JEE Mains Aieee 2008 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQdual nature of radiation

+4 / -1

In an experiment, electrons are made to pass through a narrow slit of width

'd'

comparable to their de Broglie wavelength. They are detected on a screen at a distance

'D'

from the slit (see figure). qImage-matter-waves-davisson-and-germer-experiment-dual-nature-of-radiation-modern-physics-Jeemate

Which of the following graphs can be expected to represent the number of electrons $'N'$ detected as a function of the detector position $'y'\left( {y = 0} \right.$ corresponds to the middle of the slit $\left. \, \right)$

A

B

C

D

Q 2PhysicsSection A • MCQrotational motion

+4 / -1

Consider a uniform square plate of side

' a '

and mass

'm'

. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A

{5 \over 6}m{a^2}

B

{1 \over 12}m{a^2}

C

{7 \over 12}m{a^2}

D

{2 \over 3}m{a^2}

Q 3PhysicsSection A • MCQray optics

+4 / -1

A student measures the focal length of a convex lens by putting an object pin at a distance

'u'

from the lens and measuring the distance

'v'

of the image pin. The graph between

'u'

and

'v'

plotted by the student should look like

A

qImage-lenses-geometrical-optics-optics-Jeemate

B

C

D

Q 4PhysicsSection A • MCQgravitation

+4 / -1

This question contains Statement -

1

and Statement -

2

. of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $1$ :

For a mass

M

kept at the center of a cube of side

'a'

, the flux of gravitational field passing through its sides

4\,\pi \,GM.

Statement - 2:

If the direction of a field due to a point source is radial and its dependence on the distance

'r'

from the source is given as

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

its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

A

Statement -

1

is false, Statement -

2

is true

B

Statement -

1

is true, Statement -

2

is true; Statement -

2

is a correct explanation for Statement -

1

C

Statement -

1

is true, Statement -

2

is true; Statement -

2

is not a correct explanation for Statement -

1

D

Statement -

1

is true, Statement -

2

is false

Q 5PhysicsSection A • MCQdual nature of radiation

+4 / -1

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). qImage-davisson-and-germer-experiment-dual-nature-of-radiation-modern-physics-Jeemate

qImage-davisson-and-germer-experiment-dual-nature-of-radiation-modern-physics-Jeemate

Electrons accelerated by potential $V$ are diffracted from a crystal. If $d = 1\mathop A\limits^ \circ$ and $i = {30^ \circ },\,\,\,V$ should be about
$\left( {h = 6.6 \times {{10}^{ - 34}}Js,{m_e} = 9.1 \times {{10}^{ - 31}}kg,\,e = 1.6 \times {{10}^{ - 19}}C} \right)$

A

2000

V

B

50

V

C

500

V

D

1000

V

Q 6PhysicsSection A • MCQcurrent electricity

+4 / -1

Consider a block of conducting material of resistivity

'\rho '

shown in the figure. Current

'I'

enters at

'A'

and leaves from

'D'

. We apply superposition principle to find voltage

'\Delta V'

developed between

'B'

and

'C'

. The calculation is done in the following steps:
(i) Take current

'I'

entering from

'A'

and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field

E(r)

at distance

'r'

from A by using Ohm's law

E = \rho j,

where

j

is the current per unit area at

'r'

.
(iii) From the

'r'

dependence of

E(r)

, obtain the potential

V(r)

at

r

.
(iv) Repeat (i), (ii) and (iii) for current

'I'

leaving

'D'

and superpose results for

'A'

and

'D'.

qImage-resistance-and-resistivity-current-electricity-electricity-Jeemate

For current entering at $A,$ the electric field at a distance $'r'$ from $A$ is

A

{{\rho I} \over {8\pi {r^2}}}

B

{{\rho I} \over {{r^2}}}

C

{{\rho I} \over {2\pi {r^2}}}

D

{{\rho I} \over {4\pi {r^2}}}

Q 7PhysicsSection A • MCQcenter of mass

+4 / -1

A thin rod of length

'L'

is lying along the

x

-axis with its ends at

x=0

and

x=L

. Its linear density (mass/length) varies with

x

as

k{\left( {{x \over L}} \right)^n},

where

n

can be zero or any positive number. If the position

{X_{CM}}

of the center of mass of the rod is plotted against

'n',

which of the following graphs best approximates the dependence of

{X_{CM}}

on

n

?

A

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

B

C

D

Q 8PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

Relative permittivity and permeability of a material

{\varepsilon _r}

and

{\mu _r},

respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

A

{\varepsilon _r} = 0.5,\,\,{\mu _r} = 1.5

B

{\varepsilon _r} = 1.5,\,\,{\mu _r} = 0.5

C

{\varepsilon _r} = 0.5,\,\,{\mu _r} = 0.5

D

{\varepsilon _r} = 1.5,\,\,{\mu _r} = 1.5

Q 9PhysicsSection A • MCQdual nature of radiation

+4 / -1

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). qImage-davisson-and-germer-experiment-dual-nature-of-radiation-modern-physics-Jeemate

If a strong diffraction peak is observed when electrons are incident at an angle $'i'$ from the normal to the crystal planes with distance $'d'$ between them (see figure), de Broglie wavelength ${\lambda _{dB}}$ of electrons can be calculated by the relationship ( $n$ is an integer)

A

d\,\sin \,i = n{\lambda _{dB}}

B

2d\,\cos \,i = n{\lambda _{dB}}

C

2d\,\sin \,i = n{\lambda _{dB}}

D

d\,\cos \,i = n{\lambda _{dB}}

Q 10PhysicsSection A • MCQcurrent electricity

+4 / -1

A

5V

battery with internal resistance

2\Omega

and a

2V

battery with internal resistance

1\Omega

are connected to a

10\Omega

resistor as shown in the figure. qImage-kirchhoffs-circuit-laws-current-electricity-electricity-Jeemate

The current in the $10\Omega$ resistor is

A

0.27A{P_2}\,\,to\,\,{P_1}

B

0.03A{P_1}\,\,to\,\,{P_2}

C

0.03A{P_2}\,\,to\,\,{P_1}

D

0.27A{P_1}\,\,to\,\,{P_2}

Q 11PhysicsSection A • MCQwaves

+4 / -1

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of

18

cm

during winter. Repeating the same experiment during summer, she measures the column length to be

x

cm

for the second resonance. Then

A

18 > x

B

x > 54

C

54 > x > 36

D

36 > x > 18

Q 12PhysicsSection A • MCQatoms and nuclei

+4 / -1

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements:
Statement- 1:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and

Statement- 2:
For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei it decreases with increasing $Z.$

A

Statement -

1

is false, Statement -

2

is true

B

Statement -

1

is true, Statement -

2

is true; Statement -

2

is a correct explanation for Statement -

1

C

Statement -

1

is true, Statement -

2

is true; Statement -

2

is not a correct explanation for Statement -

1

D

Statement -

1

is true, Statement -

2

is false

Q 13PhysicsSection A • MCQmagnetics

+4 / -1

A horizontal overhead powerline is at height of

4m

from the ground and carries a current of

100A

from east to west. The magnetic field directly below it on the ground is

\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)

A

2.5 \times {10^{ - 7}}\,T

southward

B

5 \times {10^{ - 6}}\,T

northward

C

5 \times {10^{ - 6}}\,T

southward

D

2.5 \times {10^{ - 7}}\,T

northward

Q 14PhysicsSection A • MCQwork power and energy

+4 / -1

An athlete in the olympic games covers a distance of

100

m

in

10

s.

His kinetic energy can be estimated to be in the range

A

200J-500J

B

2 \times {10^5}J - 3 \times {10^5}J

C

20,000J - 50,000J

D

2,000J - 5,000J

Q 15PhysicsSection A • MCQunits and measurements

+4 / -1

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by

A

a vernier scale provided on the microscope

B

a standard laboratory scale

C

a meter scale provided on the microscope

D

a screw gauge provided on the microscope

Q 16PhysicsSection A • MCQheat and thermodynamics

+4 / -1

The speed of sound in oxygen

\left( {{O_2}} \right)

at a certain temperature is

460\,\,m{s^{ - 1}}.

The speed of sound in helium

(He)

at the same temperature will be (assume both gases to be ideal)

A

1421\,\,m{s^{ - 1}}

B

500\,\,m{s^{ - 1}}

C

650\,\,m{s^{ - 1}}

D

300\,\,m{s^{ - 1}}

Q 17PhysicsSection A • MCQgravitation

+4 / -1

A planet in a distant solar system is

10

times more massive than the earth and its radius is

10

times smaller. Given that the escape velocity from the earth is

11\,\,km\,{s^{ - 1}},

the escape velocity from the surface of the planet would be

A

1.1\,\,km\,{s^{ - 1}}

B

100\,\,km\,{s^{ - 1}}

C

110\,\,km\,{s^{ - 1}}

D

0.11\,\,km\,{s^{ - 1}}

Q 18PhysicsSection A • MCQcurrent electricity

+4 / -1

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. qImage-galvanometer-voltmeter-and-ammeter-current-electricity-electricity-Jeemate

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

The value of the unknown resister $R$ is

A

13.75\Omega

B

220\Omega

C

110\Omega

D

55\Omega

Q 19PhysicsSection A • MCQelectronic devices

+4 / -1

In the circuit below,

A

and

B

represent two inputs and

C

represents the output. qImage-digital-circuits-electronic-devices-modern-physics-Jeemate

The circuit represents

A

NOR gate

B

AND gate

C

NAND gate

D

OR gate

Official Correct Answer:Option (D)

Step-by-Step Solution:

A	B	C
1	1	1
1	0	1
0	1	1
0	0	0

The truth table for the above logic gate is :

This truth table follows the boolean algebra

C=A+B

which is for

OR

gate

Q 20PhysicsSection A • MCQmotion

+4 / -1

A body is at rest at

x=0.

At

t=0,

it starts moving in the positive

x

-direction with a constant acceleration. At the same instant another body passes through

x=0

moving in the positive

x

direction with a constant speed. The position of the first body is given by

{x_1}\left( t \right)

after time

't';

and that of the second body by

{x_2}\left( t \right)

after the same time interval. Which of the following graphs correctly describes

\left( {{x_1} - {x_2}} \right)

as a function of time

't'

?

A

qImage-graph-based-problem-motion-mechanics-Jeemate

B

C

D

Q 21PhysicsSection A • MCQproperties of matter

+4 / -1

A spherical solid ball of volume

V

is made of a material of density

{\rho _1}

. It is falling through a liquid of density

{\rho _2}\left( {{\rho _2} < {\rho _1}} \right)

. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed

v,

i.e.,

{F_{viscous}} = - k{v^2}\left( {k > 0} \right).

The terminal speed of the ball is

A

\sqrt {{{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}}

B

{{{Vg{\rho _1}} \over k}}

C

\sqrt {{{Vg{\rho _1}} \over k}}

D

{{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}

Q 22PhysicsSection A • MCQcenter of mass

+4 / -1

A block of mass

0.50

kg

is moving with a speed of

2.00

m{s^{ - 1}}

on a smooth surface. It strike another mass of

1.0

kg

and then they move together as a single body. The energy loss during the collision is :

A

0.16J

B

1.00J

C

0.67J

D

0.34

J

Q 23PhysicsSection A • MCQproperties of matter

+4 / -1

A jar is filled with two non-mixing liquids

1

and

2

having densities

{\rho _1}

and

{\rho _2}

respectively. A solid ball, made of a material of density

{\rho _3}

, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for

{\rho _1}

,

{\rho _1}

and

{\rho _3}

?

qImage-pressure-density-pascals-law-and-archimedes-principle-properties-of-matter-mechanics-Jeemate

A

{\rho _3} < {\rho _1} < \rho {}_2

B

{\rho _1} > {\rho _3} > \rho {}_2

C

{\rho _1} < {\rho _2} < \rho {}_3

D

{\rho _1} < {\rho _3} < \rho {}_2

Q 24PhysicsSection A • MCQunits and measurements

+4 / -1

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms⁻¹. The magnitude of its momentum is recorded as

A

17.6 kg ms^-1

B

17.565 kg ms^-1

C

17.56 kg ms^-1

D

17.57 kg ms^-1

Q 25PhysicsSection A • MCQproperties of matter

+4 / -1

A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

A

qImage-surface-tension-excess-pressure-and-capillarity-properties-of-matter-mechanics-Jeemate

B

C

D

Q 26PhysicsSection A • MCQelectronic devices

+4 / -1

A working transistor with its three legs marked

P,Q

and

R

is tested using a multi-meter. No conduction is found between

P

and

Q

. By connecting the common (negative) terminal of the multi-meter to

R

and the other (positive) terminal to

P

or

Q,

some resistance is seen on the multi-meter. Which of the following is true for the transistor?

A

It is an

npn

transistor with

R

as base

B

It is an

pnp

transistor with

R

as collector

C

It is an

pnp

transistor with

R

as emitter

D

It is an

npn

transistor with

R

as collector

Q 27PhysicsSection A • MCQelectromagnetic induction

+4 / -1

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area

A=

10\,\,c{m^2}

and length

=20

cm

. If one of the solenoid has

300

turns and the other

400

turns, their mutual inductance is

\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,Tm\,{A^{ - 1}}} \right)

A

2.4\pi \times {10^{ - 5}}H

B

4.8\pi \times {10^{ - 4}}H

C

4.8\pi \times {10^{ - 5}}H

D

2.4\pi \times {10^{ - 4}}H

Q 28PhysicsSection A • MCQwaves

+4 / -1

A wave travelling along the

x

-axis is described by the equation

y(x, t)=0.005

\cos \,\left( {\alpha \,x - \beta t} \right).

If the wavelength and the time period of the wave are

0.08

m

and

2.0s

, respectively, then

\alpha

and

\beta

in appropriate units are

A

\alpha = 25.00\pi ,\,\beta = \pi

B

\alpha = {{0.08} \over \pi },\,\beta = {{2.0} \over \pi }

C

\alpha = {{0.04} \over \pi },\,\beta = {{1.0} \over \pi }

D

\alpha = 12.50\pi ,\,\beta = {\pi \over {2.0}}

Q 29PhysicsSection A • MCQelectrostatics

+4 / -1

A thin spherical shell of radius

R

has charge

Q

spread uniformly over its surface. Which of the following graphs most closely represents the electric field

E(r)

produced by the shell in the range

0 \le r < \infty ,

where

r

is the distance from the center of the shell?

A

qImage-electric-field-and-electric-field-intensity-electrostatics-electricity-Jeemate

B

c

C

D

Q 30PhysicsSection A • MCQunits and measurements

+4 / -1

The dimension of magnetic field in M, L, T and C (coulomb) is given as

A

MLT^-1C^-1

B

MT²C^-2

C

MT^-1C^-1

D

MT^-2C^-1

Q 31PhysicsSection A • MCQatoms and nuclei

+4 / -1

Suppose an electron is attracted towards the origin by a force

{k \over r}

where

'k'

is a constant and

'r'

is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the

{n^{th}}

orbital of the electron is found to be

'{r_n}'

and the kinetic energy of the electron to be

'{T_n}'.

Then which of the following is true?

A

{T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}

B

{T_n}

independent of

n,{r_n} \propto n

C

{T_n} \propto {1 \over n},{r_n} \propto n

D

{T_n} \propto {1 \over n},{r_n} \propto {n^2}

Q 32PhysicsSection A • MCQunits and measurements

+4 / -1

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

A

3.32 mm

B

3.73 mm

C

3.67 mm

D

3.38 mm

Q 33PhysicsSection A • MCQcurrent electricity

+4 / -1

Consider a block of conducting material of resistivity

'\rho '

shown in the figure. Current

'I'

enters at

'A'

and leaves from

'D'

. We apply superposition principle to find voltage

'\Delta V'

developed between

'B'

and

'C'

. The calculation is done in the following steps:
(i) Take current

'I'

entering from

'A'

and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field

E(r)

at distance

'r'

from A by using Ohm's law

E = \rho j,

where

j

is the current per unit area at

'r'

.
(iii) From the

'r'

dependence of

E(r)

, obtain the potential

V(r)

at

r

.
(iv) Repeat (i), (ii) and (iii) for current

'I'

leaving

'D'

and superpose results for

'A'

and

'D'.

qImage-electric-current-current-density-and-drift-velocity-current-electricity-electricity-Jeemate

$\Delta V$ measured between $B$ and $C$ is

A

{{\rho I} \over {\pi a}} - {{\rho I} \over {\pi \left( {a + b} \right)}}

B

{{\rho I} \over a} - {{\rho I} \over {\left( {a + b} \right)}}

C

{{\rho I} \over {2\pi a}} - {{\rho I} \over {2\pi \left( {a + b} \right)}}

D

{{\rho I} \over {2\pi \left( {a - b} \right)}}

Q 34PhysicsSection A • MCQheat and thermodynamics

+4 / -1

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume

{V_1}

and contains ideal gas at pressure

{P_1}

and temperature

{T_1}

. The other chamber has volume

{V_2}

and contains ideal gas at pressure

{P_2}

and temperature

{T_2}

. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

A

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

B

{{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}

C

{{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \over {{P_1}{V_1} + {P_2}{V_2}}}

D

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

Q 35PhysicsSection A • MCQcapacitor

+4 / -1

A parallel plate capacitor with air between the plates has capacitance of

9

pF.

The separation between its plates is

'd'.

The space between the plates has dielectric constant

{k_1}

=3

and thickness

{d \over 3}

while the other one has dielectric constant

{k_2} = 6

and thickness

{{2d} \over 3}

. Capacitance of the capacitor is now

A

1.8

pF

B

45

pF

C

40.5

pF

D

20.25

pF

Q 36ChemistrySection A • MCQcoordination compounds

+4 / -1

The coordination number and the oxidation state of the element ‘E’ in the complex [E(en)₂(C₂O₄)]NO₂ (where (en) is ethylene diamine) are, respectively,

A

6 and 2

B

4 and 2

C

4 and 3

D

6 and 3

Q 37ChemistrySection A • MCQpolymers

+4 / -1

Bakelite is obtained from phenol by reacting with

A

(CH₂OH)₂

B

CH₃CHO

C

CH₃COCH₃

D

HCHO

Q 38ChemistrySection A • MCQisolation of elements

+4 / -1

Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

A

Metal sulphides are thermodynamically more stable than CS₂

B

CO₂ is thermodynamically more stable than CS₂

C

Metal sulphides are less stable than the corresponding oxides

D

CO₂ is more volatile than CS₂

Q 39ChemistrySection A • MCQd and f block elements

+4 / -1

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :

A

4f orbitals more diffused than the 5f orbitals

B

lesser energy difference between 5f and 6d than between 4f and 5d orbitals

C

more energy difference between 5f and 6d than between 4f and 5d orbitals

D

more reactive nature of the actinoids than the lanthanoids

Q 40ChemistrySection A • MCQthermodynamics

+4 / -1

Standard entropy of X₂, Y₂ and XY₃ are 60, 40 and 50 JK⁻¹ mol⁻¹ , respectively. For the reaction,

{1 \over 2} X_2

+

{3 \over 2} Y_2 \to

XY₃,

\Delta H

= -30 kJ, to be at equilibrium, the temperature will be :

A

1250 K

B

500 K

C

750 K

D

1000 K

Q 41ChemistrySection A • MCQsolid state

+4 / -1

In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be :

A

X₄Y₃

B

X₂Y₃

C

X₂Y

D

X₃Y₄

Q 42ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The absolute configuration of

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

A

S,S

B

R,R

C

R,S

D

S,R

Q 43ChemistrySection A • MCQhydrocarbons

+4 / -1

The treatment of

C{H_3}MgX\,\,

with

C{H_3}C \equiv C - H

produces

A

C{H_3} - CH = C{H_2}

B

C{H_3}C \equiv C - C{H_3}

C

qImage-reaction-of-alkynes-hydrocarbons-organic-chemistry-Jeemate

D

C{H_4}

Q 44ChemistrySection A • MCQcoordination compounds

+4 / -1

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of

\Delta _o

be the highest?

A

[Co(CN)₆]³⁻

B

[Co(C₂O₄)₃]³⁻

C

[Co(H₂O)₆]³⁺

D

[Co(NH₃)₆]³⁺

Q 45ChemistrySection A • MCQthermodynamics

+4 / -1

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:

{1 \over 2}C{l_2}(g)

\buildrel {{1 \over 2}{\Delta _{diss}}{H^\Theta }} \over \longrightarrow

Cl(g)

\buildrel {{\Delta _{eg}}{H^\Theta }} \over \longrightarrow

C{l^ - }(g)

\buildrel {{\Delta _{Hyd}}{H^\Theta }} \over \longrightarrow

C{l^ - }(aq)

(Using the data,

{\Delta _{diss}}H_{C{l_2}}^\Theta

= 240 kJ/mol,

{\Delta _{eg}}H_{Cl}^\Theta

= -349 kJ/mol,

{\Delta _{hyd}}H_{C{l^ - }}^\Theta

= - 381 kJ/mol) will be :

A

+152 kJ mol⁻¹

B

−610 kJ mol⁻¹

C

−850 kJ mol⁻¹

D

+120 kJ mol⁻¹

Q 46ChemistrySection A • MCQsurface chemistry

+4 / -1

Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective powers is

A

D < A < C < B

B

C < B < D < A

C

A < C < B < D

D

B < D < A < C

Q 47ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

The organic chloro compound, which shows complete stereochemical inversion during a S_N2 reaction, is

A

(C₂H₅)₂CHC

B

(CH₃)₃CCl

C

(CH₃)₂CHCl

D

CH₃Cl

Q 48ChemistrySection A • MCQd and f block elements

+4 / -1

Amount of oxalic acid present in a solution can be determined by its titration with

KMn{O_4}

solution in the presence of

{H_2}S{O_4}.

The titration gives unsatisfactory result when carried out in the presence of

HCl,

because

HCl

:

A

gets oxidised by oxalic acid to chlorine

B

furnishes

{H^ + }

ions in addition to those from oxalic acid

C

reduces permanganate to

M{n^{2 + }}

D

oxaidises oxalic acid to carbon doxide and water

Q 49ChemistrySection A • MCQhydrocarbons

+4 / -1

The hydrocarbon which can react with sodium in liquid ammonia is

A

CH₃CH₂CH₂C≡CCH₂CH₂CH₃

B

CH₃CH₂C≡CH

C

CH₃CH=CHCH₃

D

CH₃CH₂C≡CCH₂CH₃

Q 50ChemistrySection A • MCQbiomolecules

+4 / -1

\alpha

-D-(+)-glucose and

\beta

-D-(+)-glucose are

A

conformers

B

epimers

C

anomers

D

enantiomers

Q 51ChemistrySection A • MCQp block elements

+4 / -1

Which one of the following is the correct statement?

A

Boric acid is a protonic acid

B

Beryllium exhibits coordination number of six

C

Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase

D

B₂H₆.2NH₃ is known as ‘inorganic benzene’

Q 52ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The bond dissociation energy of B - F in BF₃ is 646 kJ mol^-1 whereas that of C - F in CF₄ is 515 kj mol^-1. The correct reason for higher B - F bond dissociation energy as compared to that of C - F is

A

stronger

\sigma

bond between B and F in BF₃ as compared to that between C and F in CF₄

B

significant

p\pi - p\pi

interaction between B and F in BF₃ whereas there is no possibility of such interaction between C and F in CF₄

C

lower degree of

p\pi - p\pi

interaction between B and F in BF₃ than that between C and F in CF₄

D

smaller size of B - atom as compared to that of C- atom.

Q 53ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The electrophile,

{E^ \oplus }

attacks the benzene ring to generate the intermediate

\sigma -

complex. Of the following, which

\sigma -

complex is lowest energy?

A

qImage-stability-of-intermediate-basics-of-organic-chemistry-organic-chemistry-Jeemate

B

C

D

Q 54ChemistrySection A • MCQelectrochemistry

+4 / -1

Given

E_{C{r^{3 + }}/Cr}^o

= -0.72 V;

E_{Fe^{2+}/Fe}^o

= -0.42V, The potential for the cell Cr | Cr³⁺ (0.1M) || Fe²⁺ (0.01 M) | Fe is

A

0.26 V

B

0.399 V

C

−0.339 V

D

−0.26 V

Q 55ChemistrySection A • MCQsolutions

+4 / -1

At 80^oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80^oC and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mm Hg)

A

52 mol percent

B

34 mol percent

C

48 mol percent

D

50 mol percent

Q 56ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Which of the following pair of species have the same bond order?

A

CN^- and NO⁺

B

CN^- and CN⁺

C

O_2^-

and CN^-

D

NO⁺ and CN⁺

Q 57ChemistrySection A • MCQp block elements

+4 / -1

Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is :

A

R₄Si

B

RSiCl₃

C

R₂SiCl₂

D

R₃SiCl

Q 58ChemistrySection A • MCQchemical equilibrium

+4 / -1

For the following three reactions a, b and c, equilibrium constants are given:
a. CO (g) + H₂O (g)

\leftrightharpoons

CO₂(g) + H₂ (g) ; K₁
b. CH₄ (g) + H₂O (g)

\leftrightharpoons

CO(g) + 3H₂ (g) ; K₂
c. CH₄ (g) + 2H₂O (g)

\leftrightharpoons

CO₂(g) + 4H₂ (g) ; K₃

A

{K_1}\sqrt {{K_2}} = {K_3}

B

K₂K₃ = K₁

C

K₃ = K₁K₂

D

K₃.

K_2^3

=

K_1^2

Q 59ChemistrySection A • MCQionic equilibrium

+4 / -1

The pK_a of a weak acid, HA, is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

A

9.58

B

4.79

C

7.01

D

9.22

Q 60ChemistrySection A • MCQsolutions

+4 / -1

The vapour pressure of water at 20^oC is 17.5 mm Hg. If 18 g of glucose (C₆H₁₂O₆) is added to 178.2 g of water at 20^oC, the vapour pressure of the resulting solution will be

A

17.675 mm Hg

B

15.750 mm Hg

C

16.500 mm Hg

D

17.325 mm Hg

Q 61ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Identify the wrong statements in the following :

A

Chlorofluorocarbons are responsible for ozone layer depletion

B

Greenhouse effect is responsible for global warming

C

Ozone layer does not permit infrared radiation from the sun to reach the earth

D

Acid rains is mostly because of oxides of nitrogen and sulphur

Q 62ChemistrySection A • MCQionic equilibrium

+4 / -1

Four species are listed below
i.

HCO_3^−

ii.

H_3O^+

iii.

HSO_4^−

iv.

HSO_3F

Which one of the following is the correct sequence of their acid strength?

A

iv < ii < iii < I

B

ii < iii < i < iv

C

i < iii < ii < iv

D

iii < i < iv < ii

Q 63ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

A

2,4,6-trinitrobenzene

B

o-nitrophenol

C

p-nitrophenol

D

nitrobenzene

Q 64ChemistrySection A • MCQhydrocarbons

+4 / -1

Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

A

mixture of o− and p−bromotoluenes

B

mixture of o− and p−dibromobenzenes

C

mixture of o− and p−bromoanilines

D

mixture of o− and m−bromotoluenes

Q 65ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

A

−COOH, −SO₃H, −CONH₂, −CHO

B

−SO₃H, −COOH, −CONH₂, −CHO

C

−CHO, −COOH, −SO₃H, −CONH₂

D

−CONH₂, −CHO, −SO₃H, −COOH

Official Correct Answer:Option (A)

Step-by-Step Solution:

The correct order of priority for the given functional group is

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

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

	Functional group (priority order)	suffix(s)	prefix
(1)		Oic acid(when carbon(C) of this functional group present in the main chain) or Carboxylic acid (when carbon(C) of this functional group is not present in the main chain)	Carboxy
(2)		sulphonic acid	sulpho
(3)		Oic anhydrid (when carbon(C) of this functional group present in the main chain) or Carboxylic anhydride (when carbon(C) of this functional group is not present in the main chain)	$-$
(4)		Oate (when carbon(C) of this functional group present in the main chain) or Carboxylate (when carbon(C) of this functional group is not present in the main chain)	$-$
(5)		Oyl halide (when carbon(C) of this functional group present in the main chain) or Carboxyl halide (when carbon(C) of this functional group is not present in the main chain)	haloflormyl
(6)		amide (when carbon(C) of this functional group present in the main chain) or carbamide (when carbon(C) of this functional group is not present in the main chain)	carbamoyl
(7)	cynide ( $-$ C $\equiv$ N)	nitrile (when carbon(C) of this functional group present in the main chain) or carbonitrile (when carbon(C) of this functional group is not present in the main chain)	cyano
(8)		Carbylamine	isocyano
(9)		al (when carbon(C) of this functional group present in the main chain) or Carbaldehyde (when carbon(C) of this functional group is not present in the main chain)	formyl (oxo)
(10)		one	oxo
(11)	$-$ OH	ol	hydroxy
(12)	$-$ SH	thiol	mercapto
(13)	$-$ NH $_2$	amine	amino

From this table you can see -COOH has highest priority and -NH₂ has lowest priority among all functional groups.

Q 66ChemistrySection A • MCQchemical equilibrium

+4 / -1

The equilibrium constants K_P1 and K_P2 for the reactions X

\leftrightharpoons

2Y and Z

\leftrightharpoons

P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is :

A

1 : 36

B

1 : 1

C

1 : 3

D

1 : 9

Q 67ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

For a reaction

{1 \over 2}A \to 2B

rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression

A

- {{d[A]} \over {dt}}

=

{1 \over 2}{{d[B]} \over {dt}}

B

- {{d[A]} \over {dt}}

=

{1 \over 4}{{d[B]} \over {dt}}

C

- {{d[A]} \over {dt}}

=

{{d[B]} \over {dt}}

D

- {{d[A]} \over {dt}}

=

4{{d[B]} \over {dt}}

Q 68ChemistrySection A • MCQatomic structure

+4 / -1

The ionization enthalpy of hydrogen atom is 1.312 × 10⁶ J mol⁻¹. The energy required to excite the electron in the atom from n = 1 to n = 2 is

A

8.51 × 10⁵ J mol⁻¹

B

6.56 × 10⁵ J mol⁻¹

C

7.56 × 10⁵ J mol⁻¹

D

9.84 × 10⁵ J mol⁻¹

Q 69ChemistrySection A • MCQatomic structure

+4 / -1

Which one of the following constitutes a group of the isoelectronic species?

A

C_2^{2 - }

,

O_2^{-}

, CO, NO

B

NO^{+}

,

C_2^{2 - }

, CN^-,

N_2

C

CN^-,

N_2

,

O_2^{2-}

,

C_2^{2 - }

D

N_2

,

O_2^{-}

,

NO^{+}

, CO

Official Correct Answer:Option (B)

Step-by-Step Solution:

Species	No. of electrons
C₂^2-	12+2 = 14
O₂^-	16+1 = 17
CO	6+8 = 14
NO	7+8 = 15
NO⁺	7+8-1 = 14
C₂^2-	12+2 = 14
CN^-	6+7+1 = 14
N₂	14
CN^-	6+7+1 = 14
N₂	14
O₂^2-	16+2 = 18
C₂	12
N₂	14
O₂^-	16+1 = 17
NO⁺	7+8-1 = 14
CO	6+8 = 14

So, option

(B)

is correct.

Q 70ChemistrySection A • MCQhydrocarbons

+4 / -1

In the following sequence of reactions, the alkene affords the compound ‘B’
CH₃ - CH = CH - CH₃

\buildrel {{O_3}} \over \longrightarrow

A

\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Zn}^{H{}_2O}}

B
The compound B is

A

CH₃CH₂CHO

B

CH₃COCH₃

C

CH₃CH₂COCH₃

D

CH₃CHO

Q 71ChemistrySection A • MCQhydrogen

+4 / -1

In context with the industrial preparation of hydrogen from water gas (CO + H₂), which of the following is the correct statement?

A

CO and H₂ are fractionally separated using differences in their densities

B

CO is removed by absorption in aqueous Cu₂Cl₂ solution

C

H₂ is removed through occlusion with Pd

D

CO is oxidised to CO₂ with steam in the presence of a catalyst followed by absorption of CO₂ in alkali

Q 72MathematicsSection A • MCQprobability

+4 / -1

A die is thrown. Let

A

be the event that the number obtained is greater than

3.

Let

B

be the event that the number obtained is less than

5.

Then

P\left( {A \cup B} \right)

is :

A

{3 \over 5}

B

0

C

1

D

{2 \over 5}

Q 73MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let

f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.

Then which one of the following is true?

A

f

is neither differentiable at x = 0 nor at x = 1

B

f

is differentiable at x = 0 and at x = 1

C

f

is differentiable at x = 0 but not at x = 1

D

f

is differentiable at x = 1 but not at x = 0

Q 74MathematicsSection A • MCQpermutations and combinations

+4 / -1

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

A

8.{}^6{C_4}.{}^7{C_4}

B

6.7.{}^8{C_4}

C

6.8.{}^7{C_4}

.

D

7.{}^6{C_4}.{}^8{C_4}

Q 75MathematicsSection A • MCQapplication of derivatives

+4 / -1

How many real solutions does the equation

{x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0

have?

A

7

B

1

C

3

D

5

Q 76MathematicsSection A • MCQcomplex numbers

+4 / -1

The conjugate of a complex number is

{1 \over {i - 1}}

then that complex number is :

A

{{ - 1} \over {i - 1}}

B

{1 \over {i + 1}}\,

C

{{ - 1} \over {i + 1}}

D

{1 \over {i - 1}}

Q 77MathematicsSection A • MCQ3d geometry

+4 / -1

If the straight lines

\,\,\,\,\,

\,\,\,\,\,

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

\,\,\,\,\,

and

\,\,\,\,\,

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

intersects at a point, then the integer

k

is equal to

A

-5

B

5

C

2

D

-2

Q 78MathematicsSection A • MCQdifferential equations

+4 / -1

The solution of the differential equation

{{dy} \over {dx}} = {{x + y} \over x}

satisfying the condition

y(1)=1

is :

A

y = \ln x + x

B

y = x\ln x + {x^2}

C

y = x{e^{\left( {x - 1} \right)}}\,

D

y = x\,\ln x + x

Q 79MathematicsSection A • MCQpermutations and combinations

+4 / -1

In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of different ways the child can buy the six ice-cream is

{}^{10}{C_5}

.
Statement - 2: The number of different ways the child can buy the six ice-cream is equal to the number of different ways of arranging 6 A and 4 B's in a row.

A

Statement - 1 is false, Statement - 2 is true

B

Statement - 1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1

C

Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for Statement - 1

D

Statement - 1 is true, Statement - 2 is false

Q 80MathematicsSection A • MCQsets and relations

+4 / -1

Let R be the real line. Consider the following subsets of the plane

R \times R

:

S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}

T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}

,

Which one of the following is true ?

A

Neither S nor T is an equivalence relation on R

B

Both S and T are equivalence relation on R

C

S is an equivalence relation on R but T is not

D

T is an equivalence relation on R but S is not

Q 81MathematicsSection A • MCQstatistics

+4 / -1

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

A

a = 0, b = 7

B

a = 5, b = 2

C

a = 1, b = 6

D

a = 3, b = 4

Q 82MathematicsSection A • MCQsequences and series

+4 / -1

The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

A

- 4

B

- 12

C

12

D

4

Q 83MathematicsSection A • MCQprobability

+4 / -1

It is given that the events

A

and

B

are such that

P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}

and

P\left( {B|A} \right) = {2 \over 3}.

Then

P(B)

is :

A

{1 \over 6}

B

{1 \over 3}

C

{2 \over 3}

D

{1 \over 2}

Q 84MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

A

be a square matrix all of whose entries are integers.
Then which one of the following is true?

A

If det

A = \pm 1,

then

{A^{ - 1}}

exists but all its entries are not necessarily integers

B

If det

A \ne \pm 1,

then

{A^{ - 1}}

exists and all its entries are non integers

C

If det

A = \pm 1,

then

{A^{ - 1}}

exists but all its entries are integers

D

If det

A = \pm 1,

then

{A^{ - 1}}

need not exists

Q 85MathematicsSection A • MCQellipse

+4 / -1

A focus of an ellipse is at the origin. The directrix is the line

x=4

and the eccentricity is

{{1 \over 2}}

. Then the length of the semi-major axis is :

A

{{8 \over 3}}

B

{{2 \over 3}}

C

{{4 \over 3}}

D

{{5 \over 3}}

Q 86MathematicsSection A • MCQbinomial theorem

+4 / -1

Statement - 1 :

\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.}

Statement - 2 :

\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}{x^r} = {{\left( {1 + x} \right)}^n} + nx{{\left( {1 + x} \right)}^{n - 1}}.}

A

Statement - 1 is false, Statement - 2 is true

B

Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1

C

Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

D

Statement - 1 is true, Statement - 2 is false

Q 87MathematicsSection A • MCQcircle

+4 / -1

The point diametrically opposite to the point

P(1, 0)

on the circle

{x^2} + {y^2} + 2x + 4y - 3 = 0

is :

A

(3, -4)

B

(-3, 4)

C

(-3, -4)

D

(3, 4)

Q 88MathematicsSection A • MCQvector algebra

+4 / -1

The non-zero vectors are

{\overrightarrow a ,\overrightarrow b }

and

{\overrightarrow c }

are related by

{\overrightarrow a = 8\overrightarrow b }

and

{\overrightarrow c = - 7\overrightarrow b \,\,.}

Then the angle between

{\overrightarrow a }

and

{\overrightarrow c }

is :

A

0

B

{\pi \over 4}

C

{\pi \over 2}

D

\pi

Q 89MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

STATEMENT - 1 : For every natural number

n \ge 2,

&#x27; in math mode at position 1:

̲{1 \over {\sqrt…" style="color:#cc0000">

{1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \over {\sqrt n }} > \sqrt n .</span>

STATEMENT - 2 : For every natural number $n \ge 2,$ , $' in math mode at position 1:$ ̲\sqrt {n\left( …" style="color:#cc0000"> $\sqrt {n\left( {n + 1} \right)} < n + 1.</span>$

A

Statement - 1 is false, Statement - 2 is true

B

Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for statement - 1

C

Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

D

Statement - 1 is true, Statement - 2 is false

Q 90MathematicsSection A • MCQcircle

+4 / -1

The differential equation of the family of circles with fixed radius

5

units and centre on the line

y = 2

is :

A

\left( {x - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}

B

\left( {y - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}

C

{\left( {y - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}

D

{\left( {x - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}

Q 91MathematicsSection A • MCQfunctions

+4 / -1

Let

f:N \to Y

be a function defined as f(x) = 4x + 3 where
Y = { y

\in

N, y = 4x + 3 for some x

\in

N }.
Show that f is invertible and its inverse is

A

g\left( y \right) = {{3y + 4} \over 4}

B

g\left( y \right) = 4 + {{y + 3} \over 4}

C

g\left( y \right) = {{y + 3} \over 4}

D

g\left( y \right) = {{y - 3} \over 4}

Q 92MathematicsSection A • MCQmathematical reasoning

+4 / -1

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p.

Statement –2: r is equivalent to

\sim \left( {p \leftrightarrow \sim q} \right)

A

Statement − 1 is false, Statement − 2 is false

B

Statement −1 is false, Statement −2 is true

C

Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

D

Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1

Official Correct Answer:Option (A)

Step-by-Step Solution:

p : x is an irrational number

q : y is a transcendental number

r : x is a rational number, if y is a transcendental number

$\Rightarrow$ r : $\sim$ p $\leftrightarrow$ q

S₁ : r $\equiv$ q $\vee$ p

and S₂ : r $\equiv$ $\sim$ (p $\leftrightarrow$ $\sim$ q)

p	q	$\sim p$	$\sim q$	r $\sim p \leftrightarrow q$	Statement I $q \vee p$	$(p \leftrightarrow \sim q)$	Statement II $\sim (p \leftrightarrow \sim q)$
T	T	F	F	F	T	F	T
T	F	F	T	T	T	T	F
F	T	T	F	T	T	T	F
F	F	T	T	F	F	F	T

It is clear from the table that r is not equivalent to either of the statements.

Therefore, both statements are false.

Q 93MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The quadratic equations

{x^2} - 6x + a = 0

and

{x^2} - cx + 6 = 0

have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

A

1

B

4

C

3

D

2

Q 94MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

A

be

a\,2 \times 2

matrix with real entries. Let

I

be the

2 \times 2

identity matrix. Denote by tr

(A)

, the sum of diagonal entries of

a

. Assume that

{a^2} = I.

Statement-1 : If

A \ne I

and

A \ne - I

, then det

(A)=-1

Statement- 2 : If

A \ne I

and

A \ne - I

, then tr

(A)

\ne 0

.

A

statement - 1 is false, statement -2 is true

B

statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.

C

statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.

D

statement - 1 is true, statement - 2 is false.

Q 95MathematicsSection A • MCQparabola

+4 / -1

A parabola has the origin as its focus and the line

x=2

as the directrix. Then the vertex of the parabola is at :

A

(0,2)

B

(1,0)

C

(0,1)

D

(2,0)

Q 96MathematicsSection A • MCQvector algebra

+4 / -1

The vector

\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k

lies in the plane of the vectors

\overrightarrow b = \widehat i + \widehat j

and

\overrightarrow c = \widehat j + \widehat k

and bisects the angle between

\overrightarrow b

and

\overrightarrow c

.Then which one of the following gives possible values of

\alpha

and

\beta

?

A

\alpha = 2,\,\,\beta = 2

B

\alpha = 1,\,\,\beta = 2

C

\alpha = 2,\,\,\beta = 1

D

\alpha = 1,\,\,\beta = 1

Q 97MathematicsSection A • MCQheight and distance

+4 / -1

AB

is a vertical pole with

B

at the ground level and

A

at the top.

A

man finds that the angle of elevation of the point

A

from a certain point

C

on the ground is

{60^ \circ }

. He moves away from the pole along the line

BC

to a point

D

such that

CD=7

m. From

D

the angle of elevation of the point

A

is

{45^ \circ }

. Then the height of the pole is :

A

{{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 - 1} }}m

B

{{7\sqrt 3 } \over 2}\left( {\sqrt {3 } + 1 } \right)m

C

{{7\sqrt 3 } \over 2}\left( {\sqrt {3 } - 1 } \right)m

D

{{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 + 1} }}m

Q 98MathematicsSection A • MCQindefinite integration

+4 / -1

The value of

\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}}

is

A

\,x + \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c

B

\,x - \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c

C

\,x + \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c

D

\,x - \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c

Q 99MathematicsSection A • MCQarea under the curves

+4 / -1

The area of the plane region bounded by the curves

x + 2{y^2} = 0

and

\,x + 3{y^2} = 1

is equal to :

A

{5 \over 3}

B

{1 \over 3}

C

{2 \over 3}

D

{4 \over 3}

Q 100MathematicsSection A • MCQapplication of derivatives

+4 / -1

Suppose the cubic

{x^3} - px + q

has three distinct real roots
where

p>0

and

q>0

. Then which one of the following holds?

A

The cubic has minima at

\sqrt {{p \over 3}}

and maxima at

-\sqrt {{p \over 3}}

B

The cubic has minima at

-\sqrt {{p \over 3}}

and maxima at

\sqrt {{p \over 3}}

C

The cubic has minima at both

\sqrt {{p \over 3}}

and

-\sqrt {{p \over 3}}

D

The cubic has maxima at both

\sqrt {{p \over 3}}

and

-\sqrt {{p \over 3}}

Q 101MathematicsSection A • MCQ3d geometry

+4 / -1

The line passing through the points

(5,1,a)

and

(3, b, 1)

crosses the

yz

-plane at the point

\left( {0,{{17} \over 2}, - {{ - 13} \over 2}} \right)

. Then

A

a=2,

b=8

B

a=4,

b=6

C

a=6,

b=4

D

a=8,

b=2

Q 102MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The value of

cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)

is :

A

{{6 \over 17}}

B

{{3 \over 17}}

C

{{4 \over 17}}

D

{{5 \over 17}}

Q 103MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is :

A

1

B

2

C

-2

D

-4

Q 104MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

a, b, c

be any real numbers. Suppose that there are real numbers

x, y, z

not all zero such that

x=cy+bz,

y=az+cx,

and

z=bx+ay.

Then

{a^2} + {b^2} + {c^2} + 2abc

is equal to :

A

2

B

-1

C

0

D

1

Q 105MathematicsSection A • MCQmathematical reasoning

+4 / -1

The statement

p \to \left( {q \to p} \right)

is equivalent to

A

p \to \left( {p \leftrightarrow q} \right)

B

p \to \left( {p \to q} \right)

C

p \to \left( {p \vee q} \right)

D

p \to \left( {p \wedge q} \right)

Official Correct Answer:Option (C)

Step-by-Step Solution:

q	p	$q \to p$	$p \to (q \to p)$	$(p \vee q)$	$p \to (p \vee q)$
T	T	T	T	T	T
T	F	F	T	T	T
F	T	T	T	T	T
F	F	T	T	F	T

$\therefore$ Statement p $\to$ (q $\to$ p) is equivalent to p $\to$ (p $\vee$ q).

AIEEE 2008 Question Paper with Solutions