JEE Mains Aieee 2005 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQmagnetics

+4 / -1

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

A

its velocity will increase

B

Its velocity will decrease

C

it will turn towards left of a direction of motion

D

it will turn towards right of direction of motion

Q 2PhysicsSection A • MCQelectromagnetic induction

+4 / -1

One conducting

U

tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field

B

is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed

v,

then the

emf

induced in the circuit in terms of

B,l

and

v

where

l

is the width of each tube, will be qImage-motional-emf-and-eddy-current-electromagnetic-induction-electricity-Jeemate

A

-Blv

B

blv

C

2

Blv

D

zero

Q 3PhysicsSection A • MCQmagnetics

+4 / -1

Two thin, long, parallel wires, separated by a distance

'd'

carry a current of

'i'

A

in the same direction. They will

A

repel each other with a force of

{\mu _0}{i^2}/\left( {2\pi d} \right)

B

attract each other with a force of

{\mu _0}{i^2}/\left( {2\pi d} \right)

C

repel each other with a force

_0{i^2}/\left( {2\pi {d^2}} \right)

D

attract each other with a force of

{\mu _0}{i^2}/\left( {2\pi {d^2}} \right)

Q 4PhysicsSection A • MCQrotational motion

+4 / -1

The moment of inertia of a uniform semicircular disc of mass

M

and radius

r

about a line perpendicular to the plane of the disc through the center is

A

{2 \over 5}M{r^2}

B

{1 \over 4}Mr

C

{1 \over 2}M{r^2}

D

M{r^2}

Q 5PhysicsSection A • MCQwave optics

+4 / -1

Two point white dots are

1

mm

apart on a black paper. They are viewed by eye of pupil diameter

3

mm.

Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light

=500

nm

]

A

1m

B

5m

C

3m

D

6m

Q 6PhysicsSection A • MCQelectrostatics

+4 / -1

Two point charges

+8q

and

-2q

are located at

x=0

and

x=L

respectively. The location of a point on the

x

axis at which the net electric field due to these two point charges is zero is

A

{L \over 4}

B

2

L

C

4

L

D

8

L

Q 7PhysicsSection A • MCQcurrent electricity

+4 / -1

In a potentiometer experiment the balancing with a cell is at length

240

cm.

On shunting the cell with a resistance of

2\Omega ,

the balancing length becomes

120

cm

. The internal resistance of the cell is

A

0.5\Omega

B

1\Omega

C

2\Omega

D

4\Omega

Q 8PhysicsSection A • MCQproperties of matter

+4 / -1

A

20

cm

long capillary tube is dipped in water. The water rises up to

8

cm.

If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

A

10

cm

B

8

cm

C

20

cm

D

4

cm

Q 9PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

A

first decrease and then increase to the original value

B

first increase and then decrease to the original value

C

increase towards a saturation value

D

remain unchanged

Q 10PhysicsSection A • MCQray optics

+4 / -1

A thin glass (refractive index

1.5

) lens has optical power of

-5

D

in air. Its optical power in a liquid medium with refractive index

1.6

will be

A

-1

D

B

1

D

C

-25

D

D

25

D

Q 11PhysicsSection A • MCQwave optics

+4 / -1

If

{I_0}

is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

A

4{I_0}

B

2{I_0}

C

{{{I_0}} \over 2}

D

{I_0}

Q 12PhysicsSection A • MCQatoms and nuclei

+4 / -1

A nuclear transformation is denoted by

X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li.

Which of the following is the nucleus of element

X

?

A

{}_5^{10}B

B

{}^{12}{C_6}

C

{}_4^{11}Be

D

{}_5^9B

Q 13PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The function

{\sin ^2}\left( {\omega t} \right)

represents

A

a periodic, but not

SHM

with a period

{\pi \over \omega }

B

a periodic, but not

SHM

with a period

{{2\pi } \over \omega }

C

a

SHM

with a period

{\pi \over \omega }

D

a

SHM

with a period

{{2\pi } \over \omega }

Q 14PhysicsSection A • MCQsimple harmonic motion

+4 / -1

If a simple harmonic motion is represented by

{{{d^2}x} \over {d{t^2}}} + \alpha x = 0.

its time period is

A

{{2\pi } \over {\sqrt \alpha }}

B

{{2\pi } \over \alpha }

C

2\pi \sqrt \alpha

D

2\pi \alpha

Q 15PhysicsSection A • MCQalternating current

+4 / -1

A circuit has a resistance of

12

ohm

and an impedance of

15

ohm

. The power factor of the circuit will be

A

0.4

B

0.8

C

0.125

D

1.25

Q 16PhysicsSection A • MCQatoms and nuclei

+4 / -1

The intensity of gamma radiation from a given source is

L

. On passing through

36

mm

of lead, it is reduced to

{{\rm I} \over 8}.

The thickness of lead which will reduce the intensity to

{{\rm I} \over 2}

will be

A

9mm

B

6mm

C

12mm

D

18mm

Q 17PhysicsSection A • MCQheat and thermodynamics

+4 / -1

The figure shows a system of two concentric spheres of radii

{r_1}

and

{r_2}

are kept at temperatures

{T_1}

and

{T_2}

, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to qImage-heat-transfer-heat-and-thermodynamics-mechanics-Jeemate

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

A

In\left( {{{{r_2}} \over {{r_1}}}} \right)

B

{{\left( {{r_2} - {r_1}} \right)} \over {\left( {{r_1}{r_2}} \right)}}

C

{\left( {{r_2} - {r_1}} \right)}

D

{{{r_1}{r_2}} \over {\left( {{r_2} - {r_1}} \right)}}

Q 18PhysicsSection A • MCQsimple harmonic motion

+4 / -1

Two simple harmonic motions are represented by the equations

{y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right)

and

{y_2} = 0.1\,\cos \,\pi t.

The phase difference of the velocity of particle

1

with respect to the velocity of particle

2

is

A

{\pi \over 3}

B

{{ - \pi } \over 6}

C

{\pi \over 6}

D

{{ - \pi } \over 3}

Q 19PhysicsSection A • MCQcapacitor

+4 / -1

A fully charged capacitor has a capacitance

'C'

. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity

's'

and mass

'm'.

If the temperature of the block is raised by

'\Delta T',

the potential difference

'v'

across the capacitance is

A

{{mCAT} \over s}

B

\sqrt {{{2mCAT} \over s}}

C

\sqrt {{{2msAT} \over C}}

D

{{ms\Delta T} \over C}

Q 20PhysicsSection A • MCQelectronic devices

+4 / -1

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than

2480

nm

is incident on it. The band gap in

(eV)

for the semiconductor is

A

2.5

eV

B

1.1

eV

C

0.7

eV

D

0.5

eV

Q 21PhysicsSection A • MCQlaws of motion

+4 / -1

A particle of mass 0.3 kg subjected to a force

F=-kx

with

k=15

N/m

. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

A

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

B

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

C

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

D

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

Q 22PhysicsSection A • MCQmotion

+4 / -1

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

A

{1 \over 2}m{s^{ - 2}}

towards north

B

{1 \over {\sqrt 2 }}m{s^{ - 2}}

towards north-east

C

{1 \over {\sqrt 2 }}m{s^{ - 2}}

towards north-west

D

zero

Q 23PhysicsSection A • MCQlaws of motion

+4 / -1

A block is kept on a frictionless inclined surface with angle of inclination

'\,\alpha \,'.

The incline is given an acceleration

a

to keep the block stationary. Then

a

is equal to qImage-motion-on-an-inclined-plane-laws-of-motion-mechanics-Jeemate

A

g

cosec

\alpha

B

g/tan

\alpha

C

g

tan

\alpha

D

g

Q 24PhysicsSection A • MCQlaws of motion

+4 / -1

A smooth block is released at rest on a

{45^ \circ }

incline and then slides a distance

'd'

. The time taken to slide is

'n'

times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A

{\mu _k} = \sqrt {1 - {1 \over {{n^2}}}}

B

{\mu _k} = 1 - {1 \over {{n^2}}}

C

{\mu _k} = \sqrt {1 - {1 \over {{n^2}}}}

D

{\mu _s} = 1 - {1 \over {{n^2}}}

Q 25PhysicsSection B • Numericalheat and thermodynamics

+4 / -1

Which of the following is incorrect regarding the first law of thermodynamics?

Q 26PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A gaseous mixture consists of

16

g

of helium and

16

g

of oxygen. The ratio

{{Cp} \over {{C_v}}}

of the mixture is

A

1.62

B

1.59

C

1.54

D

1.4

Q 27PhysicsSection A • MCQmotion

+4 / -1

The relation between time t and distance x is t = ax² + bx where a and b are constants. The acceleration is

A

2bv³

B

-2abv²

C

2av²

D

-2av³

Q 28PhysicsSection A • MCQgravitation

+4 / -1

Average density of the earth

A

is a complex function of

g

B

does not depend on

g

C

is inversely proportional to

g

D

is directly proportional to

g

Q 29PhysicsSection A • MCQdual nature of radiation

+4 / -1

A photocell is illuminated by a small bright source placed

1

m

away. When the same source of light is placed

{1 \over 2}

m

away, the number of electrons emitted by photo-cathode would

A

increases by a factor of

4

B

decreases by a factor of

4

C

increases by a factor of

2

D

decreases by a factor of

2

Q 30PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A coil of inductance

300

mH

and resistance

2\,\Omega

is connected to a source of voltage

2

V

. The current reaches half of its steady state value in

A

0.1

s

B

0.05

s

C

0.3

s

D

0.15

s

Q 31PhysicsSection A • MCQatoms and nuclei

+4 / -1

Starting with a sample of pure

{}^{66}Cu,{7 \over 8}

of it decays into

Zn

in

15

minutes. The corresponding half life is

A

15

minutes

B

10

minutes

C

7{1 \over 2}

minutes

D

5

minutes

Q 32PhysicsSection A • MCQelectrostatics

+4 / -1

Two thin wire rings each having a radius

R

are placed at a distance

d

apart with their axes coinciding. The charges on the two rings are

+q

and

-q.

The potential difference between the centres of the two rings is

A

{q \over {2\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]

B

{{qR} \over {4\pi \,{ \in _0}\,{d^2}}}

C

{q \over {4\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]

D

zero

Q 33PhysicsSection A • MCQproperties of matter

+4 / -1

If

S

is stress and

Y

is young's modulus of material of a wire, the energy stored in the wire per unit volume is

A

{{{S^2}} \over {2Y}}

B

2{S^2}Y

C

{S \over {2Y}}

D

{{2Y} \over {{S^2}}}

Q 34PhysicsSection A • MCQcenter of mass

+4 / -1

A body

A

of mass

M

while falling vertically downloads under gravity breaks into two-parts; a body

B

of mass

{1 \over 3}

M

and a body

C

of mass

{2 \over 3}

M.

The center of mass of bodies

B

and

C

taken together shifts compared to that of bodies

B

and

C

taken together shifts compared to that of body

A

towards

A

does not shift

B

depends on height of breaking

C

body

B

D

body

C

Q 35PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

A magnetic needle is kept in a non-uniform magnetic field. It experiences :

A

neither a force nor a torque

B

a torque but not a force

C

a force but not a torque

D

a force and a torque

Q 36PhysicsSection A • MCQrotational motion

+4 / -1

An annular ring with inner and outer radii

{R_1}

and

{R_2}

is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring,

{{{F_1}} \over {{F_2}}}\,

is

A

{\left( {{{{R_1}} \over {{R_2}}}} \right)^2}

B

{{{{R_2}} \over {{R_1}}}}

C

{{{{R_1}} \over {{R_2}}}}

D

1

Q 37PhysicsSection A • MCQmagnetics

+4 / -1

A charged particle of mass

m

and charge

q

travels on a circular path of radius

r

that is perpendicular to a magnetic field

B.

The time taken by the particle to complete one revolution is

A

{{2\pi {q^2}B} \over m}

B

{{2\pi mq} \over B}

C

{{2\pi m} \over {qB}}

D

{{2\pi qB} \over m}

Q 38PhysicsSection A • MCQcapacitor

+4 / -1

A parallel plate capacitor is made by stacking

n

equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is

'C'

then the resultant capacitance is

A

\left( {n + 1} \right)C

B

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

C

nC

D

C

Q 39PhysicsSection A • MCQwave optics

+4 / -1

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

A

circle

B

hyperbola

C

parabola

D

straight line

Q 40PhysicsSection A • MCQcurrent electricity

+4 / -1

The resistance of hot tungsten filament is about

10

times the cold resistance. What will be resistance of

100

W

and

200

V

lamp when not in use ?

A

20\Omega

B

40\Omega

C

200\Omega

D

400\Omega

Q 41PhysicsSection A • MCQelectronic devices

+4 / -1

In a full wave rectifier circuit operating from

50

Hz

mains frequency, the fundamental frequency in the ripple would be

A

25

Hz

B

50

Hz

C

70.7

Hz

D

100

Hz

Q 42PhysicsSection A • MCQray optics

+4 / -1

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is

{4 \over 3}

and the fish is

12

cm

below the surface, the radius of this circle in

cm

is

A

{{36} \over {\sqrt 7 }}

B

{36\sqrt 7 }

C

{4\sqrt 5 }

D

{36\sqrt 5 }

Q 43PhysicsSection A • MCQwork power and energy

+4 / -1

A spherical ball of mass

20

kg

is stationary at the top of a hill of height

100

m

. It rolls down a smooth surface to the ground, then climbs up another hill of height

30

m

and finally rolls down to a horizontal base at a height of

20

m

above the ground. The velocity attained by the ball is

A

20

m/s

B

40

m/s

C

10\sqrt {30} \,\,\,m/s

D

10\,\,m/s

Q 44PhysicsSection A • MCQwaves

+4 / -1

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

A

0.5\%

B

zero

C

20\%

D

5\%

Q 45PhysicsSection A • MCQwaves

+4 / -1

When two tuning forks (fork

1

and fork

2

) are sounded simultaneously,

4

beats per second are heated. Now, some tape is attached on the prong of the fork

2.

When the tuning forks are sounded again,

6

beats per second are heard. If the frequency of fork

1

is

200

Hz

, then what was the original frequency of fork

2

?

A

202

Hz

B

200

Hz

C

204

Hz

D

196

Hz

Q 46PhysicsSection A • MCQmotion

+4 / -1

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate

{f \over 2}

to come to rest. If the total distance traversed is 15 S, then

A

S = {1 \over 6}f{t^2}

B

S = ft

C

S = {1 \over 4}f{t^2}

D

S = {1 \over 72}f{t^2}

Q 47PhysicsSection A • MCQcenter of mass

+4 / -1

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force

'\,\,\overrightarrow F \,\,'

is applied at the point

P

parallel to

AB,

such that the object has only the translational motion without rotation. Find the location of

P

with respect to

C.

qImage-center-of-mass-of-continuous-mass-distribution-center-of-mass-mechanics-Jeemate

A

{3 \over 2}L

B

{2 \over 3}L

C

L

D

{4 \over 3}L

Q 48PhysicsSection A • MCQatoms and nuclei

+4 / -1

If radius of the

\matrix{ {27} \cr {13} \cr }

Al

nucleus is estimated to be

3.6

fermi then the radius of

\matrix{ {125} \cr {52} \cr } \,Te

nucleus is estimated to be nearly

A

8

fermi

B

6

fermi

C

5

fermi

D

4

fermi

Q 49PhysicsSection A • MCQcurrent electricity

+4 / -1

Two sources of equal

emf

are connected to an external resistance

R.

The internal resistance of the two sources are

{R_1}

and

{R_2}\left( {{R_1} > {R_1}} \right).

If the potential difference across the source having internal resistance

{R_2}

is zero, then

A

R = {R_2} - {R_1}

B

R = {R_2} \times \left( {{R_1} + {R_2}} \right)/\left( {{R_2} - {R_1}} \right)

C

R = {R_1}{R_2}/\left( {{R_2} - {R_1}} \right)

D

R = {R_1}{R_2}/\left( {{R_1} - {R_2}} \right)

Q 50PhysicsSection A • MCQcurrent electricity

+4 / -1

A moving coil galvanometer has

150

equal divisions. Its current sensitivity is

10

- divisions per milliampere and voltage sensitivity is

2

divisions per millivolt. In order that each division reads

1

volt, the resistance in

ohms

needed to be connected in series with the coil will be -

A

{10^5}

B

{10^3}

C

9995

D

99995

Q 51PhysicsSection A • MCQelectrostatics

+4 / -1

A charged ball

B

hangs from a silk thread

S,

which makes angle

\theta

with a large charged conducting sheet

P,

as shown in the figure. The surface charge density

\sigma

of the sheet is proportional to qImage-electric-field-and-electric-field-intensity-electrostatics-electricity-Jeemate

f

A

\cot \,\theta

B

\cos \,\theta

C

\tan \,\theta

D

\sin \,\theta

Q 52PhysicsSection A • MCQcurrent electricity

+4 / -1

In the circuit, the galvanometer

G

shows zero deflection. If the batteries

A

and

B

have negligible internal resistance, the value of the resistor

R

will be -

qImage-galvanometer-voltmeter-and-ammeter-current-electricity-electricity-Jeemate

A

100\Omega

B

200\Omega

C

1000\Omega

D

500\Omega

Q 53PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A system goes from

A

to

B

via two processes

I

and

II

as shown in figure. If

\Delta {U_1}

and

\Delta {U_2}

are the changes in internal energies in the processes

I

and

II

respectively, then qImage-zeroth-and-first-law-of-thermodynamics-heat-and-thermodynamics-mechanics-Jeemate

A

relation between

\Delta {U_1}

and

\Delta {U_2}

can not be determined

B

\Delta {U_1} = \Delta {U_2}

C

\Delta {U_2} < \Delta {U_1}

D

\Delta {U_2} > \Delta {U_1}

Q 54PhysicsSection A • MCQatoms and nuclei

+4 / -1

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy? qImage-bohrs-model-and-hydrogen-spectrum-atoms-and-nuclei-modern-physics-Jeemate

qImage-bohrs-model-and-hydrogen-spectrum-atoms-and-nuclei-modern-physics-Jeemate

A

iv

B

iii

C

ii

D

i

Q 55PhysicsSection A • MCQunits and measurements

+4 / -1

Out of the following pair, which one does NOT have identical dimensions is

A

angular momentum and Planck's constant

B

impulse and momentum

C

moment of inertia and moment of a force

D

work and torque

Q 56PhysicsSection A • MCQcenter of mass

+4 / -1

A mass

'm'

moves with a velocity

'v'

and collides inelastically with another identical mass. After collision the

{1^{st}}

mass moves with velocity

{v \over {\sqrt 3 }}

in a direction perpendicular to the initial direction of motion. Find the speed of the

{2^{nd}}

mass after collision. qImage-collision-center-of-mass-mechanics-Jeemate

A

{\sqrt 3 v}

B

v

C

{v \over {\sqrt 3 }}

D

{2 \over {\sqrt 3 }}v

Q 57PhysicsSection A • MCQcurrent electricity

+4 / -1

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge

q

flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are

{Z_1}

and

{Z_2}

respectively the charge which flows through the silver voltmeter is

A

{q \over {1 + {{{Z_2}} \over {{Z_1}}}}}

B

{q \over {1 + {{{Z_1}} \over {{Z_2}}}}}

C

q{{{Z_2}} \over {{Z_1}}}

D

q{{{Z_1}} \over {{Z_2}}}

Q 58PhysicsSection A • MCQmagnetics

+4 / -1

Two concentric coils each of radius equal to

2

\pi

cm

are placed at right angles to each other.

3

ampere and

4

ampere are the currents flowing in each coil respectively . The magnetic induction in Weber /

{m^2}

at the center of the coils will be

\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)

A

{10^{ - 5}}

B

12 \times {10^{ - 5}}

C

7 \times {10^{ - 5}}

D

5 \times {10^{ - 5}}

Q 59PhysicsSection A • MCQelectronic devices

+4 / -1

In a common base amplifier, the phase difference between the input signal voltage and output voltage is

A

\pi

B

{\pi \over 4}

C

{\pi \over 2}

D

0

Q 60PhysicsSection A • MCQwork power and energy

+4 / -1

A body of mass

m

is accelerated uniformly from rest to a speed

v

in a time

T.

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

A

{{m{v^2}} \over {{T^2}}}.{t^2}

B

{{m{v^2}} \over {{T^2}}}.t

C

{1 \over 2}{{m{v^2}} \over {{T^2}}}.{t^2}

D

{1 \over 2}{{m{v^2}} \over {{T^2}}}.t

Q 61PhysicsSection A • MCQlaws of motion

+4 / -1

Consider a car moving on a straight road with a speed of

100

m/s

. The distance at which car can be stopped is

\left[ {{\mu _k} = 0.5} \right]

A

1000

m

B

800

m

C

400

m

D

100

m

Q 62PhysicsSection A • MCQheat and thermodynamics

+4 / -1

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is qImage-heat-engine-second-law-of-thermodynamics-and-carnot-engine-heat-and-thermodynamics-mechanics-Jeemate

qImage-heat-engine-second-law-of-thermodynamics-and-carnot-engine-heat-and-thermodynamics-mechanics-Jeemate

A

{1 \over 4}

B

{1 \over 2}

C

{2 \over 3}

D

{1 \over 3}

Q 63PhysicsSection A • MCQmotion

+4 / -1

A parachutist after bailing out falls

50

m

without friction. When parachute opens, it decelerates at

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

He reaches the ground with a speed of

3

m/s

. At what height, did he bail out?

A

182

m

B

91

m

C

111

m

D

293

m

Q 64PhysicsSection A • MCQcenter of mass

+4 / -1

The block of mass

M

moving on the frictionless horizontal surface collides with the spring of spring constant

k

and compresses it by length

L.

The maximum momentum of the block after collision is qImage-collision-center-of-mass-mechanics-Jeemate

A

{{k{L^2}} \over {2M}}

B

\sqrt {Mk} \,\,L

C

{{M{L^2}} \over k}

D

Zero

Q 65PhysicsSection A • MCQgravitation

+4 / -1

The change in the value of

g

at a height

h

above the surface of the earth is the same as at a depth

d

below the surface of earth. When both

d

and

h

are much smaller than the radius of earth, then which one of the following is correct?

A

d = {{3h} \over 2}

B

d = {h \over 2}

C

d = h

D

d = 2\,h

Q 66PhysicsSection A • MCQwork power and energy

+4 / -1

The upper half of an inclined plane with inclination

\phi

is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

A

2\,\cos \,\,\phi

B

2\,sin\,\,\phi

C

\,\tan \,\,\phi

D

2\,\tan \,\,\phi

Q 67PhysicsSection A • MCQcurrent electricity

+4 / -1

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

A

four times

B

doubled

C

halved

D

one fourth

Q 68PhysicsSection A • MCQalternating current

+4 / -1

The self inductance of the motor of an electric fan is

10

H

. In order to impart maximum power at

50

Hz

, it should be connected to a capacitance of

A

8\mu F

B

4\mu F

C

2\mu F

D

1\mu F

Q 69PhysicsSection A • MCQwave optics

+4 / -1

When an unpolarized light of intensity

{{I_0}}

is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

A

{1 \over 4}\,{I_0}

B

{1 \over 2}\,{I_0}

C

{I_0}

D

zero

Q 70PhysicsSection A • MCQalternating current

+4 / -1

The phase difference between the alternating current and

emf

is

{\pi \over 2}.

Which of the following cannot be the constituent of the circuit?

A

R,L

B

C

alone

C

L

alone

D

L, C

Q 71PhysicsSection A • MCQwork power and energy

+4 / -1

A bullet fired into a fixed target loses half of its velocity after penetrating

3

cm.

How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A

2.0

cm

B

3.0

cm

C

1.0

cm

D

1.5

cm

Q 72PhysicsSection A • MCQcurrent electricity

+4 / -1

An energy source will supply a constant current into the load if its internal resistance is

A

very large as compared to the load resistance

B

equal to the resistance of the load

C

non-zero but less than the resistance of the load

D

zero

Q 73PhysicsSection A • MCQgravitation

+4 / -1

A particle of mass

10

g

is kept on the surface of a uniform sphere of mass

100

kg

and radius

10

cm.

Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take

G

= 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}

)

A

3.33 \times {10^{ - 10}}\,J

B

13.34 \times {10^{ - 10}}\,J

C

6.67 \times {10^{ - 10}}\,J

D

6.67 \times {10^{ - 9}}\,J

Q 74PhysicsSection A • MCQdual nature of radiation

+4 / -1

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

A

2

B

{1 \over 2}

C

{\sqrt 2 }

D

{1 \over {\sqrt 2 }}

Q 75ChemistrySection A • MCQp block elements

+4 / -1

Heating an aqueous solution of aluminium chloride to dryness will give :

A

AlCl₃

B

Al₂Cl₆

C

Al₂O₃

D

Al(OH)Cl₂

Q 76ChemistrySection A • MCQthermodynamics

+4 / -1

Consider the reaction: N₂ + 3H₂

\to

2NH₃ carried out at constant temperature and pressure. If

\Delta H

and

\Delta U

are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

A

\Delta H

>

\Delta U

B

\Delta H

<

\Delta U

C

\Delta H

=

\Delta U

D

\Delta H

= 0

Q 77ChemistrySection A • MCQsolutions

+4 / -1

Benzene and toluene form nearly ideal solutions. At 20 ^oC, the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at 20 ^oC for a solution containing 78 g of benzene and 46 g of toluene in torr is

A

50

B

25

C

53.5

D

37.5

Q 78ChemistrySection A • MCQelectrochemistry

+4 / -1

Aluminium oxide may be electrolysed at 1000^oC to furnish aluminium metal (Atomic mass = 27 amu; 1 Faraday = 96,500 Coulombs). The cathode reaction is Al³⁺ + 3e^-

\to

Al^o To prepare 5.12 kg of aluminium metal by this method would require

A

5.49

\times

10⁷ C of electricity

B

1.83

\times

10⁷ C of electricity

C

5.49

\times

10⁴ C of electricity

D

5.49

\times

10¹ C of electricity

Q 79ChemistrySection A • MCQatomic structure

+4 / -1

Pick out the isoelectronic structure from the following :

\eqalign{ & \left( i \right)\,\,\,\,\,\,C{H_3}^ + \cr & \left( {ii} \right)\,\,\,\,{H_3}{O^ + } \cr & \left( {iii} \right)\,\,\,N{H_3} \cr & \left( {iv} \right)\,\,\,\,C{H_3}^ - \cr}

A

(i)

and

(ii)

B

(iii)

and

(iv)

C

(i)

and

(iii)

D

(ii), (iii)

and

(iv)

Official Correct Answer:Option (D)

Step-by-Step Solution:

Ions	No. of electrons
CH₃⁺	8
H₃O⁺	10
NH₃	10
CH₃^-	10

\therefore

\,\,\,

{H_3}{O^ + },N{H_3}

and

C{H_3}^ -

are isoelectronic.

Q 80ChemistrySection A • MCQhydrocarbons

+4 / -1

Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is

A

n-hexane

B

2, 3-dimethylbutane

C

2,2-dimethylbutane

D

2-methylpentane

Q 81ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Lattice energy of an ionic compounds depends upon

A

Charge on the ion only

B

Size of the ion only

C

Packing of ions only

D

Charge on the ion and size of the ion

Q 82ChemistrySection A • MCQsolutions

+4 / -1

Equimolar solutions in the same solvent have

A

Same boiling point but different freezing point

B

Same freezing point but different boiling point

C

Same boiling and same freezing points

D

Different boiling and different freezing points

Q 83ChemistrySection A • MCQd and f block elements

+4 / -1

Which of the following factors may be regarded as the main cause of lanthanide contraction?

A

Poor shielding of one of 4f electron by another in the subshell

B

Effective shielding of one of 4f electrons by another in the subshell

C

Poorer shielding of 5d electrons by 4f electrons

D

Greater shielding of 5d electrons by 4f electrons

Q 84ChemistrySection A • MCQgaseous state

+4 / -1

Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

A

The most probable speed increases

B

The fraction of the molecules with the most probable speed increases

C

The distribution becomes broader

D

The area under the distribution curve remains the same as under the lower temperature

Q 85ChemistrySection A • MCQcoordination compounds

+4 / -1

The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is :

A

d⁴ (in strong ligand field)

B

d⁴ (in weak ligand field)

C

d³ (in weak as well as in strong fields)

D

d⁵ (in strong ligand field)

Q 86ChemistrySection A • MCQatomic structure

+4 / -1

Of the following sets which one does NOT contain isoelectronic species?

A

BO_3^{3 - }

,

CO_3^{2 - }

,

NO_3^{- }

B

SO_3^{2 - }

,

CO_3^{2 - }

,

NO_3^{-}

C

CN^{- }

,

N_2

,

C_2^{2 - }

D

PO_4^{3 - }

,

SO_4^{2 - }

,

ClO_4^{ - }

Q 87ChemistrySection A • MCQcoordination compounds

+4 / -1

The IUPAC name of the coordination compound K₃[Fe(CN)₆] is

A

Potassium hexacyanoferrate (II)

B

Potassium hexacyanoferrate (III)

C

Potassium hexacyanoiron (II)

D

Tripotassium hexcyanoiron (II)

Q 88ChemistrySection A • MCQd and f block elements

+4 / -1

Calomel

\left( {H{g_2}C{l_2}} \right)

on reaction with ammonium hydroxide gives :

A

HgO

B

H{g_2}O

C

N{H_2} - Hg - Hg - Cl

D

HgN{H_2}Cl

Q 89ChemistrySection A • MCQhydrogen

+4 / -1

Which of the following statements in relation to the hydrogen atom is correct?

A

3s orbital is lower in energy than 3p orbital

B

3p orbital is lower in energy than 3d orbital

C

3s and 3p orbitals are of lower energy than 3d orbital

D

3s, 3p and 3d orbitals all have the same energy

Q 90ChemistrySection A • MCQd and f block elements

+4 / -1

The lanthanide contraction is responsible for the fact that :

A

Zr and Y have about the same radius

B

Zr and Nb have similar oxidation state

C

Zr and Hf have about the same radius

D

Zr and Zn have the same oxidation

Q 91ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The reaction

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

is fastest when

X

is

A

OCOR

B

O{C_2}{H_5}

C

N{H_2}

D

Cl

Q 92ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Tertiary alkyl halides are practically inert to substitution by S_N2 mechanism because of

A

insolubility

B

instability

C

inductive effect

D

steric hindrance

Q 93ChemistrySection A • MCQsolutions

+4 / -1

If

\alpha

is the degree of dissociation of Na₂SO₄, the vant Hoff’s factor (i) used for calculating the molecular mass is :

A

1 +

\alpha

B

1 +

2\alpha

C

1 -

\alpha

D

1 -

2\alpha

Q 94ChemistrySection A • MCQthermodynamics

+4 / -1

If the bond dissociation energies of XY, X₂ and Y₂ (all diatomic molecules) are in the ratio of 1:1:0.5 and

\Delta H_f

for the formation of XY is -200 kJ mole^-1. The bond dissociation energy of X₂ will be :

A

100 kJ mol^-1

B

200 kJ mol^-1

C

300 kJ mol^-1

D

800 kJ mol^-1

Q 95ChemistrySection A • MCQcoordination compounds

+4 / -1

The oxidation state of Cr in [Cr(NH₃)₄Cl₂]⁺ is :

A

+3

B

+2

C

+1

D

0

Q 96ChemistrySection A • MCQp block elements

+4 / -1

In silicon dioxide :

A

Each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms

B

Each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bonded to two silicon atoms

C

Silicon atoms is bonded to two oxygen atoms

D

there are double bonds between silicon and oxygen atoms

Q 97ChemistrySection A • MCQionic equilibrium

+4 / -1

What is the conjugate base of OH^-?

A

O₂

B

H₂O

C

O^-

D

O^-2

Q 98ChemistrySection A • MCQhydrocarbons

+4 / -1

Which types of isomerism is shown by 2,3-dichlorobutane?

A

Diastereo

B

Optical

C

Geometric

D

Structural

Q 99ChemistrySection A • MCQd and f block elements

+4 / -1

The oxidation state of chromium in the final product formed the reaction between

K{\rm I}

and acidified potassium dichromate solution is :

A

+3

B

+2

C

+6

D

+4

Q 100ChemistrySection A • MCQpolymers

+4 / -1

Which of the following is a polyamide?

A

Teflon

B

Nylon – 6, 6

C

Terylene

D

Bakelite

Q 101ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Amongst the following the most basic compound is

A

benzylamine

B

aniline

C

acetanilide

D

p-nitroaniline

Q 102ChemistrySection A • MCQisolation of elements

+4 / -1

During the process of electrolytic refining of copper, some metals present as impurity settle as ‘anode mud’ These are

A

Sn and Ag

B

Pb and Zn

C

Ag and Au

D

Fe and Ni

Q 103ChemistrySection A • MCQhydrocarbons

+4 / -1

Reaction of one molecule of HBr with one molecule of 1,3-butadiene at 40^oC gives predominantly

A

3-bromobutene under kinetically controlled conditions

B

1-bromo-2-butene under thermodymically controlled conditions

C

3-bromobutene under thermodynamically controlled conditions

D

1-bromo-2-butene under kinetically controlled conditions

Q 104ChemistrySection A • MCQp block elements

+4 / -1

The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous acid is :

A

zero

B

two

C

one

D

three

Q 105ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound if water during the reaction is continuously removed. The compound formed is generally known as

A

a Schiff’s base

B

an enamine

C

an imine

D

an amine

Q 106ChemistrySection A • MCQcoordination compounds

+4 / -1

Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour?
(At. No. Cr = 24, Mn = 25, Fe = 26, Co = 27)

A

[Cr(CN)₆]^-3

B

[Mn(CN)₆]^-3

C

[Fe(CN)₆]^-3

D

[Co(CN)₆]^-3

Official Correct Answer:Option (D)

Step-by-Step Solution:

		No. of unpaired electron
a)	Co³⁺	0
b)	Fe³⁺	1
c)	Mn³⁺	2
d)	Cr³⁺	3

The effective magnetic moment is given by the number of unpaired electrons in a substance, the lesser the number of unpaired electrons lower is its magnetic moment in Bohr

-

Magneton and lower shall be its paramagnetism

Q 107ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Elimination of bromine from 2-bromobutane results in the formation of-

A

equimolar mixture of 1 and 2-butene

B

predominantly 2-butene

C

predominantly 1-butene

D

predominantly 2-butyne

Q 108ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

Hydrogen bomb is based on the principle of

A

Nuclear fission

B

Natural radioactivity

C

Nuclear fusion

D

Artificial radioactivity

Q 109ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The decreasing order of nucleophilicity among the nucleophiles

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

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

A

\left( C \right),\left( B \right),\left( A \right),\left( D \right)

B

\left( B \right),\left( C \right),\left( A \right),\left( D \right)

C

\left( D \right),\left( C \right),\left( B \right),\left( A \right)

D

\left( A \right),\left( B \right),\left( C \right),\left( D \right)

Q 110ChemistrySection A • MCQelectrochemistry

+4 / -1

For a spontaneous reaction the ∆G , equilibrium constant (K) and

E_{cell}^o

will be respectively

A

-ve, >1, +ve

B

+ve, >1, -ve

C

-ve, <1, -ve

D

-ve, >1, -ve

Q 111ChemistrySection A • MCQelectrochemistry

+4 / -1

Electrolyte:	KCl	KNO₃	HCl	NaOAc	NaCl
${ \wedge ^\infty }(Sc{m^2}mo{l^{ - 1}}):$	149.9	145	426.2	91	126.5

Calculate

\wedge _{HOAc}^\infty

Using appropriate molar conductances of the electrolytes listed above at infinite dilution in H₂O at 25^oC

A

517.2

B

552.7

C

390.7

D

217.5

Q 112ChemistrySection A • MCQs block elements

+4 / -1

Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point :

A

LiCl

B

NaCl

C

KCl

D

RbCl

Q 113ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

t_1/4 can be taken as the time taken for the concentration of a reactant to drop to

3 \over 4

of its initial value. If the rate constant for a first order reaction is K, the t_1/4 can be written as

A

0.10 / K

B

0.29 / K

C

0.69 / K

D

0.75 / K

Q 114ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Which one of the following types of drugs reduces fever?

A

Analgesic

B

Antipyretic

C

Antibiotic

D

Tranquiliser

Q 115ChemistrySection A • MCQpolymers

+4 / -1

Which of the following is fully fluorinated polymer?

A

Neoprene

B

Teflon

C

Thiokol

D

PVC

Q 116ChemistrySection A • MCQchemical equilibrium

+4 / -1

The exothermic formation of ClF₃ is represented by the equation:
Cl₂ (g) + 3F₂ (g)

\leftrightharpoons

2ClF₃ (g);

\Delta H

= -329 kJ
Which of the following will increase the quantity of ClF₃ in an equilibrium mixture of Cl₂, F₂ and ClF₃?

A

Increasing the temperature

B

Removing Cl₂

C

Increasing the volume of the container

D

Adding F₂

Q 117ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Acid catalyzed hydration of alkenes except ethene leads to the formation of

A

primary alcohol

B

secondary or tertiary alcohol

C

mixture of primary and secondary alcohols

D

mixture of secondary and tertiary alcohols

Q 118ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 ml of 1.2 M second solution. What is the molarity of the final mixture?

A

2.70 M

B

1.344 M

C

1.50 M

D

1.20 M

Q 119ChemistrySection A • MCQelectrochemistry

+4 / -1

The highest electrical conductivity of the following aqueous solutions is of :

A

0.1 M acetic acid

B

0.1 M chloroacetic acid

C

0.1 M fluoroacetic acid

D

0.1 M difluoroacetic acid

Q 120ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Due to the presence of an unpaired electron, free radicals are:

A

Chemically reactive

B

Chemically inactive

C

Anions

D

Cations

Q 121ChemistrySection A • MCQd and f block elements

+4 / -1

On heating mixture of

C{u_2}O

and

C{u_2}S

will give :

A

C{u_2}S{O_3}

B

CuO + CuS

C

Cu + S{O_3}

D

Cu + S{O_2}

Q 122ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

p

-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound

B.

The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is :

A

qImage-preparation-properties-and-uses-of-carboxylic-acids-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

B

C

D

Q 123ChemistrySection A • MCQperiodic classification of elements

+4 / -1

In which of the following arrangements the order is NOT according to the property indicated against it?

A

Li < Na < K < Rb Increasing metallic radius

B

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

C

B < C < N < O Increasing first ionization enthalpy

D

Al³⁺ < Mg²⁺ < Na⁺ < F^- Increasing ionic size

Q 124ChemistrySection A • MCQionic equilibrium

+4 / -1

Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be :

A

3.98

\times

10^-6

B

3.68

\times

10^-6

C

3.88

\times

10⁶

D

3.98

\times

10⁸

Q 125ChemistrySection A • MCQchemical equilibrium

+4 / -1

For the reaction 2NO₂ (g)

\leftrightharpoons

2NO (g) + O₂ (g), (K_c = 1.8

\times

10^-6 at 184^oC) (R = 0.0831 kJ/(mol. K))
When K_p and K_c are compared at 184^oC , it is found that :

A

K_p is greater than K_c

B

K_p is less than K_c

C

K_p = K_c

D

Whether K_p is greater than, less than or equal to K_c depends upon the total gas pressure

Q 126ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one is

A

Acidic permanganate

B

Acidic dichromate

C

Chromic anhydride in glacial acetic acid

D

Pyridinium chloro – chromate

Q 127ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Alkyl halides react with dialkyl copper reagents to give

A

alkenes

B

alkyl copper halides

C

alkanes

D

alkenyl halides

Q 128ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

A schematic plot of

ln

{K_{eq}}

versus inverse of temperature for a reaction is shown below

qImage-arrhenius-equation-chemical-kinetics-and-nuclear-chemistry-physical-chemistry-Jeemate

qImage-arrhenius-equation-chemical-kinetics-and-nuclear-chemistry-physical-chemistry-Jeemate

The reaction must be

A

highly spontaneous at ordinary temperature

B

one with negligible enthalpy change

C

endothermic

D

exothermic

Q 129ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Among the following acids which has the lowest pK_a value?

A

CH₃COOH

B

HCOOH

C

(CH₃)₂COOH

D

CH₃CH₂COOH

Q 130ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

A reaction involving two different reactants can never be

A

Unimolecular reaction

B

First order reaction

C

second order reaction

D

Bimolecular reaction

Q 131ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

Which one of the following methods is neither meant for the synthesis nor for separation of amines?

A

Hinsberg method

B

Hofmann method

C

Wurtz reaction

D

Curtius reaction

Q 132ChemistrySection A • MCQp block elements

+4 / -1

The correct order of the thermal stability of hydrogen halides (H – X) is :

A

HI > HBr > HCl > HF

B

HF > HCl > HBr > HI

C

HCl < HF > HBr < HI

D

HI > HCl < HF < HBr

Q 133ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

The photon of hard gamma radiation knocks a proton out of

{}_{12}^{24}Mg

nucleus to form

A

the isotope of parent nucleus

B

the isobar of parent nucleus

C

the nuclide

{}_{11}^{23}Na

D

the isobar of

{}_{11}^{23}Na

Q 134ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Which one of the following species is diamagnetic in nature?

A

He_2^+

B

H₂

C

H_2^+

D

H_2^-

Q 135ChemistrySection A • MCQthermodynamics

+4 / -1

Consider an endothermic reaction, X

\to

Y with the activation energies E_b and E_f for the backward and forward reactions, respectively. In general :

A

E_b < E_f

B

E_b > E_f

C

E_b = E_f

D

There is no definite relation between E_b and E_f

Q 136ChemistrySection A • MCQbiomolecules

+4 / -1

In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-

A

C_5^{'}

and

C_2^{'}

respectively of the sugar molecule

B

C_2^{'}

and

C_5^{'}

respectively of the sugar molecule

C

C_1^{'}

and

C_5^{'}

respectively of the sugar molecule

D

C_5^{'}

and

C_1^{'}

respectively of the sugar molecule

Q 137ChemistrySection A • MCQatomic structure

+4 / -1

In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same energy in the absence of magnetic and electric fields?
(A) n = 1, l = 0, m = 0
(B) n = 2, l = 0, m = 0
(C) n = 2, l = 1, m = 1
(D) n = 3, l = 2, m = 1
(E) n = 3, l = 2, m = 0

A

(D) and (E)

B

(C) and (D)

C

(B) and (C)

D

(A) and (B)

Q 138ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Which of the following oxides is amphoteric in character?

A

CaO

B

CO₂

C

SiO₂

D

SnO₂

Q 139ChemistrySection A • MCQsolid state

+4 / -1

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be :

A

AB

B

A₂B

C

AB₃

D

A₃B

Q 140ChemistrySection A • MCQsurface chemistry

+4 / -1

The volume of a colloidal particle, V_C as compared to the volume of a solute particle in a true solution V_S, could be

A

{V_C \over V_S } \simeq 1

B

{V_C \over V_S } \simeq 10^{-3}

C

{V_C \over V_S } \simeq 10^3

D

{V_C \over V_S } \simeq 10^{23}

Q 141ChemistrySection A • MCQsurface chemistry

+4 / -1

The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively, which of the following statements is NOT correct?

A

magnesium chloride solution coagulates, the gold sol more readily than the iron (III) hydroxide sol.

B

sodium sulphate solution causes coagulation in both sols

C

mixing the sols has no effect

D

coagulation in both sols can be brought about by electrophoresis

Q 142ChemistrySection A • MCQionic equilibrium

+4 / -1

The solubility product of a salt having general formula MX₂, in water is: 4

\times

10^-12 . The concentration of M²⁺ ions in the aqueous solution of the salt is :

A

2.0

\times

10^-6 M

B

4.0

\times

10^-10 M

C

1.0

\times

10^-4 M

D

1.6

\times

10^-4 M

Q 143ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of the substance will

A

be a function of the molecular mass of the substance

B

remain unchanged

C

increase two fold

D

decrease twice

Q 144ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% and N = 46.67% while rest is oxygen. On heating it gives NH₃ along with a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is

A

CH₃NCO

B

CH₃CONH₂

C

(NH₂)₂CO

D

CH₃CH₂CONH₂

Official Correct Answer:Option (C)

Step-by-Step Solution:

Elements	%	Relative number of atoms	Simple Ratio
C	20%	20/12=1.66	1.66/1.66=1
H	6.67%	6.67/1=6.67	6.67/1.66=4.16
N	46.67%	46.67/14=3.33	3.33/1.66=2.02
O	26.64%	26.64/16=1.66	1.66/1.66=1.0

The compound is

C{H_4}{N_2}O

Empirical weight

=60;

Mol. wt.

=60;

\therefore

\,\,\,\,

n = {{60} \over {60}} = 1

On heating urea losses ammonia to give Biuret
qImage--compounds-containing-nitrogen-organic-chemistry-Jeemate

Biuret with alkaline

CuS{O_4}

gives violet colour. Test for

-CONH-

group.

Q 145ChemistrySection A • MCQp block elements

+4 / -1

The structure of diborane (B₂H₆) contains :

A

four 2c-2e bonds and two 3c-2e bonds

B

two 2c-2e bonds and four 3c-2e bonds

C

two 2c-2e bonds and two 3c-3e bonds

D

four 2c-2e bonds and four 3c-2e bonds

Q 146ChemistrySection A • MCQchemical equilibrium

+4 / -1

An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. Pressure. Ammonium hydrogen sulphide decomposes to yield NH₃ and H₂S gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm. The equilibrium constant for NH₄HS decomposition at this temperature is :

A

0.30

B

0.11

C

0.17

D

0.18

Q 147ChemistrySection A • MCQhydrocarbons

+4 / -1

2 methylbutane on reacting with bromine in the presence of sunlight gives mainly

A

1 – bromo -2 - methylbutane

B

2 – bromo -2 - methylbutane

C

2 – bromo -3 - methylbutane

D

1 – bromo -3 – methylbutane

Q 148ChemistrySection A • MCQcoordination compounds

+4 / -1

Which of the following compounds shows optical isomerism?

A

[Cu(NH₃)₄]⁺²

B

[ZnCl₄]^-2

C

[Cr(C₂O₄)₃]^-3

D

[Co(CN)₆]^-3

Q 149MathematicsSection A • MCQ3d geometry

+4 / -1

The plane

x+2y-z=4

cuts the sphere

{x^2} + {y^2} + {z^2} - x + z - 2 = 0

in a circle of radius

A

3

B

1

C

2

D

{\sqrt 2 }

Q 150MathematicsSection A • MCQ3d geometry

+4 / -1

If the angel

\theta

between the line

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

and

the plane

2x - y + \sqrt \lambda \,\,z + 4 = 0

is such that

\sin \,\,\theta = {1 \over 3}

then value of

\lambda

is :

A

{5 \over 3}

B

{-3 \over 5}

C

{3 \over 4}

D

{-4 \over 3}

Q 151MathematicsSection A • MCQellipse

+4 / -1

An ellipse has

OB

as semi minor axis,

F

and

F

' its focii and theangle

FBF

' is a right angle. Then the eccentricity of the ellipse is :

A

{1 \over {\sqrt 2 }}

B

{1 \over 2}

C

{1 \over 4}

D

{1 \over {\sqrt 3 }}

Q 152MathematicsSection A • MCQcircle

+4 / -1

If the pair of lines

a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0

lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then :

A

3{a^2} - 10ab + 3{b^2} = 0

B

3{a^2} - 2ab + 3{b^2} = 0

C

3{a^2} + 10ab + 3{b^2} = 0

D

3{a^2} + 2ab + 3{b^2} = 0

Q 153MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

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

are in G.P., then the determinant

&#x27; in math mode at position 1:

̲\Delta = \left|…" style="color:#cc0000">$\Delta = \left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|$
is equal to :

A

1

B

0

C

4

D

2

Q 154MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

If

f

is a real valued differentiable function satisfying

\left| {f\left( x \right) - f\left( y \right)} \right|

\le {\left( {x - y} \right)^2}

,

x, y

\in R

and

f(0)

= 0, then

f(1)

equals

A

-1

B

0

C

2

D

1

Q 155MathematicsSection A • MCQvector algebra

+4 / -1

For any vector

{\overrightarrow a }

, the value of

{\left( {\overrightarrow a \times \widehat i} \right)^2} + {\left( {\overrightarrow a \times \widehat j} \right)^2} + {\left( {\overrightarrow a \times \widehat k} \right)^2}

is equal to :

A

3{\overrightarrow a ^2}

B

{\overrightarrow a ^2}

C

2{\overrightarrow a ^2}

D

4{\overrightarrow a ^2}

Q 156MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If non zero numbers

a, b, c

are in

H.P.,

then the straight line

{x \over a} + {y \over b} + {1 \over c} = 0

always passes through a fixed point. That point is :

A

(-1,2)

B

(-1, -2)

C

(1, -2)

D

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

Q 157MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If a vertex of a triangle is

(1, 1)

and the mid points of two sides through this vertex are

(-1, 2)

and

(3, 2)

then the centroid of the triangle is :

A

\left( { - 1,{7 \over 3}} \right)

B

\left( {{{ - 1} \over 3},{7 \over 3}} \right)

C

\left( { 1,{7 \over 3}} \right)

D

\left( {{{ 1} \over 3},{7 \over 3}} \right)

Q 158MathematicsSection A • MCQcircle

+4 / -1

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

A

an ellipse

B

a circle

C

a hyperbola

D

a parabola

Q 159MathematicsSection A • MCQsets and relations

+4 / -1

Let

R=\{(3,3),(6,6),(9,9),(12,12),(6,12)

,

(3,9),(3,12),(3,6)\}

be a relation on the set

A=\{3,6,9,12\}

. The relation is :

A

reflexive and symmetric only

B

an equivalence relation

C

reflexive only

D

reflexive and transitive only

Q 160MathematicsSection A • MCQdefinite integration

+4 / -1

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]

equals

A

{1 \over 2}\sec 1

B

{1 \over 2}

cosec 1

C

tan 1

D

{1 \over 2}

tan 1

Q 161MathematicsSection A • MCQdifferential equations

+4 / -1

If

x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),

then the solution of the equation is :

A

y\log \left( {{x \over y}} \right) = cx

B

x\log \left( {{y \over x}} \right) = cy

C

\log \left( {{y \over x}} \right) = cx

D

\log \left( {{x \over y}} \right) = cy

Q 162MathematicsSection A • MCQprobability

+4 / -1

Let

A

and

B

two events such that

P\left( {\overline {A \cup B} } \right) = {1 \over 6},

P\left( {A \cap B} \right) = {1 \over 4}

and

P\left( {\overline A } \right) = {1 \over 4},

where

{\overline A }

stands for complement of event

A

. Then events

A

and

B

are :

A

equally likely and mutually exclusive

B

equally likely but not independent

C

independent but not equally likely

D

mutually exclusive and independent

Q 163MathematicsSection A • MCQdefinite integration

+4 / -1

The value of

\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\,\,a > 0,}

is

A

a\,\pi

B

{\pi \over 2}

C

{\pi \over a}

D

{2\pi }

Q 164MathematicsSection A • MCQstatistics

+4 / -1

Let x₁, x₂,...........,x_n be n observations such that

\sum {x_i^2} = 400

and

\sum {{x_i}} = 80

. Then a possible value of n among the following is

A

18

B

15

C

12

D

9

Q 165MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If the roots of the equation

{x^2} - bx + c = 0

be two consecutive integers, then

{b^2} - 4c

equals

A

-2

B

3

C

2

D

1

Q 166MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

If

{\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,

then

4{x^2} - 4xy\cos \alpha + {y^2}

is equal to :

A

2\sin 2\alpha

B

4

C

4{\sin ^2}\alpha

D

-4{\sin ^2}\alpha

Q 167MathematicsSection A • MCQcircle

+4 / -1

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

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

orthogonally, then the equation of the locus of its centre is :

A

{x^2}\, + \,{y^2} - \,3ax\, - \,4\,by\,\, + \,({a^2}\, + \,{b^2} - {p^2}) = 0

B

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

C

{x^2}\, + \,{y^2} - \,2ax\, - \,\,3\,by\,\, + \,({a^2}\, - \,{b^2} - {p^2}) = 0

D

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

Q 168MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Suppose

f(x)

is differentiable at x = 1 and

\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) = 5

, then

f'\left( 1 \right)

equals

A

3

B

4

C

5

D

6

Q 169MathematicsSection A • MCQarea under the curves

+4 / -1

Let

f(x)

be a non - negative continuous function such that the area bounded by the curve

y=f(x),

x

-axis and the ordinates

x = {\pi \over 4}

and

x = \beta > {\pi \over 4}

is

\left( {\beta \sin \beta + {\pi \over 4}\cos \beta + \sqrt 2 \beta } \right).

Then

f\left( {{\pi \over 2}} \right)

is

A

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

B

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

C

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

D

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

Q 170MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The value of

a

for which the sum of the squares of the roots of the equation

{x^2} - \left( {a - 2} \right)x - a - 1 = 0

assume the least value is :

A

1

B

0

C

3

D

2

Q 171MathematicsSection A • MCQstatistics

+4 / -1

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :

A

20.5

B

22.0

C

24.0

D

25.5

Q 172MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

{A^2} - A + 1 = 0

, then the inverse of

A

is :

A

A+I

B

A

C

A-I

D

I-A

Q 173MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

{a^2} + {b^2} + {c^2} = - 2

and

f $\left( x \right) = \left| {\matrix{ {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \cr } } \right|,$

then f $(x)$ is a polynomial of degree :

A

1

B

0

C

3

D

2

Q 174MathematicsSection A • MCQarea under the curves

+4 / -1

The parabolas

{y^2} = 4x

and

{x^2} = 4y

divide the square region bounded by the lines

x=4,

y=4

and the coordinate axes. If

{S_1},{S_2},{S_3}

are respectively the areas of these parts numbered from top to bottom ; then

{S_1},{S_2},{S_3}

is :

A

1:2:1

B

1:2:3

C

2:1:2

D

1:1:1

Q 175MathematicsSection A • MCQvector algebra

+4 / -1

If

\overrightarrow a ,\overrightarrow b ,\overrightarrow c

are non coplanar vectors and

\lambda

is a real number then

\left[ {\lambda \left( {\overrightarrow a + \overrightarrow b } \right)\,\,\,\,\,\,\,\,{\lambda ^2}\overrightarrow b \,\,\,\,\,\,\,\,\lambda \overrightarrow c } \right] = \left[ {\overrightarrow a \,\,\,\,\,\,\,\,\overrightarrow b + \overrightarrow c \,\,\,\,\,\,\,\,\overrightarrow b } \right]

for :

A

exactly one value of

\lambda

B

no value of

\lambda

C

exactly three values of

\lambda

D

exactly two values of

\lambda

Q 176MathematicsSection A • MCQfunctions

+4 / -1

A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to

A

- f(x)

B

f(x)

C

f(a) + f(a - x)

D

f(- x)

Q 177MathematicsSection A • MCQhyperbola

+4 / -1

The locus of a point

P\left( {\alpha ,\beta } \right)

moving under the condition that the line

y = \alpha x + \beta

is tangent to the hyperbola

{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

is :

A

an ellipse

B

a circle

C

a parabola

D

a hyperbola

Q 178MathematicsSection A • MCQpermutations and combinations

+4 / -1

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

A

601

B

600

C

603

D

602

Q 179MathematicsSection A • MCQmathematical induction

+4 / -1

If

A = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]

and

I = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],

then which one of the following holds for all

n \ge 1,

by the principle of mathematical induction?

A

{A^n} = nA - \left( {n - 1} \right){\rm I}

B

{A^n} = {2^{n - 1}}A - \left( {n - 1} \right){\rm I}

C

{A^n} = nA + \left( {n - 1} \right){\rm I}

D

{A^n} = {2^{n - 1}}A + \left( {n - 1} \right){\rm I}

Q 180MathematicsSection A • MCQ3d geometry

+4 / -1

The distance between the line

\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),

and the plane

\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5

is

A

{{10} \over 9}

B

{{10} \over {3\sqrt 3 }}

C

{{3} \over 10}

D

{{10} \over 3}

Q 181MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let f be differentiable for all x. If f(1) = -2 and f'(x)

\ge

2 for
x

\in \left[ {1,6} \right]

, then

A

f(6)

\ge

8

B

f(6) < 8

C

f(6) < 5

D

f(6) = 5

Q 182MathematicsSection A • MCQdefinite integration

+4 / -1

If

{I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}}dx} } }

and

{I_4} = \int\limits_1^2 {{2^{{x^3}}}dx}

then

A

{I_2} > {I_1}

B

{I_1} > {I_2}

C

{I_3} = {I_4}

D

{I_3} > {I_4}

Q 183MathematicsSection A • MCQprobability

+4 / -1

A random variable

X

has Poisson distribution with mean

2

.
Then

P\left( {X > 1.5} \right)

equals :

A

{2 \over {{e^2}}}

B

0

C

1 - {3 \over {{e^2}}}

D

{3 \over {{e^2}}}

Q 184MathematicsSection A • MCQbinomial theorem

+4 / -1

If the coefficient of

{x^7}

in

{\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}

equals the coefficient of

{x^{ - 7}}

in

{\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}

, then

a

and

b

satisfy the relation

A

a - b = 1

B

a + b = 1

C

{a \over b} = 1

D

ab = 1

Q 185MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If both the roots of the quadratic equation

{x^2} - 2kx + {k^2} + k - 5 = 0

are less than 5, then

k

lies in the interval

A

\left( {5,6} \right]

B

\left( {6,\,\infty } \right)

C

\left( { - \infty ,\,4} \right)

D

\left[ {4,\,5} \right]

Q 186MathematicsSection A • MCQarea under the curves

+4 / -1

The area enclosed between the curve

y = {\log _e}\left( {x + e} \right)

and the coordinate axes is :

A

1

B

2

C

3

D

4

Q 187MathematicsSection A • MCQapplication of derivatives

+4 / -1

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

A

Interval	Function
(- $\infty$ , $\infty$ )	x³ - 3x² + 3x + 3

B

Interval	Function
[2, $\infty$ )	2x³ - 3x² - 12x + 6

C

Interval	Function
$\left( { - \infty ,{1 \over 3}} \right]$	3x² - 2x + 1

D

Interval	Function
( $- \infty$ , - 4 )	x³ + 6x² + 6

Q 188MathematicsSection A • MCQparabola

+4 / -1

Let

P

be the point

(1, 0)

and

Q

a point on the parabola

{y^2} = 8x

. The locus of mid point of

PQ

is :

A

{y^2} - 4x + 2 = 0

B

{y^2} + 4x + 2 = 0

C

{x^2} + 4y + 2 = 0

D

{x^2} - 4y + 2 = 0

Q 189MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let

\alpha

and

\beta

be the distinct roots of

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

, then

\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}

is equal to

A

{{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}

B

0

C

- {{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}

D

{{{{\left( {\alpha - \beta } \right)}^2}} \over 2}

Q 190MathematicsSection A • MCQapplication of derivatives

+4 / -1

Area of the greatest rectangle that can be inscribed in the
ellipse

{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1

A

2ab

B

ab

C

\sqrt {ab}

D

{a \over b}

Q 191MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The value of

a

for which the sum of the squares of the roots of the equation

{x^2} - \left( {a - 2} \right)x - a - 1 = 0

assume the least value is

A

1

B

0

C

3

D

2

Q 192MathematicsSection A • MCQcircle

+4 / -1

If the circles

{x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0

and

{x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0

intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

A

exactly one value of a

B

no value of a

C

infinitely many values of a

D

exactly two values of a

Q 193MathematicsSection A • MCQvector algebra

+4 / -1

Let

a, b

and

c

be distinct non-negative numbers. If the vectors

a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k

and

c\widehat i + c\widehat j + b\widehat k

lie in a plane, then

c

is :

A

the Geometric Mean of

a

and

b

B

the Arithmetic Mean of

a

and

b

C

equal to zero

D

the Harmonic Mean of

a

and

b

Q 194MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The line parallel to the

x

- axis and passing through the intersection of the lines

ax + 2by + 3b = 0

and

bx - 2ay - 3a = 0,

where

(a, b)

\ne

(0, 0)

is :

A

below the

x

- axis at a distance of

{3 \over 2}

from it

B

below the

x

- axis at a distance of

{2 \over 3}

from it

C

above the

x

- axis at a distance of

{3 \over 2}

from it

D

above the

x

- axis at a distance of

{2 \over 3}

from it

Q 195MathematicsSection A • MCQsequences and series

+4 / -1

The sum of the series

1 + {1 \over {4.2!}} + {1 \over {16.4!}} + {1 \over {64.6!}} + .......

ad inf. is

A

{{e - 1} \over {\sqrt e }}\,

B

{{e + 1} \over {\sqrt e }}

C

{{e - 1} \over {2\sqrt e }}

D

{{e + 1} \over {2\sqrt e }}

Q 196MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If the roots of the equation

{x^2} - bx + c = 0

be two consecutive integers, then

{b^2} - 4c

equals

A

-2

B

3

C

2

D

1

Q 197MathematicsSection A • MCQapplication of derivatives

+4 / -1

A spherical iron ball

10

cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of

50

cm

^3

/min. When the thickness of ice is

5

cm, then the rate at which the thickness of ice decreases is

A

{1 \over {36\pi }}

cm/min

B

{1 \over {18\pi }}

cm/min

C

{1 \over {54\pi }}

cm/min

D

{5 \over {6\pi }}

cm/min

Q 198MathematicsSection A • MCQvector algebra

+4 / -1

If

C

is the mid point of

AB

and

P

is any point outside

AB,

then :

A

\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC}

B

\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC}

C

\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC} = \overrightarrow 0

D

\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC} = \overrightarrow 0

Q 199MathematicsSection A • MCQbinomial theorem

+4 / -1

If the coefficients of r^th, (r+1)^th, and (r + 2)^th terms in the binomial expansion of

{{\rm{(1 + y )}}^m}

are in A.P., then m and r satisfy the equation

A

{m^2} - m(4r - 1) + 4\,{r^2} - 2 = 0

B

{m^2} - m(4r + 1) + 4\,{r^2} + 2 = 0

C

{m^2} - m(4r + 1) + 4\,{r^2} - 2 = 0

D

{m^2} - m(4r - 1) + 4\,{r^2} + 2 = 0

Q 200MathematicsSection A • MCQfunctions

+4 / -1

Let

f:( - 1,1) \to B

, be a function defined by

f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}

,
then

f

is both one-one and onto when B is the interval

A

\left( {0,{\pi \over 2}} \right)

B

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

C

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

D

\left( { - {\pi \over 2},{\pi \over 2}} \right)

Q 201MathematicsSection A • MCQdifferential equations

+4 / -1

The differential equation representing the family of curves

{y^2} = 2c\left( {x + \sqrt c } \right),

where

c>0,

is a parameter, is of order and degree as follows:

A

order

1,

degree

2

B

order

1,

degree

1

C

order

1,

degree

3

D

order

2,

degree

2

Q 202MathematicsSection A • MCQapplication of derivatives

+4 / -1

If the equation

{a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0

{a_1} \ne 0,n \ge 2,

has a positive root

x = \alpha

, then the equation

n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0

has a positive root, which is

A

greater than

\alpha

B

smaller than

\alpha

C

greater than or equal to smaller than

\alpha

D

equal to smaller than

\alpha

Q 203MathematicsSection A • MCQbinomial theorem

+4 / -1

The value of

\,{}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}} {C_3}

is

A

{}^{55}{C_4}

B

{}^{55}{C_3}

C

{}^{56}{C_3}

D

{}^{56}{C_4}

Q 204MathematicsSection A • MCQmatrices and determinants

+4 / -1

The system of equations

$\matrix{ {\alpha \,x + y + z = \alpha - 1} \cr {x + \alpha y + z = \alpha - 1} \cr {x + y + \alpha \,z = \alpha - 1} \cr }$

has no solutions, if $\alpha$ is :

A

-2

B

either

-2

or

1

C

not

-2

D

1

Q 205MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a \,\, = \,\,\widehat i - \widehat k,\,\,\,\,\,\overrightarrow b \,\,\, = \,\,\,x\widehat i + \widehat j\,\,\, + \,\,\,\left( {1 - x} \right)\widehat k

and

\overrightarrow c \,\, = \,\,y\widehat i + x\widehat j + \left( {1 + x - y} \right)\widehat k.

Then

\left[ {\overrightarrow a ,\overrightarrow b ,\overrightarrow c } \right]

depends on :

A

only

y

B

only

x

C

both

x

and

y

D

neither

x

nor

y

Q 206MathematicsSection A • MCQsequences and series

+4 / -1

If

x = \sum\limits_{n = 0}^\infty {{a^n},\,\,y = \sum\limits_{n = 0}^\infty {{b^n},\,\,z = \sum\limits_{n = 0}^\infty {{c^n},} } } \,\,

where a, b, c are in A.P and

\,\left| a \right| < 1,\,\left| b \right| < 1,\,\left| c \right| < 1

then x, y, z are in

A

G.P.

B

A.P.

C

Arithmetic-Geometric Progression

D

H.P.

Q 207MathematicsSection A • MCQbinomial theorem

+4 / -1

If

x

is so small that

{x^3}

and higher powers of

x

may be neglected, then

{{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}}

may be approximated as

A

1 - {3 \over 8}{x^2}

B

3x + {3 \over 8}{x^2}

C

- {3 \over 8}{x^2}

D

{x \over 2} - {3 \over 8}{x^2}

Q 208MathematicsSection A • MCQapplication of derivatives

+4 / -1

The normal to the curve

x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)

at any point

\theta\, '

is such that

A

it passes through the origin

B

it makes an angle

{\pi \over 2} + \theta

with the

x

-axis

C

it passes through

\left( {a{\pi \over 2}, - a} \right)

D

it is at a constant distance from the origin

Q 209MathematicsSection A • MCQproperties of triangles

+4 / -1

In a triangle

ABC

, let

\angle C = {\pi \over 2}

. If

r

is the inradius and

R

is the circumradius of the triangle

ABC

, then

2(r+R)

equals :

A

b+c

B

a+b

C

a+b+c

D

c+a

Q 210MathematicsSection A • MCQproperties of triangles

+4 / -1

If in a

\Delta ABC

, the altitudes from the vertices

A, B, C

on opposite sides are in H.P, then

\sin A,\sin B,\sin C

are in :

A

G. P.

B

A. P.

C

A.P-G.P.

D

H. P

Q 211MathematicsSection A • MCQprobability

+4 / -1

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A

{2 \over 9}

B

{1 \over 9}

C

{8 \over 9}

D

{7 \over 9}

Q 212MathematicsSection A • MCQdefinite integration

+4 / -1

Let

f:R \to R

be a differentiable function having

f\left( 2 \right) = 6

,

f'\left( 2 \right) = \left( {{1 \over {48}}} \right)

. Then

\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt}

equals :

A

24

B

36

C

12

D

18

Q 213MathematicsSection A • MCQapplication of derivatives

+4 / -1

A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of

2 \mathrm{~cm} / \mathrm{s}^2

and pursues the insect which is crawling uniformly along a straight line at a speed of

20 \mathrm{~cm} / \mathrm{s}

. Then the lizard will catch the insect after :

A

20 s

B

1 s

C

21 s

D

24 s

Q 214MathematicsSection A • MCQindefinite integration

+4 / -1

\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx}

is equal to

A

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

B

{x \over {{x^2} + 1}} + C

C

{{x{e^x}} \over {1 + {x^2}}} + C

D

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

Q 215MathematicsSection A • MCQ3d geometry

+4 / -1

The angle between the lines

2x=3y=-z

and

6x=-y=-4z

is :

A

{0^ \circ }

B

{90^ \circ }

C

{45^ \circ }

D

{30^ \circ }

Q 216MathematicsSection A • MCQcomplex numbers

+4 / -1

If the cube roots of unity are 1,

\omega \,,\,{\omega ^2}

then the roots of the equation

{(x - 1)^3}

+ 8 = 0, are :

A

- 1, - 1 + 2\,\,\omega , - 1 - 2\,\,{\omega ^2}

B

- 1, - 1, - 1

C

- 1,1 - 2\omega ,1 - 2{\omega ^2}

D

- 1,1 + 2\omega ,1 + 2{\omega ^2}

Q 217MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

In a triangle

PQR,\;\;\angle R = {\pi \over 2}.\,\,If\,\,\tan \,\left( {{P \over 2}} \right)

and

\tan \left( {{Q \over 2}} \right)

are the roots of

a{x^2} + bx + c = 0,\,\,a \ne 0

then

A

a = b + c

B

c = a + b

C

b = c

D

b = a + c

Q 218MathematicsSection A • MCQcomplex numbers

+4 / -1

If

{z_1}

and

{z_2}

are two non-zero complex numbers such that

\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|

, then arg

{z_1}

- arg

{z_2}

is equal to :

A

{\pi \over 2}\,

B

- \pi

C

0

D

{{ - \pi } \over 2}

Q 219MathematicsSection A • MCQdefinite integration

+4 / -1

The value of integral,

\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \sqrt x }}} dx

is

A

{1 \over 2}

B

{3 \over 2}

C

2

D

1

Q 220MathematicsSection A • MCQ3d geometry

+4 / -1

If the plane

2ax-3ay+4az+6=0

passes through the midpoint of the line joining the centres of the spheres

{x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13

and

{x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8

then a equals :

A

-1

B

1

C

-2

D

2

Q 221MathematicsSection A • MCQcomplex numbers

+4 / -1

If

\,\omega = {z \over {z - {1 \over 3}i}}\,

and

\left| \omega \right| = 1

, then

z

lies on :

A

an ellipse

B

a circle

C

a straight line

D

a parabola

AIEEE 2005 Question Paper with Solutions