4x + C

(c) − 12

cos 2x + C (d) none of these

30. The integral 2 2

2x 3(x x 1)

−+ +∫ is equal to

(a) − 12

8x 7 16 2x 1tan Cx x 1 3 3 3

−+ +− +

+ + (b) 1

2

1 4 tan (4x 3) C3x x 1

−− + ++ +

(c) 2

2 2 2

1 (2x 1) C2(x x 1) (x x 1)

+− +

+ + + + (d) 1

2

1 2 tan (2x 1) c34(x x 1)

−+ + ++ +



India’s No. 1 Institute For JEE/PMT 31. The value of sin

1 cosα

+ α∫ d α

(a) −2 2 cos α /2 +C (b) 2 2 cos α /2 +C (c) 2 cos α /2 +C (d) − 2 cos α /2 + C

32. The value of dx5 4cos x+∫ is

(a) 11 tanxtan C3 3

− ⎛ ⎞ +⎜ ⎟⎝ ⎠

(b) 11 tanx / 2tan C3 3

− ⎛ ⎞ +⎜ ⎟⎝ ⎠

(c) 12 1tan tanx C3 3

− ⎛ ⎞ +⎜ ⎟⎝ ⎠

(d) 12 1/ 2 tan(x / 2)tan C3 3

− ⎛ ⎞ +⎜ ⎟⎝ ⎠

33. dxsinx cos x+∫ is equal to

(a) log tan (π/4+x/8) +C (b) 2 log tan (x/2+π/8 ) + C

(c) 1 logtan2

(x/2+π/8) +C (d) 2 log tan (x/4 –π/8) + C

34. The value of sec xdxsin(2x ) sin+ θ + θ∫ is

(a) (tanx tan )sec C+ θ θ + (b) 2(tanx tan )sec C+ θ θ + (c) 2(sinx tan )sec C+ θ θ + (d) none of these 35. If a < b < c < d, then the roots of the equation (x – a) (x – c) + 2 (x –b) (x – d) = 0 are (a) imaginary and same (b) real and same (c) real and distinct (d) imaginary and distinct 36. Both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are (a) positive (b) negative (c) real (d) none of these 37. The roots of ax2 + bx + c = 0; (where a ≠ 0 and the coefficients are real) are non–real complex and a + c

< b. Then (a) 4a + c > 2b (b) 4a + c < 2b (c) 4a + c = 2b (d) none of these 38. The smallest +ve integer n for which (1 + i)n is purely imaginary is (a) 2 (b) 4 (c) 8 (d) none of these 39. Which of the following is correct (a) 5 + 6i > 3 + 5i (b) 2 + 4i < 3i + 1 (c) 9 + 8i > 5 + 7i (d) none of these

40. The value of 8 8

1 I 1 i2 2− +⎛ ⎞ ⎛ ⎞

+⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

is

(a) 1 (b) 2 (c) – 2 (d) – 1 41. Let z be a complex number then the equation z4 + z + 2 = 0 can not have a root such that |z| < 1 (a) true (b) false (c) cannot say anything (d) none of these




42. If the imaginary part of 2z 1iz 1

⎛ ⎞+⎜ ⎟+⎝ ⎠

is – 2, then the locus of the point representing z in the complex plane is

(a) a circle (b) a straight line (c) a parabola (d) none of these 43. The equation | z + i | – |z – i | = k represents a hyperbola if (a) – 2 < k < 2 (b) k > 2 (c) 0 < k < 2 (d) none of these

44. If f (x) =

n 1/x

1/x

x .e ; x 01 e2 ; x 2

⎧≠⎪

+⎨⎪ = −⎩

then for n = 1, 2, 3,…………..

(a) f (x) is not continuous (b) f (x) is continuous and differentiable (c) f (x) = is continuous and differentiable if n ≥ 3 (d) f(x) is continuous but not differentiable

45. If 1 3p 1 p,3 4+ − and 1 2p

2− are the probabilities of three mutually exclusive events then the set of all values

of p is (a)[–3, 13/3] (b) [0,13/3] (c) [1/3,1/2] (d) [1/3,2/3]

46. If f (x) =

1

| x 2 | ; x 2tan (x 2)

; then f is2 ; x 2

−

+⎧ ≠ −⎪ +⎪⎪⎨⎪ = −⎪⎪⎩

(a) continuous everywhere (b) non differentiable at x = – 2 (c) neither continuous nor differentiable (d) continuous but non differentiable at x = – 2

47. If 1 2

1 2

Z Z1

1 Z Z−

=−

; then

(a) | Z 1|=1, | Z 2| = 1 (b) | Z 1| = 2 (c) | Z 2| = 2 (d) None of these 48. The number of ways in which 5 boys and 3 girls can be seated on eight seats in a row so that no two

girls sit on two consecutive seats is: (a) (6C3) (3!) (5!) (b) 2400 (c) (720) (5!) (d) none of these 49. If the third term in the expansion of ( )10

5log xx x+ is 106, then x is

(a) 10–1/3 (b) 10 (c) 10–7/2 (d) 102 50. If a,b and c are three positive real numbers, which one of the following holds? (a) a2 + b2 + c2 ≥ bc + ca + ab (b) a3 + b3 + c3 ≥ 3abc

(c) (b + c) (c + a) (a + b) ≥ 8abc (d) bc ca ab a b ca b c+ + ≥ + +

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India's No. 1 Institute For JEE/PMT