JEE Mains Aieee 2004 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The bob of a simple pendulum executes simple harmonic motion in water with a period

t,

while the period of oscillation of the bob is

{t_0}

in air. Neglecting frictional force of water and given that the density of the bob is

\left( {4/3} \right) \times 1000\,\,kg/{m^3}.

What relationship between

t

and

{t_0}

is true

A

t = 2{t_0}

B

t = {t_0}/2

C

t = {t_0}

D

t = 4{t_0}

Q 2PhysicsSection A • MCQmagnetics

+4 / -1

Two long conductors, separated by a distance

d

carry current

{I_1}

and

{I_2}

in the same direction. They exert a force

F

on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to

3d

. The new value of the force between them is

A

- {{2F} \over 3}

B

{F \over 3}

C

-2F

D

- {F \over 3}

Q 3PhysicsSection A • MCQmagnetics

+4 / -1

The magnetic field due to a current carrying circular loop of radius

3

cm

at a point on the axis at a distance of

4

cm

from the centre is

54\,\mu T.

What will be its value at the center of loop?

A

125\,\mu T

B

150\,\mu T

C

250\,\mu T

D

75\,\mu T

Q 4PhysicsSection A • MCQvector algebra

+4 / -1

If

\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A

, then the angle beetween A and B is

A

{\pi \over 2}

B

{\pi \over 3}

C

\pi

D

{\pi \over 4}

Q 5PhysicsSection A • MCQmotion

+4 / -1

A ball is thrown from a point with a speed ν₀ at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed

{{{v_0}} \over 2}

to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?

A

No

B

Yes,

30^\circ

C

Yes,

60^\circ

D

Yes,

45^\circ

Q 6PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is

2s.

The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

A

2\sqrt 3 \,s

B

{2 \over 3}\,\,s

C

2\,s

D

{2 \over {\sqrt 3 }}\,s

Q 7PhysicsSection A • MCQcurrent electricity

+4 / -1

A material

'B'

has twice the specific resistance of

'A'.

A circular wire made of

'B'

has twice the diameter of a wire made of

'A'

. Then for the two wires to have the same resistance, the ratio

{l \over B}/{l \over A}

of their respective lengths must be

A

1

B

{l \over 2}

C

{l \over 4}

D

2

Q 8PhysicsSection A • MCQproperties of matter

+4 / -1

Spherical balls of radius

R

are falling in a viscous fluid of viscosity

\eta

with a velocity

v.

The retarding viscous force acting on the spherical ball is

A

inversely proportional to both radius

R

and velocity

v

B

directly proportional to both radius

R

and velocity

v

C

directly proportional to

R

but inversely proportional to

v

D

inversely proportional to

R,

but directly proportional to velocity

v

Q 9PhysicsSection A • MCQrotational motion

+4 / -1

One solid sphere

A

and another hollow sphere

B

are of same mass and same outer radii. Their moment of inertia about their diameters are respectively

{I_A}

and

{I_B}

such that

A

{I_A} < {I_B}

B

{I_A} > {I_B}

C

{I_A} = {I_B}

D

{{{I_A}} \over {{I_B}}} = {{{d_A}} \over {{d_B}}}

where

{d_A}

and

{d_B}

are their densities.

Q 10PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Two thermally insulated vessels

1

and

2

are filled with air at temperatures

\left( {{T_1},{T_2}} \right),

volume

\left( {{V_1},{V_2}} \right)

and pressure

\left( {{P_1},{P_2}} \right)

respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A

{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \right)

B

\left( {{T_1} + {T_2}} \right)/2

C

{{T_1} + {T_2}}

D

{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)

Q 11PhysicsSection A • MCQmagnetics

+4 / -1

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is

B.

It is then bent into a circular loop of

n

turns. The magnetic field at the center of the coil will be

A

2n

B

B

{n^2}\,B

C

nB

D

2{n^2}\,B

Q 12PhysicsSection A • MCQelectrostatics

+4 / -1

A charge particle

'q'

is shot towards another charged particle

'Q'

which is fixed, with a speed

'v'

. It approaches

'Q'

upto a closest distance

r

and then returns. If

q

were given a speed of

'2v'

the closest distances of approaches would be

A

r/2

B

2r

C

r

D

r/4

Q 13PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Time taken by a

836

W

heater to heat one litre of water from

10{}^ \circ C

to

40{}^ \circ C

is

A

150

s

B

100

s

C

50

s

D

200

s

Q 14PhysicsSection A • MCQunits and measurements

+4 / -1

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A

ML^-1T^-1

B

MLT^-1

C

ML^-1T^-2

D

ML^-2T^-2

Q 15PhysicsSection A • MCQcurrent electricity

+4 / -1

The total current supplied to the circuit by the battery is qImage-kirchhoffs-circuit-laws-current-electricity-electricity-Jeemate

A

4A

B

2A

C

1A

D

6A

Q 16PhysicsSection A • MCQelectrostatics

+4 / -1

Four charges equal to -

Q

are placed at the four corners of a square and a charge

q

is at its center. If the system is in equilibrium the value of

q

is

A

- {Q \over 2}\left( {1 + 2\sqrt 2 } \right)

B

{Q \over 4}\left( {1 + 2\sqrt 2 } \right)

C

- {Q \over 4}\left( {1 + 2\sqrt 2 } \right)

D

{Q \over 2}\left( {1 + 2\sqrt 2 } \right)

Q 17PhysicsSection A • MCQray optics

+4 / -1

A plano convex lens of refractive index

1.5

and radius of curvature

30

cm

. Is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object

A

60

cm

B

30

cm

C

20

cm

D

80

cm

Q 18PhysicsSection A • MCQrotational motion

+4 / -1

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the following will not be affected ?

A

Angular velocity

B

Angular momentum

C

Moment of inertia

D

Rotational kinetic energy

Q 19PhysicsSection A • MCQalternating current

+4 / -1

In an

LCR

series

a.c.

circuit, the voltage across each of the components,

L,C

and

R

is

50V

. The voltage across the

L.C

combination will be :

A

100V

B

50\sqrt 2

C

50

V

D

0

V

(zero)

Q 20PhysicsSection A • MCQcurrent electricity

+4 / -1

The Kirchhoff's first law

\left( {\sum i = 0} \right)

and second law

\left( {\sum iR = \sum E} \right),

where the symbols have their usual meanings, are respectively based on

A

conservation of charge, conservation of momentum

B

conservation of energy, conservation of charge

C

conservation of momentum, conservation of charge

D

conservation of charge, conservation of energy

Q 21PhysicsSection A • MCQproperties of matter

+4 / -1

If two soap bubbles of different radii are connected by a tube

A

air flows from the smaller bubble to the bigger

B

air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C

air flows from the bigger bubble to the smaller bubble till the sizes become equal

D

there is no flow of air.

Q 22PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

The materials suitable for making electromagnets should have

A

high retentivity and low coercivity

B

low retentivity and low coercivity

C

high retentivity and high coercivity

D

low retentivity and high coercivity

Q 23PhysicsSection A • MCQgravitation

+4 / -1

The time period of an earth satellite in circular orbit is independent of

A

both the mass and radius of the orbit

B

radius of its orbit

C

the mass of the satellite

D

neither the mass of the satellite nor the radius of its orbit

Q 24PhysicsSection A • MCQalternating current

+4 / -1

In a

LCR

circuit capacitance is changed from

C

to

2

C

. For the resonant frequency to remain unchaged, the inductance should be changed from

L

to

A

L/2

B

2L

C

4L

D

L/4

Q 25PhysicsSection A • MCQelectrostatics

+4 / -1

A charged oil drop is suspended in a uniform field of

3 \times {10^4}

v/m

so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge

= 9.9 \times {10^{ - 15}}\,\,kg

and

g = 10\,m/{s^2}

)

A

1.6 \times {10^{ - 18}}\,C

B

3.2 \times {10^{ - 18}}\,C

C

3.3 \times {10^{ - 18}}\,C

D

4.8 \times {10^{ - 18}}\,C

Q 26PhysicsSection A • MCQmotion

+4 / -1

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A

60 m

B

40 m

C

20 m

D

80 m

Q 27PhysicsSection A • MCQcurrent electricity

+4 / -1

Thermistors are usually made of

A

metal oxides with high temperature coefficient of resistivity

B

metals with high temperature coefficient of resistivity

C

metals with low temperature coefficient of resistivity

D

semiconducting materials having low temperature

Q 28PhysicsSection A • MCQwork power and energy

+4 / -1

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement

x

is proportional to

A

x

B

{e^x}

C

{x^2}

D

{\log _e}x

Q 29PhysicsSection A • MCQwork power and energy

+4 / -1

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

A

its kinetic energy is constant

B

is acceleration is constant

C

its velocity is constant

D

it moves in a straight line

Q 30PhysicsSection A • MCQgravitation

+4 / -1

A satellite of mass

m

revolves around the earth of radius

R

at a height

x

from its surface. If

g

is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

A

{{g{R^2}} \over {R + x}}

B

{{gR} \over {R - x}}

C

{gx}

D

{\left( {{{g{R^2}} \over {R + x}}} \right)^{1/2}}

Q 31PhysicsSection A • MCQmotion

+4 / -1

A projectile can have the same range 'R' for two angles of projection. If T₁ and T₂ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

A

R

B

{1 \over R}

C

{1 \over {{R^2}}}

D

{R^2}

Q 32PhysicsSection A • MCQheat and thermodynamics

+4 / -1

One mole of ideal monatomic gas

\left( {\gamma = 5/3} \right)

is mixed with one mole of diatomic gas

\left( {\gamma = 7/5} \right)

. What is

\gamma

for the mixture?

\gamma

Denotes the ratio of specific heat at constant pressure, to that at constant volume

A

35/23

B

23/15

C

3/2

D

4/3

Q 33PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A coil having

n

turns and resistance

R\Omega

is connected with a galvanometer of resistance

4R\Omega .

This combination is moved in time

t

seconds from a magnetic field

{W_1}

weber to

{W_2}

weber. The induced current in the circuit is

A

{{\left( {{W_2} - {W_1}} \right)} \over {Rnt}}

B

- {{n\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rt}}

C

- {{\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rnt}}

D

- {{n\left( {{W_2} - {W_1}} \right)} \over {Rt}}

Q 34PhysicsSection A • MCQcenter of mass

+4 / -1

A machine gun fires a bullet of mass

40

g

with a velocity

1200m{s^{ - 1}}.

The man holding it can exert a maximum force of

144

N

on the gun. How many bullets can he fire per second at the most?

A

Two

B

Four

C

One

D

Three

Q 35PhysicsSection A • MCQcurrent electricity

+4 / -1

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of

{4 \over 3}

and

{2 \over 3}

, then the ratio of the current passing through the wires will be

A

8/9

B

1/3

C

3

D

2

Q 36PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Which of the following statements is correct for any thermodynamic system ?

A

The change in entropy can never be zero

B

Internal energy and entropy and state functions

C

The internal energy changes in all processes

D

The work done in an adiabatic process is always zero,

Q 37PhysicsSection A • MCQsimple harmonic motion

+4 / -1

A particle at the end of a spring executes

S.H.M

with a period

{t_1}

. While the corresponding period for another spring is

{t_2}

. If the period of oscillation with the two springs in series is

T

then

A

{T^{ - 1}} = t_1^{ - 1} + t_2^{ - 1}

B

{T^2} = t_1^2 + t_2^2

C

T = {t_1} + {t_2}

D

{T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}

Q 38PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The total energy of particle, executing simple harmonic motion is

A

independent of

x

B

\propto \,{x^2}

C

\propto \,x

D

\propto \,{x^{1/2}}

Q 39PhysicsSection A • MCQheat and thermodynamics

+4 / -1

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity

K

and

2K

and thickness

x

and

4x,

respectively, are

{T_2}

and

{T_1}\left( {{T_2} > {T_1}} \right).

The rate of heat transfer through the slab, in a steady state is

\left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f,

with

f

equal to

qImage-heat-transfer-heat-and-thermodynamics-mechanics-Jeemate

A

{2 \over 3}

B

{1 \over 2}

C

1

D

{1 \over 3}

Q 40PhysicsSection A • MCQcurrent electricity

+4 / -1

In a meter bridge experiment null point is obtained at

20

cm

, from one end of the wire when resistance

X

is balanced against another resistance

Y.

If

X < Y

, then where will be the new position of the null point from the same end, if one decides to balance a resistance of

4

X

against

Y

A

40

cm

B

80

cm

C

50

cm

D

70

cm

Q 41PhysicsSection A • MCQelectromagnetic induction

+4 / -1

In a uniform magnetic field of induction

B

a wire in the form of a semicircle of radius

r

rotates about the diameter of the circle with an angular frequency

\omega .

The axis of rotation is perpendicular to the field. If the total resistance of the circuit is

R,

the mean power generated per period of rotation is

A

{{{{\left( {B\pi r\omega } \right)}^2}} \over {2R}}

B

{{{{\left( {B\pi {r^2}\omega } \right)}^2}} \over {8R}}

C

{{B\pi {r^2}\omega } \over {2R}}

D

{{{{\left( {B\pi r{\omega ^2}} \right)}^2}} \over {8R}}

Q 42PhysicsSection A • MCQgravitation

+4 / -1

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius

R

around the sun will be proportional to

A

{R^n}

B

{R^{\left( {{{n - 1} \over 2}} \right)}}

C

{R^{\left( {{{n + 1} \over 2}} \right)}}

D

{R^{\left( {{{n - 2} \over 2}} \right)}}

Q 43PhysicsSection A • MCQmotion

+4 / -1

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in

{T \over 3}

seconds?

A

{{8h} \over 9}

meters from the ground

B

{{7h} \over 9}

meters from the ground

C

{h \over 9}

meters from the ground

D

{{7h} \over {18}}

meters from the ground

Q 44PhysicsSection A • MCQwork power and energy

+4 / -1

A force

\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N

is applied over a particle which displaces it from its origin to the point

\overrightarrow r = \left( {2\overrightarrow i - \overrightarrow j } \right)m.

The work done on the particle in joules is

A

+10

B

+7

C

-7

D

+13

Q 45PhysicsSection A • MCQalternating current

+4 / -1

Alternating current can not be measured by

D.C.

ammeter because

A

Average value of current for complete cycle is zero

B

A.C.

Changes direction

C

A.C.

can not pass through

D.C.

Ammeter

D

D.C.

Ammeter will get damaged.

Q 46PhysicsSection A • MCQlaws of motion

+4 / -1

Two masses

{m_1} = 5kg

and

{m_2} = 4.8kg

tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move?

\left( {g = 9.8m/{s^2}} \right)

qImage-motion-of-connected-bodies-laws-of-motion-mechanics-Jeemate

A

5\,\,m/{s^2}

B

9.8\,\,m/{s^2}

C

0.2\,\,m/{s^2}

D

4.8\,\,m/{s^2}

Q 47PhysicsSection A • MCQheat and thermodynamics

+4 / -1

If the temperature of the sun were to increase from

T

to

2T

and its radius from

R

to

2R

, then the ratio of the radiant energy received on earth to what it was previously will be

A

32

B

16

C

4

D

64

Q 48PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

Curie temperature is the temperature above which

A

a ferromagnetic material becomes paramagnetic

B

a paramagnetic material becomes diamagnetic

C

a ferromagnetic material becomes diamagnetic

D

a paramagnetic material becomes ferromagnetic

Q 49PhysicsSection A • MCQelectrostatics

+4 / -1

Two spherical conductors

B

and

C

having equal radii and carrying equal charges on them repel each other with a force

F

when kept apart at some distance. A third spherical conductor having same radius as that

B

but uncharged is brought in contact with

B,

then brought in correct with

C

and finally removed away from both. The new force of repulsion between

B

and

C

is

A

F/8

B

3

F/4

C

F/4

D

3

F/8

Q 50PhysicsSection A • MCQlaws of motion

+4 / -1

A block rests on a rough inclined plane `making an angle of

{30^ \circ }

with the horizontal. The coefficient of static friction between the block and the plane is

0.8.

If the frictionless force on the block is

10

N,

the mass of the block (in

kg

) is

\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)

A

1.6

B

4.0

C

2.0

D

2.5

Q 51PhysicsSection A • MCQwork power and energy

+4 / -1

A uniform chain of length

2

m

is kept on a table such that a length of

60

cm

hangs freely from the edge of the table. The total mass of the chain is

4

kg.

What is the work done in pulling the entire chain on the table?

A

12

J

B

3.6

J

C

7.2

J

D

1200

J

Q 52PhysicsSection A • MCQwave optics

+4 / -1

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index

n

) is :

A

{\tan ^{ - 1}}\left( {1/n} \right)

B

{\sin ^{ - 1}}\left( {1/n} \right)

C

{\sin ^{ - 1}}\left( n \right)

D

{\tan ^{ - 1}}\left( n \right)

Q 53PhysicsSection A • MCQwave optics

+4 / -1

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is :

A

three

B

five

C

infinite

D

zero

Q 54PhysicsSection A • MCQwaves

+4 / -1

The displacement

y

of a particle in a medium can be expressed as,

y = {10^{ - 6}}\,\sin

\left( {100t + 20x + {\pi \over 4}} \right)

m

where

t

is in second and

x

in meter. The speed of the wave is

A

20\,\,m/s

B

5\,m/s

C

2000\,m/s

D

5\,\pi \,m/s

Q 55PhysicsSection A • MCQwork power and energy

+4 / -1

A body of mass

' m ',

acceleration uniformly from rest to

'{v_1}'

in time

{T}

. The instantaneous power delivered to the body as a function of time is given by

A

{{m{v_1}{t^2}} \over {{T}}}

B

{{mv_1^2t} \over {T^2}}

C

{{m{v_1}t} \over {{T}}}

D

{{mv_1^2t} \over {{T}}}

Q 56PhysicsSection A • MCQcircular motion

+4 / -1

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

A

The velocity vector is tangent to the circle.

B

The acceleration vector is tangent to the circle.

C

The acceleration vector points to the centre of the circle.

D

The velocity and acceleration vectors are perpendicular to each other.

Q 57PhysicsSection A • MCQsimple harmonic motion

+4 / -1

In forced oscillation of a particle the amplitude is maximum for a frequency

{\omega _1}

of the force while the energy is maximum for a frequency

{\omega _2}

of the force; then

A

{\omega _1} < {\omega _2}

when damping is small and

{\omega _1} > {\omega _2}

when damping is large

B

{\omega _1} > {\omega _2}

C

{\omega _1} = {\omega _2}

D

{\omega _1} < {\omega _2}

Q 58PhysicsSection A • MCQmagnetics

+4 / -1

A current

i

ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A

{{{\mu _0}} \over {4\pi }},{{2i} \over r}

tesla

B

zero

C

infinite

D

{{2i} \over r}

tesla

Q 59PhysicsSection A • MCQcurrent electricity

+4 / -1

The resistance of the series combination of two resistances is

S.

When they are jointed in parallel the total resistance is

P.

If

S = nP

then the Minimum possible value of

n

is

A

2

B

3

C

4

D

1

Q 60PhysicsSection A • MCQcurrent electricity

+4 / -1

The thermo

emf

of a thermocouple varies with temperature

\theta

of the hot junction as

E = a\theta + b{\theta ^2}

in volts where the ratio

a/b

is

{700^ \circ }C.

If the cold junction is kept at

{0^ \circ }C,

then the neutral temperature is

A

{1400^ \circ }C

B

{350^ \circ }C

C

{700^ \circ }C

D

No neutral temperature is possible for this termocouple.

Q 61PhysicsSection A • MCQelectromagnetic waves

+4 / -1

An electromagnetic wave of frequency

v=3.0

MHz

passes from vacuum into a dielectric medium with permittivity

\in = 4.0.

Then

A

wave length is halved and frequency remains unchanged

B

wave length is doubled and the frequency becomes half

C

wave length is doubled and the frequency remains unchanged

D

wave length and frequency both remain unchanged.

Q 62PhysicsSection A • MCQgravitation

+4 / -1

If

g

is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass

m

raised from the surface of the earth to a height equal to the radius

R

of the earth is

A

{1 \over 4}mgR

B

2mgR

C

{1 \over 2}mgR

D

mgR

Q 63PhysicsSection A • MCQproperties of matter

+4 / -1

A wire fixed at the upper end stretches by length

l

by applying a force

F.

The work done in stretching is

A

2Fl

B

Fl

C

{F \over {2l}}

D

{{Fl} \over 2}

Q 64PhysicsSection A • MCQsimple harmonic motion

+4 / -1

A particle of mass

m

is attached to a spring (of spring constant

k

) and has a natural angular frequency

{\omega _0}.

An external force

F(t)

proportional to

\cos \,\omega t\left( {\omega \ne {\omega _0}} \right)

is applied to the oscillator. The time displacement of the oscillator will be proportional to

A

{1 \over {m\left( {\omega _0^2 + {\omega ^2}} \right)}}

B

{1 \over {m\left( {\omega _0^2 - {\omega ^2}} \right)}}

C

{m \over {\omega _0^2 - {\omega ^2}}}

D

{m \over {\omega _0^2 + {\omega ^2}}}

Q 65PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A metal conductor of length

1

m

rotates vertically about one of its ends at angular velocity

5

radians per second. If the horizontal component of earth's magnetic field is

0.2 \times {10^{ - 4}}T,

then the

e.m.f.

developed between the two ends of the conductor is

A

5mV

B

50\mu V

C

5\mu V

D

50mV

Q 66PhysicsSection A • MCQcurrent electricity

+4 / -1

The electrochemical equivalent of a metal is

{3.35109^{ - 7}}

kg

per Coulomb. The mass of the metal liberated at the cathode when a

3A

current is passed for

2

seconds will be

A

6.6 \times {10^{57}}/kg

B

9.9 \times {10^{ - 7}}\,kg

C

19.8 \times {10^{ - 7}}\,kg

D

1.1 \times {10^{ - 7}}\,kg

Q 67PhysicsSection A • MCQelectronic devices

+4 / -1

When

npn

transistor is used as an amplifer

A

electrons move from collector to base

B

holes move from emitter to base

C

electrons move from base to collector

D

holes move from base to emitter

Q 68PhysicsSection A • MCQatoms and nuclei

+4 / -1

An

\alpha

-particle of energy

5

MeV

is scattered through

{180^ \circ }

by a fixed uranium nucleus. The distance of closest approach is of the order of

A

{10^{ - 12}}\,cm

B

{10^{ - 10}}\,cm

C

1A

D

{10^{ - 15a}}\,cm

Q 69PhysicsSection A • MCQelectromagnetic waves

+4 / -1

A radiation of energy

E

falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

A

Ec

B

2E/c

C

E/c

D

E/{c^2}

Q 70PhysicsSection A • MCQatoms and nuclei

+4 / -1

The binding energy per nucleon of deuteron

\left( {{}_1^2\,H} \right)

and helium nucleus

\left( {{}_2^4\,He} \right)

is

1.1

MeV

and

7

MeV

respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

A

23.6\,\,MeV

B

26.9\,\,MeV

C

13.9\,\,MeV

D

19.2\,\,MeV

Q 71PhysicsSection A • MCQelectronic devices

+4 / -1

For a transistor amplifier in common emitter configuration for load impedance of

1k\,\Omega

\left( {{h_{fe}} = 50} \right.

and

\left. {{h_{oe}} = 25} \right)

the current gain is

A

-24.8

B

-15.7

C

-5.2

D

-48.78

Q 72PhysicsSection A • MCQatoms and nuclei

+4 / -1

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of

2:1.

The ratio of their nuclear sizes will be

A

{3^{{\raise0.5ex\hbox{

B

1:{2^{1/3}}

C

{2^{1/3}}:1

D

1:{3^{{\raise0.5ex\hbox{

Q 73PhysicsSection A • MCQelectronic devices

+4 / -1

A piece of copper and another of germanium are cooled from room temperature to

77K,

the resistance of

A

copper increases and germanium decreases

B

each of them decreases

C

each of them increases

D

copper decreases and germanium increases

Q 74PhysicsSection A • MCQdual nature of radiation

+4 / -1

The work function of a substance is

4.0

eV.

The longest wavelength of light that can cause photo-electron emission from this substance is approximately.

A

310

nm

B

400

nm

C

540

nm

D

220

nm

Q 75PhysicsSection A • MCQdual nature of radiation

+4 / -1

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal

Vs

the frequency, of the incident radiation gives as straight the whose slope

A

depends both on the intensity of the radiation and the metal used

B

depends on the intensity of the radiation

C

depends on the nature of the metal used

D

is the same for the all metals and independent of the intensity of the radiation

Q 76PhysicsSection A • MCQelectronic devices

+4 / -1

The manifestation of band structure in solids is due to

A

Bohr's correspondence principle

B

Pauli's exclusion principle

C

Heisenberg's uncertainty principle

D

Boltzmann's law

Q 77PhysicsSection A • MCQray optics

+4 / -1

A light ray is incident perpendicularly to one face of a

{90^ \circ }

prism and is totally internally reflected at the glass-air interface. If the angle of reflection is

{45^ \circ }

, we conclude that the refractive index

n

$qImage-refraction-tir-and-prism-geometrical-optics-optics-Jeemate$

A

n > {1 \over {\sqrt 2 }}

B

n > \sqrt 2

C

n < {1 \over {\sqrt 2 }}

D

n < \sqrt 2

Q 78PhysicsSection A • MCQelectronic devices

+4 / -1

When

p

-

n

junction diode is forward biased then

A

both the depletion region and barrier height are reduced

B

the depletion region is widened and barrier height is reduced

C

the depletion region is reduced and barrier height is increased

D

both the depletion region and barrier height are increased

Q 79ChemistrySection A • MCQatomic structure

+4 / -1

Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 are respectively

A

16 and 4

B

12 and 5

C

12 and 4

D

16 and 5

Q 80ChemistrySection A • MCQchemical equilibrium

+4 / -1

What is the equilibrium expression for the reaction
P₄ (s) + 5O₂

\leftrightharpoons

P₄O₁₀ (s)?

A

K_c = [P₄O₁₀] / 5[P₄] [O₂]

B

K_c = 1/[O₂]⁵

C

K_c = [P₄O₁₀] / [P₄] [O₂]⁵

D

K_c = [O₂]⁵

Q 81ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

6.02

\times

10²⁰ molecules of urea are present in 100 ml of its solution. The concentration of urea solution is
(Avogadro constant, N_A = 6.02

\times

10²³ mol^-1)

A

0.02 M

B

0.01 M

C

0.001 M

D

0.1 M

Q 82ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is

A

urea

B

benzamide

C

acetamide

D

thiourea

Q 83ChemistrySection A • MCQbiomolecules

+4 / -1

Identify the correct statements regarding enzymes

A

Enzymes are specific biological catalysts that can normally function at very high temperature (T ~ 1000 K)

B

Enzymes are specific biological catalysts that the posses well – defined active sites

C

Enzymes are specific biological catalysts that can not be poisoned

D

Enzymes are normally heterogeneous catalysts that are very specific in their action

Q 84ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following compound is not chiral?

A

1- chloropentane

B

3-chloro-2- methyl pentane

C

1-chloro -2- methyl pentane

D

2- chloropentane

Q 85ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The states of hybridization of boron and oxygen atoms in boric acid (H₃BO₃) are respectively

A

sp² and sp²

B

sp³ and sp³

C

sp³ and sp²

D

sp² and sp³

Q 86ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is

A

gammexene

B

hexachloroethane

C

Freon

D

DDT

Q 87ChemistrySection A • MCQcoordination compounds

+4 / -1

The coordination number of central metal atom in a complex is determined by :

A

the number of ligands around a metal ion bonded by sigma bonds

B

the number of only anionic ligands bonded to the metal ion

C

the number of ligands around a metal ion bonded by sigma and pi- bonds both

D

the number of ligands around a metal ion bonded by pi-bonds

Q 88ChemistrySection A • MCQd and f block elements

+4 / -1

Excess of KI reacts with CuSO₄ solution and then Na₂S₂O₃ solution is added to it. Which of the statements is incorrect for this reaction?

A

Cu₂I₂ is reduced

B

Evolved I₂ is reduced

C

Na₂S₂O₃ is oxidized

D

CuI₂ is formed

Q 89ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Among the following compounds which can be dehydrated very easily is

A

qImage-properties-preparation-and-uses-of-alcohols-alcohols-phenols-and-ethers-organic-chemistry-Jeemate

B

C

D

Q 90ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The correct order of bond angles (smallest first) in H₂S, NH₃, BF₃ and SiH₄ is

A

H₂S < SiH₄ < NH₃ < BF₃

B

H₂S < NH₃ < BF₃ < SiH₄

C

H₂S < NH₃ < SiH₄ < BF₃

D

NH₃ < H₂S < SiH₄ < BF₃

Q 91ChemistrySection A • MCQp block elements

+4 / -1

Which among the following factors is the most important in making fluorine the strongest oxidizing halogen?

A

Electron affinity

B

Bond dissociation energy

C

Hydration enthalpy

D

Ionization enthalpy

Q 92ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

The rate equation for the reaction 2A + B

\to

C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that the

A

unit of K must be s^-1

B

values of k is independent of the initial concentration of A and B

C

rate of formation of C is twice the rate of disappearance of A

D

t_1/2 is a constant

Q 93ChemistrySection A • MCQionic equilibrium

+4 / -1

The molar solubility (in ol L^-1) of a sparingly soluble salt MX₄ is "s". The corresponding solubility product is K_sp. 's' is given in term of K_sp by the relation :

A

s = (256 K_sp)^1/5

B

s = (128 K_sp)^1/4

C

s = ( K_sp / 128)^1/4

D

s = (K_sp / 256)^1/5

Q 94ChemistrySection A • MCQp block elements

+4 / -1

Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in :

A

exhibiting maximum covalency in compound

B

exhibiting amphoteric nature in their oxides

C

forming covalent halides

D

forming polymeric hydrides

Q 95ChemistrySection A • MCQcoordination compounds

+4 / -1

The correct order of magnetic moments (spin only values in B.M.) among is :
(Atomic numbers: Mn = 25; Fe = 26, Co =27)

A

[MnCl₄]^2- > [CoCl₄]^-2 > [Fe(CN)₆]^-4

B

[Fe(CN)₆]^-4 > [CoCl₄]^2- > [MnCl₄]^2-

C

[Fe(CN)₆]^4- > [MnCl₄]^2- > [CoCl₄]^2-

D

[MnCl₄]^2- > [Fe(CN)₆]^4- > [CoCl₄]^2-

Q 96ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following is the strongest base ?

A

qImage-acid-and-base-strength-basics-of-organic-chemistry-organic-chemistry-Jeemate

B

C

D

Q 97ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following will have meso-isomer also?

A

2- chlorobutane

B

2- hydroxyopanoic acid

C

2,3 – dichloropentane

D

2-3- dichlorobutane

Q 98ChemistrySection A • MCQatomic structure

+4 / -1

Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

A

n = 4, l = 3, m = +1, s = + 1/2

B

n = 4, l = 4, m = -4, s = - 1/2

C

n = 4, l = 3, m = +4, s = + 1/2

D

n = 3, l = 2, m = -2, s = + 1/2

Q 99ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

A

30 minutes

B

60 minutes

C

7.5 minutes

D

15 minutes

Q 100ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

Consider the following nuclear reactions

{}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He

{}_Y^XN \to {}_B^AL + 2{\beta ^ + }

The number of neutrons in the element L is

A

140

B

144

C

142

D

146

Q 101ChemistrySection A • MCQsolutions

+4 / -1

Which one of the following aqueous solutions will exhibit highest boiling point?

A

0.01 M Na₂SO₄

B

0.015 M glucose

C

0.015 M urea

D

0.01 M KNO₃

Q 102ChemistrySection A • MCQsolutions

+4 / -1

Which of the following liquid pairs shows a positive deviation from Raoult’s law?

A

Water – hydrochloric acid

B

Acetone – chloroform

C

Water – nitric acid

D

Benzene – methanol

Q 103ChemistrySection A • MCQperiodic classification of elements

+4 / -1

The formation of the oxide ion O^2-(g) requires first an exothermic and then an endothermic step as shown below

O_(g) + e^- =

O_{(g)}^{-}

\Delta

H^o = -142 kJmol^-1

O_{(g)}^{-}

+ e^- =

O_{(g)}^{2-}

\Delta

H^o = 844 kJmol^-1

This because

A

O^- ion will tend to resist the addition of another electron

B

Oxygen has high electron affinity

C

Oxygen is more electronegative

D

O^- ion has comparatively larger size than oxygen atom

Q 104ChemistrySection A • MCQelectrochemistry

+4 / -1

In a cell that utilises the reaction Zn(s) + 2H⁺ (aq)

\to

Zn2+(aq) + H2(g) addition of H₂SO₄ to cathode compartment, will

A

lower the E and shift equilibrium to the left

B

increases the E and shift equilibrium to the left

C

increase the E and shift equilibrium to the right

D

Lower the E and shift equilibrium to the right

Q 105ChemistrySection A • MCQp block elements

+4 / -1

Which one the following statement regarding helium is incorrect?

A

It is used to fill gas balloons instead of hydrogen because it is lighter and non–inflammable

B

It is used in gas – cooled nuclear reactors

C

It is used to produce and sustain powerful superconducting reagents

D

It is used as cryogenic agent for carrying out experiments at low temperatures

Q 106ChemistrySection A • MCQcoordination compounds

+4 / -1

Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect?

A

Chlorophylls are green pigments in plants and contains calcium

B

Carboxypeptidase – A is an enzyme and contains zinc

C

Cyanocobalamin is B₁₂ and contains cobalt

D

Haemoglobin is the red pigment of blood and contains iron

Q 107ChemistrySection A • MCQchemical equilibrium

+4 / -1

For the reaction, CO(g) + Cl₂(g)

\leftrightharpoons

COCl₂(g) the

{{{K_p}} \over {{K_c}}}

is equal to :

A

\sqrt {RT}

B

RT

C

1/RT

D

1.0

Q 108ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Which one of the following ions has the highest value of ionic radius?

A

O^2-

B

B³⁺

C

Li⁺

D

F^-

Official Correct Answer:Option (A)

Step-by-Step Solution:

From a neutral atom where a electron is removed then it become cation and when a electron is added to the atom then it becomes anion.

For a atom

x

when it loose a electron then it becomes cation

x - {e^ - } \to {x^ + }

Let atomic no. of

x

is

z

then no. of proton in

{x^ + } = z

and no. of electron in

{x^ + } = z - 1

So the ratio

{z \over e}

as no. of electrons decreases. And when no of electron decreases then per electron attraction increases from nucleus and radius of cation deceases.

Similarly when atom

x

becomes

{x^ - }

by adding a electron

\left( {x + {e^ - } \to {x^ - }} \right)

then no. of proton in

{x^ - } = z

and no. of electron in

{x^ - } = z + 1.

Now the ratio of

{z \over e}\,\,

in

{x^ - }

decreases as no. of electron increases. As electron increases in

{x^ - }

then attraction from nucleus decreases on per electron and the distance between electron and nucleus increases so the radius also increase in anion.

All

4

ions are from second period and for

{O^{2 - }}\,\,

and

{F^ - }

both have

1s,

2s

and

2p

shell and for

L{i^ + }\,\,

and

{B^{3 + }}

both have

1s

shell.

So, size of

{O^{2 - }}\,\,\,

and

\,\,\,{F^ - }\,\,\,

are more then

L{i^ + }\,\,\,\,

and

\,\,\,\,{B^{3 + }}

and among

{O^{2 - }}\,\,\,

and

\,\,\,\,{F^ - }

For

\,\,\,

{O^{2 - }},\,\,{z \over e} = {8 \over {10}} = 0.8

For

\,\,\,

{F^ - },\,\,\,{z \over e} = {9 \over {10}} = 0.9

as for

{O^{2 - }},\,\,{z \over e}\,\,\,

is less so per electron attraction from nucleus decreases and radius increases more than

{F^ - }.

Q 109ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The

IUPAC

name of the compound is

qImage-iupac-nomenclature-basics-of-organic-chemistry-organic-chemistry-Jeemate

A

3,3

-dimethyl -

1

- cyclohexanol

B

1,1

-dimethyl-

3

-hydroxy cyclohexane

C

3,3

-dimethyl-

1

-hydroxy cyclohexane

D

1,1

-dimethyl -

3

- cyclohexanol

Q 110ChemistrySection A • MCQelectrochemistry

+4 / -1

The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25^oC. The equilibrium constant of the reaction is (F = 96,500 C mol^-1: R = 8.314 JK^-1 mol^-1)

A

1.0

\times

10¹

B

1.0

\times

10³⁰

C

1.0

\times

10¹⁰

D

1.0

\times

10⁵

Q 111ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?

A

Ethyl acetate

B

Butan -2-one

C

Acetamide

D

Acetic acid

Q 112ChemistrySection A • MCQisolation of elements

+4 / -1

Which one of the following ores is best concentrated by froth – floatation method?

A

Magnetite

B

Malachite

C

Galena

D

Cassiterite

Q 113ChemistrySection A • MCQd and f block elements

+4 / -1

Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

A

\left( {n - 1} \right){d^3}n{s^2}

B

\left( {n - 1} \right){d^5}n{s^1}

C

\left( {n - 1} \right){d^8}n{s^2}

D

\left( {n - 1} \right){d^5}n{s^2}

Q 114ChemistrySection A • MCQcoordination compounds

+4 / -1

Which one of the following complexes in an outer orbital complex?

A

[Fe(CN)₆]^4-

B

[Ni(NH₃)₆]²⁺

C

[Co(NH₃)₆]³⁺

D

[Mn(CN)₆]^4-

Q 115ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H₃PO₃), the volume of 0.1 M aqueous KOH solution required is

A

40 mL

B

20 mL

C

10 mL

D

60 mL

Q 116ChemistrySection A • MCQp block elements

+4 / -1

Aluminium chloride exists as dimer, Al₂Cl₆ in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives :

A

Al3⁺ + 3Cl^-

B

Al₂O₃ + 6HCl

C

[Al(OH)₆]^3-

D

[Al(H₂O)₆]³⁺ + 3Cl^-

Q 117ChemistrySection A • MCQpractical organic chemistry

+4 / -1

The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is

A

Fe₄[Fe(CN)₆]₃

B

Na₄[Fe(CN)₅NOS]

C

Fe(CN)₃

D

Na₃[Fe(CN)₆]

Q 118ChemistrySection A • MCQd and f block elements

+4 / -1

Cerium (Z = 58) is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?

A

The common oxidation states of cerium are +3 and +4

B

Cerium (IV) acts as an oxidizing agent

C

The +4 oxidation state of cerium is not known in solutions

D

The +3 oxidation state of cerium is more stable than the +4 oxidation state

Q 119ChemistrySection A • MCQthermodynamics

+4 / -1

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1 respectively. The enthalpy of formation of carbon monoxide per mole is :

A

110.5 kJ

B

-110.5 kJ

C

-676.5 kJ

D

676.5 kJ

Q 120ChemistrySection A • MCQcoordination compounds

+4 / -1

Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

A

[Ru(NH₃)₄Cl₂]⁺

B

[Co(en)₂Cl₂]⁺

C

[Ir(PR₃)₂ H(CO)]²⁺

D

[Co(NH₃)₅Cl]²⁺

Q 121ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is

A

CH₃COOC₂H₅ + NaCl

B

CH₃Cl + C₂H₅COONa

C

CH₃COCl + C₂H₅OH + NaOH

D

CH₃COONa + C₂H₅OH

Q 122ChemistrySection A • MCQsolutions

+4 / -1

For which of the following parameters the structural isomers C₂H₅OH and CH₃OCH₃ would be expected to have the same values? (Assume ideal behaviour)

A

Heat of vaporization

B

Gaseous densities at the same temperature and pressure

C

Boiling points

D

Vapour pressure at the same temperature

Q 123ChemistrySection A • MCQsolid state

+4 / -1

What type of crystal defect is indicated in the diagram below?

qImage-defects-in-crystal-solid-state-physical-chemistry-Jeemate

A

Interstitial defect

B

Schottky defect

C

Frenkel defect

D

Frenkel and Schottky defects

Q 124ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Rate of the reaction

qImage-electron-displacement-effect-basics-of-organic-chemistry-organic-chemistry-Jeemate

is fastest when

Z

is

A

O{C_2}{H_5}

B

N{H_2}

C

Cl

D

OCOC{H_3}

Q 125ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

A

1.042 g

B

4.167 g

C

3.125 g

D

2.084 g

Q 126ChemistrySection A • MCQelectrochemistry

+4 / -1

The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm² mol^-1 respectively. The Λ° for NaBr is

A

128 S cm² mol^-1

B

278 S cm² mol^-1

C

176 S cm² mol^-1

D

302 S cm² mol^-1

Q 127ChemistrySection A • MCQelectrochemistry

+4 / -1

Consider the following E^o values

E_{F{e^{3 + }}/F{e^{2 + }}}^o

= 0.77 V;

E_{S{n^{2 + }}/S{n}}^o

= -0.14 V

Under standard conditions the potential for the reaction

Sn(s) + 2Fe³⁺(aq)

\to

2Fe²⁺(aq) + Sn²⁺(aq) is :

A

1.68 V

B

0.63 V

C

0.91 V

D

1.40 V

Q 128ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The bond order in NO is 2.5 while that in NO⁺ is 3. Which of the following statements is true for these two species?

A

Bond length in NO⁺ is greater than in NO

B

Bond length is unpredictable

C

Bond length in NO⁺ in equal to that in NO

D

Bond length in NO is greater than in NO⁺

Q 129ChemistrySection A • MCQp block elements

+4 / -1

The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey power. The transformation is related to :

A

a change in the partial pressure of oxygen in the air

B

a change in the crystalline structure of tin

C

an interaction with nitrogen of the air at very low temperature

D

an interaction with water vapor contained in the humid air

Q 130ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The maximum number of 90° angles between bond pair of electrons is observed in

A

dsp³ hybridization

B

sp³d² hybridization

C

dsp² hybridization

D

sp³d hybridization

Q 131ChemistrySection A • MCQsolutions

+4 / -1

Which one of the following statements is false?

A

Raoult’s law states that the vapour pressure of a components over a solution is proportional to its mole fraction

B

Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression

C

The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is BaCl₂ > KCl > CH₃COOH > sucrose

D

The osmotic pressure (

\pi

) = MRT, where M is the molarity of the solution

Q 132ChemistrySection A • MCQchemical equilibrium

+4 / -1

The equilibrium constant for the reaction N₂(g) + O₂(g)

\leftrightharpoons

2NO(g) at temperature T is 4

\times

10^-4. The value of K_c for the reaction NO(g)

\leftrightharpoons

1 \over 2

N₂ (g) +

1 \over 2

O₂ (g) at the same temperature is :

A

2.5

\times

10²

B

4

\times

10^-4

C

50

D

0.02

Q 133ChemistrySection A • MCQs block elements

+4 / -1

One mole of magnesium nitride on the reaction with an excess of water gives :

A

one mole of ammonia

B

two moles of nitric acid

C

two moles of ammonia

D

one mole of nitric acid

Q 134ChemistrySection A • MCQatomic structure

+4 / -1

Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 17, Na = 11, Mg = 12, Al = 13, K = 19, Ca = 20, Sc = 21)

A

K⁺, Cl^-, Mg²⁺, Sc³⁺

B

Na⁺, Ca²⁺, Sc³⁺, F^-

C

K⁺, Ca²⁺, Sc³⁺, Cl^-

D

Na⁺, Mg²⁺, Al³⁺, Cl^-

Official Correct Answer:Option (C)

Step-by-Step Solution:

Isoelectronic means those species whose no of electrons are same.

Ions	Atomic No	No of Electron
K⁺	19	19-1=18
Ca⁺²	20	20-2=18
Sc⁺³	21	21-3=18
Cl^-	17	17+1=18

So, option

(C)

is correct.

Q 135ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Amongst the following compounds, the optically active alkane having lowest molecular mass is

A

qImage-isomerism-basics-of-organic-chemistry-organic-chemistry-Jeemate

B

C

D

Q 136ChemistrySection A • MCQcoordination compounds

+4 / -1

Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN^– ion towards metal species is :

A

c, a

B

b, c

C

a, b

D

a, b, c

Q 137ChemistrySection A • MCQionic equilibrium

+4 / -1

The conjugate base of H₂PO₄^- is :

A

PO_4^{3-}

B

HPO_4^{2-}

C

H₃PO₄

D

P₂O₅

Q 138ChemistrySection A • MCQbiomolecules

+4 / -1

Which base is present in RNA but not in DNA?

A

Uracil

B

Thymine

C

Guanine

D

Cytosine

Q 139ChemistrySection A • MCQhydrocarbons

+4 / -1

Which one of the following has the minimum boiling point?

A

n-butane

B

isobutane

C

1- butene

D

1- butyne

Q 140ChemistrySection A • MCQenvironmental chemistry

+4 / -1

The smog is essentially caused by the presence of :

A

O₂ and O₃c

B

O₃ and N₂

C

Oxides of sulphur and nitrogen

D

O₂ and N₂

Q 141ChemistrySection A • MCQelectrochemistry

+4 / -1

The

E_{{M^{3 + }}/{M^{2 + }}}^o

values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V respectively. For which one of these metals the change in oxidation state form +2 to +3 is easiest?

A

Fe

B

Mn

C

Cr

D

Co

Q 142ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Among Al₂O₃, SiO₂, P₂O₃ and SO₂ the correct order of acid strength is

A

SO₂ < P₂O₃ < SiO₂ < Al₂O₃

B

Al₂O₃ < SiO₂ < _P2O₃ < SO₂

C

Al₂O₃ < SiO₂ < SO₂ < P₂O₃

D

SiO₂ < SO₂ < Al₂O₃ < P₂O₃

Q 143ChemistrySection A • MCQelectrochemistry

+4 / -1

In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to :

A

generate heat

B

remove adsorbed oxygen from electrode surfaces

C

produce high purity water

D

create potential difference between the two electrodes

Q 144ChemistrySection A • MCQbiomolecules

+4 / -1

Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?

A

A co- enzyme

B

An antibiotic

C

An enzyme

D

A hormone

Q 145ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which one the following does not have sp² hybridized carbon?

A

Acetone

B

Acetamide

C

Acetonitrile

D

Acetic acid

Q 146ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Which one of the following has the regular tetrahedral structure?
(Atomic nos : B = 5, S = 16, Ni = 28, Xe = 54)

A

XeF₄

B

[Ni(CN)₄]^2-

C

BF_4^-

D

SF₄

Q 147ChemistrySection A • MCQgaseous state

+4 / -1

In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure of

A

intermolecular repulsions

B

intermolecular collisions per unit volume

C

Volume occupied by the molecules

D

intermolecular attraction

Q 148ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Consider the acidity of the carboxylic acids:
(a) PhCOOH
(b) o – NO₂C₆H₄COOH
(c) p – NO₂C₆H₄COOH
(d) m – NO₂C₆H₄COOH
Which of the following order is correct?

A

(b) > (d) > (a) > (c)

B

(b) > (d) > (c) > (a)

C

(a) > (b) > (c) > (d)

D

(b) > (c) > (d) > (a)

Q 149ChemistrySection A • MCQthermodynamics

+4 / -1

An ideal gas expands in volume from 1

\times

10^-3 m³ to 1

\times

10^-2 m³ at 300 K against a constant pressure of 1

\times

10⁵ Nm^-2. The work done is :

A

-900 J

B

900 kJ

C

270 kJ

D

-900 kJ

Q 150ChemistrySection A • MCQatomic structure

+4 / -1

The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097

\times

10⁷ m^-1)

A

406 nm

B

192 nm

C

91 nm

D

9.1

\times

10^-8 nm

Q 151ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Acetyl bromide reacts with excess of CH₃MgI followed by treatment with a saturated solution of NH₄Cl given

A

acetone

B

acetyl iodide

C

2- methyl -2- propanol

D

acetamide

Q 152ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?

A

Phenol

B

Benzoic acid

C

Butanal

D

Benzaldehyde

Q 153ChemistrySection A • MCQgaseous state

+4 / -1

As the temperature is raised from 20°C to 40°C, the average kinetic energy of neon atoms changes by a factor of which of the following?

A

1/2

B

2

C

313\over293

D

\sqrt{313\over293}

Q 154MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The equation of the straight line passing through the point

(4, 3)

and making intercepts on the co-ordinate axes whose sum is

-1

is :

A

{x \over 2} - {y \over 3} = 1

and

{x \over -2} +{y \over 1} = 1

B

{x \over 2} - {y \over 3} = -1

and

{x \over -2} +{y \over 1} = -1

C

{x \over 2} + {y \over 3} = 1

and

{x \over 2} +{y \over 1} = 1

D

{x \over 2} + {y \over 3} = -1

and

{x \over -2} +{y \over 1} = -1

Q 155MathematicsSection A • MCQcircle

+4 / -1

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :

A

{(y\, - \,q)^2} = \,4\,px

B

{(x\, - \,q)^2} = \,4\,py

C

{(y\, - \,p)^2} = \,4\,qx

D

{(x\, - \,p)^2} = \,4\,qy

Q 156MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a ,\overrightarrow b

and

\overrightarrow c

be non-zero vectors such that

\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a \,\,.

If

\theta

is the acute angle between the vectors

{\overrightarrow b }

and

{\overrightarrow c },

then

sin\theta

equals :

A

{{2\sqrt 2 } \over 3}

B

{{\sqrt 2 } \over 3}

C

{2 \over 3}

D

{1 \over 3}

Q 157MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If

\left( {1 - p} \right)

is a root of quadratic equation

{x^2} + px + \left( {1 - p} \right) = 0

then its root are

A

- 1,2

B

- 1,1

C

0,-1

D

0,1

Q 158MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If the sum of the slopes of the lines given by

{x^2} - 2cxy - 7{y^2} = 0

is four times their product

c

has the value :

A

-2

B

-1

C

2

D

1

Q 159MathematicsSection A • MCQsets and relations

+4 / -1

Let

R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}

be a relation on the set

A=\{1,2,3,4\}

. The relation

R

is :

A

a function

B

transitive

C

not symmetric

D

reflexive

Q 160MathematicsSection A • MCQsequences and series

+4 / -1

Let

{{T_r}}

be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n,

m \ne n,\,\,{T_m} = {1 \over n}\,\,and\,{T_n} = {1 \over m},\,

then a - d equals

A

{1 \over m} + {1 \over n}

B

1

C

{1 \over {m\,n}}

D

0

Q 161MathematicsSection A • MCQcircle

+4 / -1

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference

10\,\pi

, then the equation of the circle is :

A

{x^2}\, + \,{y^2} + \,2x\, - \,2y - \,23\,\, = 0

B

{x^2}\, + \,{y^2} - \,2x\, - \,2y - \,23\,\, = 0

C

{x^2}\, + \,{y^2} + \,2x\, + \,2y - \,23\,\, = 0

D

{x^2}\, + \,{y^2} - \,2x\, + \,2y - \,23\,\, = 0

Q 162MathematicsSection A • MCQapplication of derivatives

+4 / -1

A function

y=f(x)

has a second order derivative

f''\left( x \right) = 6\left( {x - 1} \right).

If its graph passes through the point

(2, 1)

and at that point the tangent to the graph is

y = 3x - 5

, then the function is :

A

{\left( {x + 1} \right)^2}

B

{\left( {x - 1} \right)^3}

C

{\left( {x + 1} \right)^3}

D

{\left( {x - 1} \right)^2}

Q 163MathematicsSection A • MCQstatistics

+4 / -1

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?

A

only (a)

B

only (b)

C

only (a) and (b)

D

(a), (b) and (c)

Q 164MathematicsSection A • MCQfunctions

+4 / -1

The domain of the function

f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}

A

[1, 2]

B

[2, 3)

C

[1, 2)

D

[2, 3]

Q 165MathematicsSection A • MCQstatistics

+4 / -1

In a series of 2n observations, half of them equal

a

and remaining half equal

–a

. If the standard deviation of the observations is 2, then

|a|

equals

A

2

B

\sqrt 2

C

{1 \over n}

D

{{\sqrt 2 } \over n}

Q 166MathematicsSection A • MCQdefinite integration

+4 / -1

If

f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {xg\left\{ {x\left( {1 - x} \right)} \right\}dx}

and

{I_2} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {g\left\{ {x\left( {1 - x} \right)} \right\}dx} ,

then the value of

{{{I_2}} \over {{I_1}}}

is

A

1

B

-3

C

-1

D

2

Q 167MathematicsSection A • MCQindefinite integration

+4 / -1

If

\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}

then value of

(A, B)

is

A

\left( { - \cos \alpha ,\sin \alpha } \right)

B

\left( { \cos \alpha ,\sin \alpha } \right)

C

\left( { - \sin \alpha ,\cos \alpha } \right)

D

\left( { \sin \alpha ,\cos \alpha } \right)

Q 168MathematicsSection A • MCQdifferential equations

+4 / -1

The differential equation for the family of circle

{x^2} + {y^2} - 2ay = 0,

where a is an arbitrary constant is :

A

\left( {{x^2} + {y^2}} \right)y' = 2xy

B

2\left( {{x^2} + {y^2}} \right)y' = xy

C

\left( {{x^2} - {y^2}} \right)y' =2 xy

D

2\left( {{x^2} - {y^2}} \right)y' = xy

Q 169MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

Let

\alpha ,\,\beta

be such that

\pi < \alpha - \beta < 3\pi

.
If

sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}

and

\cos \alpha + \cos \beta = - {{27} \over {65}}

then the value of

\cos {{\alpha - \beta } \over 2}

:

A

{{ - 6} \over {65}}\,\,

B

{3 \over {\sqrt {130} }}

C

{6 \over {65}}

D

- {3 \over {\sqrt {130} }}

Q 170MathematicsSection A • MCQdefinite integration

+4 / -1

If

\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} }

then

A

is

A

2\pi

B

\pi

C

{\pi \over 4}

D

0

Q 171MathematicsSection A • MCQ3d geometry

+4 / -1

A line makes the same angle

\theta

, with each of the

x

and

z

axis.

If the angle

\beta \,

, which it makes with y-axis, is such that

\,{\sin ^2}\beta = 3{\sin ^2}\theta ,

then

{\cos ^2}\theta

equals :

A

{2 \over 5}

B

{1 \over 5}

C

{3 \over 5}

D

{2 \over 3}

Q 172MathematicsSection A • MCQcircle

+4 / -1

Intercept on the line y = x by the circle

{x^2}\, + \,{y^2} - 2x = 0

is AB. Equation of the circle on AB as a diameter is :

A

\,{x^2}\, + \,{y^2} + \,x\, - \,y\,\, = 0

B

\,{x^2}\, + \,{y^2} - \,x\, + \,y\,\, = 0

C

\,{x^2}\, + \,{y^2} + \,x\, + \,y\,\, = 0

D

\,{x^2}\, + \,{y^2} - \,x\, - \,y\,\, = 0

Q 173MathematicsSection A • MCQcircle

+4 / -1

If a circle passes through the point (a, b) and cuts the circle

{x^2}\, + \,{y^2} = 4

orthogonally, then the locus of its centre is :

A

2ax\, - 2by\, - ({a^2}\, + \,{b^2} + 4) = 0

B

2ax\, + 2by\, - ({a^2}\, + \,{b^2} + 4) = 0

C

2ax\, - 2by\, + ({a^2}\, + \,{b^2} + 4) = 0

D

2ax\, + 2by\, + ({a^2}\, + \,{b^2} + 4) = 0

Q 174MathematicsSection A • MCQcomplex numbers

+4 / -1

If

z = x - iy

and

{z^{{1 \over 3}}} = p + iq

, then

{{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}

is equal to :

A

- 2

B

- 1

C

2

D

1

Q 175MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

If

u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}\theta }

then the difference between the maximum and minimum values of

{u^2}

is given by :

A

{\left( {a - b} \right)^2}

B

2\sqrt {{a^2} + {b^2}}

C

{\left( {a + b} \right)^2}

D

2\left( {{a^2} + {b^2}} \right)

Q 176MathematicsSection A • MCQmathematical induction

+4 / -1

Let

S(K)

= 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.

Then which of the following is true

A

Principle of mathematical induction can be used to prove the formula

B

S\left( K \right) \Rightarrow S\left( {K + 1} \right)

C

S\left( K \right) \ne S\left( {K + 1} \right)

D

S\left( 1 \right)

is correct

Q 177MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

A = \left( {\matrix{ 0 & 0 & { - 1} \cr 0 & { - 1} & 0 \cr { - 1} & 0 & 0 \cr } } \right)

. The only correct

statement about the matrix $A$ is

A

{A^2} = 1

B

A=(-1)I,

where

I

is a unit matrix

C

{A^{ - 1}}

does not exist

D

A

is a zero matrix

Q 178MathematicsSection A • MCQindefinite integration

+4 / -1

\int {{{dx} \over {\cos x - \sin x}}}

is equal to

A

{1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} + {{3\pi } \over 8}} \right)} \right| + C

B

{1 \over {\sqrt 2 }}\log \left| {\cot \left( {{x \over 2}} \right)} \right| + C

C

{1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {{3\pi } \over 8}} \right)} \right| + C

D

\,{1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {\pi \over 8}} \right)} \right| + C

Q 179MathematicsSection A • MCQarea under the curves

+4 / -1

The area of the region bounded by the curves

y = \left| {x - 2} \right|,x = 1,x = 3

and the

x

-axis is :

A

4

B

2

C

3

D

1

Q 180MathematicsSection A • MCQfunctions

+4 / -1

The graph of the function y = f(x) is symmetrical about the line x = 2, then

A

f\left( x \right) = - f\left( { - x} \right)

B

f\left( {2 + x} \right) = f\left( {2 - x} \right)

C

f\left( x \right) = f\left( { - x} \right)

D

f\left( {x + 2} \right) = f\left( {x - 2} \right)

Q 181MathematicsSection A • MCQproperties of triangles

+4 / -1

The sides of a triangle are

\sin \alpha ,\,\cos \alpha

and

\sqrt {1 + \sin \alpha \cos \alpha }

for some

0 < \alpha < {\pi \over 2}

. Then the greatest angle of the triangle is :

A

{150^ \circ }

B

{90^ \circ }

C

{120^ \circ }

D

{60^ \circ }

Q 182MathematicsSection A • MCQparabola

+4 / -1

If

a \ne 0

and the line

2bx+3cy+4d=0

passes through the points of intersection of the parabolas

{y^2} = 4ax

and

{x^2} = 4ay

, then :

A

{d^2} + {\left( {3b - 2c} \right)^2} = 0

B

{d^2} + {\left( {3b + 2c} \right)^2} = 0

C

{d^2} + {\left( {2b - 3c} \right)^2} = 0

D

{d^2} + {\left( {2b + 3c} \right)^2} = 0

Q 183MathematicsSection A • MCQpermutations and combinations

+4 / -1

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

A

{}^8{C_3}

B

21

C

{3^8}

D

5

Q 184MathematicsSection A • MCQbinomial theorem

+4 / -1

The coefficient of the middle term in the binomial expansion in powers of

x

of

{\left( {1 + \alpha x} \right)^4}

and

{\left( {1 - \alpha x} \right)^6}

is the same if

\alpha

equals

A

{3 \over 5}

B

{10 \over 3}

C

{{ - 3} \over {10}}

D

{{ - 5} \over {3}}

Q 185MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

Let

A\left( {2, - 3} \right)

and

B\left( {-2, 1} \right)

be vertices of a triangle

ABC

. If the centroid of this triangle moves on the line

2x + 3y = 1

, then the locus of the vertex

C

is the line :

A

3x - 2y = 3

B

2x - 3y = 7

C

3x + 2y = 5

D

2x + 3y = 9

Q 186MathematicsSection A • MCQdefinite integration

+4 / -1

The value of

\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx}

is

A

{1 \over 3}

B

{14 \over 3}

C

{7 \over 3}

D

{28 \over 3}

Q 187MathematicsSection A • MCQapplication of derivatives

+4 / -1

If

2a+3b+6c=0

, then at least one root of the equation

a{x^2} + bx + c = 0

lies in the interval

A

(1, 3)

B

(1, 2)

C

(2, 3)

D

(0, 1)

Q 188MathematicsSection A • MCQdefinite integration

+4 / -1

\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}}

is

A

e+1

B

e-1

C

1-e

D

e

Q 189MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

{a_1},{a_2},{a_3},.........,{a_n},......

are in G.P., then the value of the determinant

$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|,$ is

A

-2

B

1

C

2

D

0

Q 190MathematicsSection A • MCQdifferential equations

+4 / -1

Solution of the differential equation

ydx + \left( {x + {x^2}y} \right)dy = 0

is

A

log

y=Cx

B

- {1 \over {xy}} + \log y = C

C

{1 \over {xy}} + \log y = C

D

- {1 \over {xy}} = C

Q 191MathematicsSection A • MCQheight and distance

+4 / -1

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is

{60^ \circ }

and when he retires

40

meters away from the tree the angle of elevation becomes

{30^ \circ }

. The breadth of the river is :

A

60\,\,m

B

30\,\,m

C

40\,\,m

D

20\,\,m

Q 192MathematicsSection A • MCQpermutations and combinations

+4 / -1

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

A

480

B

240

C

360

D

120

Q 193MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If one of the lines given by

6{x^2} - xy + 4c{y^2} = 0

is

3x + 4y = 0,

then

c

equals :

A

-3

B

-1

C

3

D

1

Q 194MathematicsSection A • MCQbinomial theorem

+4 / -1

If

{S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}},\,}

then

{{{t_{ n}}} \over {{S_n}}}

is equal to

A

{{2n - 1} \over 2}

B

{1 \over 2}n - 1

C

n - 1

D

{1 \over 2}n

Q 195MathematicsSection A • MCQsequences and series

+4 / -1

The sum of series

{1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........

is

A

{{\left( {{e^2} - 2} \right)} \over e}\,

B

{{{{\left( {e - 1} \right)}^2}} \over {2e}}

C

{{\left( {{e^2} - 1} \right)} \over {2e}}\,

D

{{\left( {{e^2} - 1} \right)} \over 2}

Q 196MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

If

\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}

, then the value of

a

and

b

, are

A

a

= 1 and

b

= 2

B

a

= 1 and

b

\in R

C

a

\in R

and

b

= 2

D

a

\in R

and

b

\in R

Q 197MathematicsSection A • MCQbinomial theorem

+4 / -1

The coefficient of

{x^n}

in expansion of

\left( {1 + x} \right){\left( {1 - x} \right)^n}

is

A

{\left( { - 1} \right)^{n - 1}}n

B

{\left( { - 1} \right)^n}\left( {1 - n} \right)

C

{\left( { - 1} \right)^{n - 1}}{\left( {n - 1} \right)^2}

D

\left( {n - 1} \right)

Q 198MathematicsSection A • MCQapplication of derivatives

+4 / -1

The normal to the curve x = a(1 + cos

\theta

),

y = a\sin \theta

at

'\theta '

always passes through the fixed point

A

(a, a)

B

(0, a)

C

(0, 0)

D

(a, 0)

Q 199MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

A = \left( {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right).

and

10

B = \left( {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right)

. if

B

is

the inverse of matrix $A$ , then $\alpha$ is

A

5

B

-1

C

2

D

-2

Q 200MathematicsSection A • MCQcomplex numbers

+4 / -1

If

\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1

, then z lies on :

A

an ellipse

B

the imaginary axis

C

a circle

D

the real axis

Q 201MathematicsSection A • MCQdifferentiation

+4 / -1

If

x = {e^{y + {e^y} + {e^{y + .....\infty }}}}

,

x > 0,

then

{{{dy} \over {dx}}}

is

A

{{1 + x} \over x}

B

{1 \over x}

C

{{1 - x} \over x}

D

{x \over {1 + x}}

Q 202MathematicsSection A • MCQvector algebra

+4 / -1

A particle acted on by constant forces

4\widehat i + \widehat j - 3\widehat k

and

3\widehat i + \widehat j - \widehat k

is displaced from the point

\widehat i + 2\widehat j + 3\widehat k

to the point

\,5\widehat i + 4\widehat j + \widehat k.

The total work done by the forces is :

A

50

units

B

20

units

C

30

units

D

40

units

Q 203MathematicsSection A • MCQellipse

+4 / -1

The eccentricity of an ellipse, with its centre at the origin, is

{1 \over 2}

. If one of the directrices is

x=4

, then the equation of the ellipse is :

A

4{x^2} + 3{y^2} = 1

B

3{x^2} + 4{y^2} = 12

C

4{x^2} + 3{y^2} = 12

D

3{x^2} + 4{y^2} = 1

Q 204MathematicsSection A • MCQ3d geometry

+4 / -1

Distance between two parallel planes

\,2x + y + 2z = 8

and

4x + 2y + 4z + 5 = 0

is :

A

{9 \over 2}

B

{5 \over 2}

C

{7 \over 2}

D

{3 \over 2}

Q 205MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If one root of the equation

{x^2} + px + 12 = 0

is 4, while the equation

{x^2} + px + q = 0

has equal roots,
then the value of

'q'

is

A

4

B

12

C

3

D

{{49} \over 4}

Q 206MathematicsSection A • MCQ3d geometry

+4 / -1

A line with direction cosines proportional to

2,1,2

meets each of the lines

x=y+a=z

and

x+a=2y=2z

. The co-ordinates of each of the points of intersection are given by :

A

\left( {2a,3a,3a} \right),\left( {2a,a,a} \right)

B

\left( {3a,2a,3a} \right),\left( {a,a,a} \right)

C

\left( {3a,2a,3a} \right),\left( {a,a,2a} \right)

D

\left( {3a,3a,3a} \right),\left( {a,a,a} \right)

Q 207MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a ,\overrightarrow b

and

\overrightarrow c

be three non-zero vectors such that no two of these are collinear. If the vector

\overrightarrow a + 2\overrightarrow b

is collinear with

\overrightarrow c

and

\overrightarrow b + 3\overrightarrow c

is collinear with

\overrightarrow a

(

\lambda

being some non-zero scalar) then

\overrightarrow a + 2\overrightarrow b + 6\overrightarrow c

equals to :

A

\overrightarrow{0}

B

\lambda \overrightarrow b

C

\lambda \overrightarrow c

D

\lambda \overrightarrow a

Q 208MathematicsSection A • MCQfunctions

+4 / -1

If

f:R \to S

, defined by

f\left( x \right) = \sin x - \sqrt 3 \cos x + 1

,
is onto, then the interval of

S

is

A

[-1, 3]

B

[-1, 1]

C

[0, 1]

D

[0, 3]

Q 209MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

A

{x^2} - 18x - 16 = 0

B

{x^2} - 18x + 16 = 0

C

{x^2} + 18x - 16 = 0

D

{x^2} + 18x + 16 = 0

Q 210MathematicsSection A • MCQdefinite integration

+4 / -1

The value of

I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx}

is

A

3

B

1

C

2

D

0

Q 211MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow u ,\overrightarrow v ,\overrightarrow w

be such that

\left| {\overrightarrow u } \right| = 1,\,\,\,\left| {\overrightarrow v } \right|2,\,\,\,\left| {\overrightarrow w } \right|3.

If the projection

{\overrightarrow v }

along

{\overrightarrow u }

is equal to that of

{\overrightarrow w }

along

{\overrightarrow u }

and

{\overrightarrow v },

{\overrightarrow w }

are perpendicular to each other then

\left| {\overrightarrow u - \overrightarrow v + \overrightarrow w } \right|

equals :

A

14

B

{\sqrt {7} }

C

{\sqrt {14} }

D

2

Q 212MathematicsSection A • MCQ3d geometry

+4 / -1

If the straight lines

x=1+s,y=-3

- \lambda s,

z = 1 + \lambda s

and

x = {t \over 2},y = 1 + t,z = 2 - t,

with parameters

s

and

t

respectively, are co-planar, then

\lambda

equals :

A

0

B

-1

C

- {1 \over 2}

D

-2

Q 213MathematicsSection A • MCQvector algebra

+4 / -1

If

{\overrightarrow a ,\overrightarrow b ,\overrightarrow c }

are non-coplanar vectors and

\lambda

is a real number, then the vectors

{\overrightarrow a + 2\overrightarrow b + 3\overrightarrow c ,\,\,\lambda \overrightarrow b + 4\overrightarrow c }

and

\left( {2\lambda - 1} \right)\overrightarrow c

are non coplanar for :

A

no value of

\lambda

B

all except one value of

\lambda

C

all except two values of

\lambda

D

all values of

\lambda

Q 214MathematicsSection A • MCQcomplex numbers

+4 / -1

Let z and w be complex numbers such that

\overline z + i\overline w = 0

and arg zw =

\pi

. Then arg z equals :

A

{{5\pi } \over 4}

B

{{\pi } \over 2}

C

{{3\pi } \over 4}

D

{{\pi } \over 4}

Q 215MathematicsSection A • MCQfunctions

+4 / -1

The range of the function f(x) =

{}^{7 - x}{P_{x - 3}}

is

A

{1, 2, 3, 4, 5}

B

{1, 2, 3, 4, 5, 6}

C

{1, 2, 3, 4}

D

{1, 2, 3}

Q 216MathematicsSection A • MCQsequences and series

+4 / -1

The sum of the first n terms of the series

{1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ....\,is\,{{n{{(n + 1)}^2}} \over 2}

when n is even. When n is odd the sum is

A

{\left[ {{{n(n + 1)} \over 2}} \right]^2}

B

{{{n^2}(n + 1)} \over 2}

C

{{n{{(n + 1)}^2}} \over 4}

D

\,{{3n(n + 1)} \over 2}

Q 217MathematicsSection A • MCQprobability

+4 / -1

The mean and the variance of a binomial distribution are

4

and

2

respectively. Then the probability of

2

successes is :

A

{28 \over 256}

B

{219 \over 256}

C

{128 \over 256}

D

{37 \over 256}

Q 218MathematicsSection A • MCQapplication of derivatives

+4 / -1

A point on the parabola

{y^2} = 18x

at which the ordinate increases at twice the rate of the abscissa is

A

\left( {{9 \over 8},{9 \over 2}} \right)

B

(2, -4)

C

\left( {{-9 \over 8},{9 \over 2}} \right)

D

(2, 4)

Q 219MathematicsSection A • MCQprobability

+4 / -1

The probability that

A

speaks truth is

{4 \over 5},

while the probability for

B

is

{3 \over 4}.

The probability that they contradict each other when asked to speak on a fact is :

A

{4 \over 5}

B

{1 \over 5}

C

{7 \over 20}

D

{3 \over 20}

Q 220MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let

f(x) = {{1 - \tan x} \over {4x - \pi }}

,

x \ne {\pi \over 4}

,

x \in \left[ {0,{\pi \over 2}} \right]

.

If

f(x)

is continuous in

\left[ {0,{\pi \over 2}} \right]

, then

f\left( {{\pi \over 4}} \right)

is

A

-1

B

{1 \over 2}

C

-{1 \over 2}

D

1

Q 221MathematicsSection A • MCQ3d geometry

+4 / -1

The intersection of the spheres

{x^2} + {y^2} + {z^2} + 7x - 2y - z = 13

and

{x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8

is the same as the intersection of one of the sphere and the plane

A

2x-y-z=1

B

x-2y-z=1

C

x-y-2z=1

D

x-y-z=1

AIEEE 2004 Question Paper with Solutions