JEE Main 2015 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQcapacitor

+4 / -1

In the given circuit, charges

{Q_2}

on the

2\mu F

capacitor changes as

C

is varied from

1\,\mu F

to

3\mu F.

{Q_2}

as a function of

'C'

is given properly by:

\left( {figures\,\,are\,\,drawn\,\,schematically\,\,and\,\,are\,\,not\,\,to\,\,scale} \right)

qImage-capacitor-in-circuit-capacitor-electricity-Jeemate

A

B

C

D

Q 2PhysicsSection A • MCQcommunication systems

+4 / -1

A signal of

5

kHz

frequency is amplitude modulated on a carrier wave of frequency

2

MHz.

The frequencies of the resultant signal is/are :

A

2005

kHz, 2000

kHz

and

1995

kHz

B

2000

kHz

and

1995

kHz

C

2

MHz

only

D

2005

kHz

and

1995

kHz

Q 3PhysicsSection A • MCQmotion

+4 / -1

Two stones are thrown up simultaneously from the edge of a cliff

240

m

high with initial speed of

10

m/s

and

40

m/s

respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take

g = 10m/{s^2}

)

(The figures are schematic and not drawn to scale)

A

B

C

D

Q 4PhysicsSection A • MCQalternating current

+4 / -1

An inductor

(L=0.03

H)

and a resistor

\left( {R = 0.15\,k\Omega } \right)

are connected in series to a battery of

15V

EMF

in a circuit shown below. The key

{K_1}

has been kept closed for a long time. Then at

t=0

,

{K_1}

is opened and key

{K_2}

is closed simultaneously. At

t=1

ms,

the current in the circuit will be :

\left( {{e^5} \cong 150} \right)

qImage-growth-and-decay-of-current-alternating-current-electricity-Jeemate

A

6.7

mA

B

0.67

mA

C

100

mA

D

67

mA

Q 5PhysicsSection A • MCQcurrent electricity

+4 / -1

When

5V

potential difference is applied across a wire of length

0.1

m,

the drift speed of electrons is

2.5 \times {10^{ - 4}}\,\,m{s^{ - 1}}.

If the electron density in the wire is

8 \times {10^{28}}\,\,{m^{ - 3}},

the resistivity of the material is close to :

A

1.6 \times {10^{ - 6}}\Omega m

B

1.6 \times {10^{ - 5}}\Omega m

C

1.6 \times {10^{ - 8}}\Omega m

D

1.6 \times {10^{ - 7}}\Omega m

Q 6PhysicsSection A • MCQatoms and nuclei

+4 / -1

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

A

kinetic energy decreases, potential energy increases but total energy remains same

B

kinetic energy and total energy decrease but potential energy increases

C

its kinetic energy increases but potential energy and total energy decrease

D

kinetic energy, potential energy and total energy decrease

Q 7PhysicsSection A • MCQelectromagnetic induction

+4 / -1

Two coaxial solenoids of different radius carry current

I

in the same direction.

\overrightarrow {{F_1}}

be the magnetic force on the inner solenoid due to the outer one and

\overrightarrow {{F_2}}

be the magnetic force on the outer solenoid due to the inner one. Then :

A

\overrightarrow {{F_1}}

is radially in wards and

\overrightarrow {{F_2}} = 0

B

\overrightarrow {{F_1}}

is radially outwards and

\overrightarrow {{F_2}} = 0

C

\overrightarrow {{F_1}} = \overrightarrow {{F_2}} = 0

D

\overrightarrow {{F_1}}

is radially inwards and

\overrightarrow {{F_2}}

is radially outards

Q 8PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as

{V^q},

where

V

is the volume of the gas. The value of

q

is:

\left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)

A

{{\gamma + 1} \over 2}

B

{{\gamma - 1} \over 2}

C

{{3\gamma + 5} \over 6}

D

{{3\gamma - 5} \over 6}

Q 9PhysicsSection A • MCQalternating current

+4 / -1

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to ${Q_0}$ and then connected to the $L$ and $R$ as shown below :

qImage-growth-and-decay-of-current-alternating-current-electricity-Jeemate

If a student plots graphs of the square of maximum charge $\left( {Q_{Max}^2} \right)$ on the capacitor with time $(t)$ for two different values ${L_1}$ and ${L_2}$ $\left( {{L_1} > {L_2}} \right)$ of $L$ then which of the following represents this graph correctly ?
$\left( {plots\,\,are\,\,schematic\,\,and\,\,niot\,\,drawn\,\,to\,\,scale} \right)$

A

B

C

D

Q 10PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Consider a spherical shell of radius

R

at temperature

T

. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u = {U \over V}\, \propto \,{T^4}

and pressure

p = {1 \over 3}\left( {{U \over V}} \right)

. If the shell now undergoes an adiabatic expansion the relation between

T

and

R

is:

A

T\, \propto {1 \over R}

B

T\, \propto {1 \over {{R^3}}}

C

T\, \propto \,{e^{ - R}}

D

T\, \propto \,{e^{ - 3R}}

Q 11PhysicsSection A • MCQcurrent electricity

+4 / -1

qImage-kirchhoffs-circuit-laws-current-electricity-electricity-Jeemate

In the circuit shown, the current in the

1\Omega

resistor is :

A

0.13

A,

from

Q

to

P

B

0.13

A

, from

P

to

Q

C

1.3A

from

P

to

Q

D

0A

Q 12PhysicsSection A • MCQmagnetics

+4 / -1

A rectangular loop of sides $10$ $cm$ and $5$ $cm$ carrying a current $1$ of $12A$ is placed in different orientations as shown in the figures below :

qImage-magnetic-moment-magnetics-electricity-Jeemate

If there is a uniform magnetic field of $0.3$ $T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium ?

A

(B)

and

(D)

, respectively

B

(B)

and

(C)

, respectively

C

(A)

and

(B)

, respectively

D

(A)

and

(C)

, respectively

Q 13PhysicsSection A • MCQwave optics

+4 / -1

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

A

bends down wards

B

bends upwards

C

becomes narrower

D

goes horizontally without any deflection

Q 14PhysicsSection A • MCQdual nature of radiation

+4 / -1

Match List - ${\rm I}$ (Fundamental Experiment) with List - ${\rm II}$ (its conclusion) and select the correct option from the choices given below the list:

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

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

A

A - ii;\,\,B - i,\,\,C - iii

B

A - iv;\,\,B - iii,\,\,C - ii

C

A - i;\,\,B - iv,\,\,C - iii

D

A - ii;\,\,B - iv,\,\,C - iii

Q 15PhysicsSection A • MCQmagnetics

+4 / -1

Two long current carrying thin wires, both with current

I,

are held by insulating threads of length

L

and are in equilibrium as shown in the figure, with threads making an angle

'\theta '

with the vertical. If wires have mass

\lambda

per unit-length then the value of

I

is :
(

g=

gravitational

acceleration

)

qImage-force-and-torque-on-current-carrying-conductor-magnetics-electricity-Jeemate

A

2\sqrt {{{\pi gL} \over {{\mu _0}}}\tan \theta }

B

\sqrt {{{\pi \lambda gL} \over {{\mu _0}}}\tan \theta }

C

\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}

D

2\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}

Q 16PhysicsSection A • MCQelectronic devices

+4 / -1

A red

LED

emits light at

0.1

watt uniformly around it. The amplitude of the electric field of the light at a distance of

1

m

from the diode is :

A

5.48

V/m

B

7.75

V/m

C

1.73

V/m

D

2.45

V/m

Q 17PhysicsSection A • MCQsimple harmonic motion

+4 / -1

A pendulum made of a uniform wire of cross sectional area

A

has time period

T.

When an additional mass

M

is added to its bob, the time period changes to

{T_{M.}}

If the Young's modulus of the material of the wire is

Y

then

{1 \over Y}

is equal to :
(

g=

gravitational

acceleration

)

A

\left[ {1 - {{\left( {{{{T_M}} \over T}} \right)}^2}} \right]{A \over {Mg}}

B

\left[ {1 - {{\left( {{T \over {{T_M}}}} \right)}^2}} \right]{A \over {Mg}}

C

\left[ {{{\left( {{{{T_M}} \over T}} \right)}^2} - 1} \right]{A \over {Mg}}

D

\left[ {{{\left( {{{{T_M}} \over T}} \right)}^2} - 1} \right]{{Mg} \over A}

Q 18PhysicsSection A • MCQlaws of motion

+4 / -1

qImage-friction-force-laws-of-motion-mechanics-Jeemate

Given in the figure are two blocks

A

and

B

of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force

F

as shown. If the coefficient of friction between the blocks is 0.1 and between block

B

and the wall is 0.15, the frictional force applied by the wall on block

B

is :

A

120

N

B

150

N

C

100

N

D

80

N

Q 19PhysicsSection A • MCQwaves

+4 / -1

A train is moving on a straight track with speed

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

It is blowing its whistle at the frequency of

1000

Hz

. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound

= 320\,m{s^{ - 1}}

) close to :

A

18\%

B

24\%

C

6\%

D

12\%

Q 20PhysicsSection A • MCQsimple harmonic motion

+4 / -1

For a simple pendulum, a graph is plotted between its kinetic energy

(KE)

and potential energy

(PE)

against its displacement

d.

Which one of the following represents these correctly?

(graphs

are

schematic

and

not

drawn

to

scale)

A

B

C

D

Q 21PhysicsSection A • MCQwave optics

+4 / -1

Assuming human pupil to have a radius of

0.25

cm

and a comfortable viewing distance of

25

cm

, the minimum separation between two objects that human eye can resolve at

500

nm

wavelength is :

A

100\,\mu m

B

300\,\mu m

C

1\,\mu m

D

30\,\mu m

Q 22PhysicsSection B • Numericalelectrostatics

+4 / -1

A uniformly charged solid sphere of radius

R

has potential

{V_0}

(measured with respect to

\infty

) on its surface. For this sphere the equipotential surfaces with potentials

{{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}} \over 4}

and

{{{V_0}} \over 4}

have radius

{R_1},\,\,{R_2},\,\,{R_3}

and

{R_4}

respectively. Then

Q 23PhysicsSection A • MCQrotational motion

+4 / -1

From a solid sphere of mass

M

and radius

R

a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:

A

{{4M{R^2}} \over {9\sqrt {3\pi } }}

B

{{4M{R^2}} \over {3\sqrt {3\pi } }}

C

{{M{R^2}} \over {32\sqrt {2\pi } }}

D

{{M{R^2}} \over {16\sqrt {2\pi } }}

Q 24PhysicsSection A • MCQcenter of mass

+4 / -1

Distance of the center of mass of a solid uniform cone from its vertex is

z{}_0

. If the radius of its base is

R

and its height is

h

then

z{}_0

is equal to :

A

{{5h} \over 8}

B

{{3{h^2}} \over {8R}}

C

{{{h^2}} \over {4R}}

D

{{3h} \over 4}

Q 25PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The period of oscillation of a simple pendulum is

T = 2\pi \sqrt {{L \over g}}

. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

A

1 %

B

5 %

C

2 %

D

3 %

Q 26PhysicsSection A • MCQcenter of mass

+4 / -1

A particle of mass

m

moving in the

x

direction with speed

2v

is hit by another particle of mass

2m

moving in the

y

direction with speed

v.

If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

A

56\%

B

62\%

C

44\%

D

50\%

Q 27PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A solid body of constant heat capacity

1

J/{}^ \circ C

is being heated by keeping it in contact with reservoirs in two ways:

(i)

Sequentially keeping in contact with

2

reservoirs such that each reservoir

\,\,\,\,\,\,\,\,

supplies same amount of heat.

(ii)

Sequentially keeping in contact with

8

reservoirs such that each reservoir

\,\,\,\,\,\,\,\,\,\,

supplies same amount of heat.
In both the cases body is brought from initial temperature

{100^ \circ }C

to final temperature

{200^ \circ }C

. Entropy change of the body in the two cases respectively is :

A

ln2, 2ln2

B

2ln2, 8ln2

C

ln2, 4ln2

D

ln2, ln2

Q 28PhysicsSection A • MCQelectrostatics

+4 / -1

A long cylindrical shell carries positives surfaces change

\sigma

in the upper half and negative surface charge -

\sigma

in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures are schematic and not drawn to scale)

A

B

C

D

Q 29PhysicsSection A • MCQray optics

+4 / -1

Monochromatic light is incident on a glass prism of angle

A

. If the refractive index of the material of the prism is

\mu

, a ray, incident at an angle

\theta

. on the face

AB

would get transmitted through the face

AC

of the prism provided :

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

A

\theta > {\cos ^{ - 1}}\left[ {\mu \,\sin \left( {A + {{\sin }^{ - 1}}} \right.\left( {{1 \over \mu }} \right)} \right]

B

\theta < {\cos ^{ - 1}}\left[ {\mu \,\sin \left( {A + {{\sin }^{ - 1}}} \right.\left( {{1 \over \mu }} \right)} \right]

C

\theta > si{n^{ - 1}}\left[ {\mu \,\sin \left( {A - {{\sin }^{ - 1}}} \right.\left( {{1 \over \mu }} \right)} \right]

D

\theta < si{n^{ - 1}}\left[ {\mu \,\sin \left( {A - {{\sin }^{ - 1}}} \right.\left( {{1 \over \mu }} \right)} \right]

Q 30PhysicsSection A • MCQgravitation

+4 / -1

From a solid sphere of mass

M

and radius

R,

a spherical portion of radius

R/2

is removed, as shown in the figure. Taking gravitational potential

V=0

at

r = \infty ,

the potential at the center of the cavity thus formed is:
(

G=gravitational

constant

)

qImage-gravitational-potential-and-gravitational-potential-energy-gravitation-mechanics-Jeemate

A

{{ - 2GM} \over {3R}}

B

{{ - 2GM} \over R}

C

{{ - GM} \over {2R}}

D

{{ - GM} \over R}

Q 31ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following compounds will exhibit geometrical isomerism?

A

3-Phenyl-1-butene

B

2-Phenyl-1-butene

C

1,1-Diphenyl-1-propane

D

1-Phenyl-2-butene

Q 32ChemistrySection A • MCQd and f block elements

+4 / -1

Match the catalysts to the correct processes :

	Catalyst		Process
(A)	TiCl₃	(i)	Wacker process
(B)	PdCl₂	(ii)	Ziegler - Natta polymerization
(C)	CuCl₂	(iii)	Contact process
(D)	V₂O₅	(iv)	Deacon's process

A

\left( A \right) - \left( {ii} \right),\,\,\left( B \right) - \left( {iii} \right),\,\,\left( C \right) - \left( {iv} \right),\,\,\left( D \right) - \left( i \right)

B

\left( A \right) - \left( {iii} \right),\,\,\left( B \right) - \left( i \right),\,\,\left( C \right) - \left( {ii} \right),\,\,\left( D \right) - \left( {iv} \right)

C

\left( A \right) - \left( {iii} \right),\,\,\left( B \right) - \left( {ii} \right),\,\,\left( C \right) - \left( {iv} \right),\,\,\left( D \right) - \left( i \right)

D

\left( A \right) - \left( {ii} \right),\,\,\left( B \right) - \left( i \right),\,\,\left( C \right) - \left( {iv} \right),\,\,\left( D \right) - \left( {iii} \right)

Q 33ChemistrySection A • MCQatomic structure

+4 / -1

Which of the following is the energy of a possible excited state of hydrogen?

A

–6.8 eV

B

–3.4 eV

C

+6.8 eV

D

+13.6 eV

Q 34ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

The molecular formula of a commercial resin used for exchanging ions in water softening is C₈H₇SO₃Na (Mol. Wt. 206). What would be the maximum uptake of Ca²⁺ ions by the resin when expressed in mole per gram resin?

A

2/309

B

1/412

C

1/103

D

1/206

Q 35ChemistrySection A • MCQd and f block elements

+4 / -1

The colour of KMnO₄ is due to :

A

d – d transition

B

L

\to

M charge transfer transition

C

\sigma

–

\sigma

* transition

D

M

\to

L charge transfer transition

Q 36ChemistrySection A • MCQbiomolecules

+4 / -1

Which of the vitamins given below is water soluble?

A

Vitamin D

B

Vitamin E

C

Vitamin K

D

Vitamin C

Q 37ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

Higher order (>3) reactions are rare due to

A

increase in entropy and activation energy as more molecules are involved

B

shifting of equilibrium towards reactants due to elastic collisions

C

loss of active species on collision

D

low probability of simultaneous collision of all the reacting species

Q 38ChemistrySection A • MCQsolid state

+4 / -1

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å . The radius of sodium atom is approximately :

A

5.72 Å

B

0.93 Å

C

1.86 Å

D

3.22 Å

Q 39ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

In the reaction

qImage-diazonium-salts-and-other-nitrogen-containing-compounds-compounds-containing-nitrogen-organic-chemistry-Jeemate

The product

E

is :

A

B

C

D

Q 40ChemistrySection A • MCQcoordination compounds

+4 / -1

The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH₃) (NH₂OH)]+ is (py = pyridine) :

A

3

B

4

C

6

D

2

Q 41ChemistrySection A • MCQchemical equilibrium

+4 / -1

The standard Gibbs energy change at 300 K for the reaction 2A

\leftrightharpoons

B + C is 2494.2 J. At a given time, the composition of the reaction mixture is [A] = 1/2, [B] = 2 and [C] = 1/2. The reaction proceeds in the: [R = 8.314 J/K/mol, e = 2.718]

A

reverse direction because Q > K_c

B

forward direction because Q < K_c

C

reverse direction because Q < K_c

D

forward direction because Q > K_c

Q 42ChemistrySection A • MCQsurface chemistry

+4 / -1

3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is:

A

36 mg

B

42 mg

C

54 mg

D

18 mg

Q 43ChemistrySection A • MCQp block elements

+4 / -1

Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen.

Reason : The reaction between nitrogen and oxygen requires high temperature.

A

Both assertion and reason are correct, and the reason is the correct explanation for the assertion

B

Both assertion and reason are correct, but the reason is not the correct explanation for the assertion

C

The assertion is incorrect, but the reason is correct

D

Both the assertion and reason are incorrect

Q 44ChemistrySection A • MCQcoordination compounds

+4 / -1

Which of the following compounds is not colored yellow?

A

K₃[Co(NO₂)₆]

B

(NH₄)₃[As(Mo₃O₁₀)₄]

C

BaCrO₄

D

Zn₂[Fe(CN)₆]

Q 45ChemistrySection A • MCQhydrogen

+4 / -1

From the following statements regarding H₂O₂, choose the incorrect statement :

A

It decomposes on exposure to light

B

It has to be stored in plastic or wax lined glass bottles in dark

C

It has to be kept away from dust

D

It can act only as an oxidizing agent

Q 46ChemistrySection A • MCQs block elements

+4 / -1

Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy?

A

BeSO₄

B

BaSO₄

C

SrSO₄

D

CaSO₄

Q 47ChemistrySection A • MCQp block elements

+4 / -1

Which one has the highest boiling point?

A

Ne

B

Kr

C

Xe

D

He

Q 48ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:

A

ion-dipole interaction

B

London force

C

hydrogen bond

D

ion-ion interaction

Q 49ChemistrySection A • MCQelectrochemistry

+4 / -1

Two Faraday of electricity is passed through a solution of CuSO₄. The mass of copper deposited at the cathode is: (at. mass of Cu = 63.5 amu)

A

63.5 g

B

2 g

C

127 g

D

0 g

Q 50ChemistrySection A • MCQpolymers

+4 / -1

Which polymer is used in the manufacture of paints and lacquers?

A

Glyptal

B

Polypropene

C

Poly vinyl chloride

D

Bakelite

Q 51ChemistrySection A • MCQp block elements

+4 / -1

Which among the following is the most reactive?

A

Br₂

B

I₂

C

ICl

D

Cl₂

Q 52ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Which compound would give

5

- keto -

2

- methylhexanal upon ozonolysis?

A

B

C

D

Q 53ChemistrySection A • MCQsolutions

+4 / -1

The vapour pressure of acetone at 20^oC is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20^oC, its vapour pressure was 183 torr. The molar mass (g mol^-1) of the substance is:

A

64

B

128

C

488

D

32

Q 54ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

The synthesis of alkyl fluorides is best accomplished by:

A

Sandmeyer’s reaction

B

Finkelstein reaction

C

Swarts reaction

D

Free radical fluorination

Q 55ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is: (at. Mass Ag = 108; Br = 80)

A

48

B

60

C

36

D

24

Q 56ChemistrySection A • MCQperiodic classification of elements

+4 / -1

The ionic radii (in Å) of N^3–, O^2– and F^– are respectively:

A

1.36, 1.71 and 1.40

B

1.71, 1.40 and 1.36

C

1.71, 1.36 and 1.40

D

1.36, 1.40 and 1.71

Q 57ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Which of the following compounds is not an antacid?

A

Cimetidine

B

Ranitidine

C

Phenelzine

D

Aluminium hydroxide

Q 58ChemistrySection A • MCQthermodynamics

+4 / -1

The following reaction is performed at 298 K
2NO(g) + O₂ (g)

\leftrightharpoons

2NO₂ (g)
The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO₂(g) at 298 K? (KP = 1.6 × 10¹²)

A

86600 + R(298) ln(1.6

\times

10¹²)

B

86600 -

ln (1.6 \times 10^{12}) \over R (298)

C

0.5[2×86,600 – R(298) ln(1.6×10¹²)]

D

R(298) ln(1.6×10¹²) – 86600

Q 59ChemistrySection A • MCQisolation of elements

+4 / -1

In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?

A

Al₂O₃ is mixed with CaF₂ which lowers the melting point of the mixture and brings conductivity

B

Al³⁺ is reduced at the cathode to form Al

C

Na₃AlF₆ serves as the electrolyte

D

CO and CO₂ are produced in this process

Q 60ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

In the following sequence of reactions:

qImage-method-of-preparation-for-aldehydes-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

qImage-method-of-preparation-for-aldehydes-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

The product C is

A

C₆H₅CH₃

B

C₆H₅CH₂OH

C

C₆H₅CHO

D

C₆H₅COOH

Q 61MathematicsSection A • MCQmathematical reasoning

+4 / -1

The negation of

\sim s \vee \left( { \sim r \wedge s} \right)

is equivalent to :

A

s \vee \left( {r \vee \sim s} \right)

B

s \wedge r

C

s \wedge \sim r

D

s \wedge \left( {r \wedge \sim s} \right)

Q 62MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

A = \left[ {\matrix{ 1 & 2 & 2 \cr 2 & 1 & { - 2} \cr a & 2 & b \cr } } \right]

is a matrix satisfying the equation

A{A^T} = 9\text{I},

where

I

is

3 \times 3

identity matrix, then the ordered

pair

(a, b)

is equal to :

A

(2, 1)

B

(-2, -1)

C

(2, -1)

D

(-2, 1)

Q 63MathematicsSection A • MCQdefinite integration

+4 / -1

The integral

\int\limits_2^4 {{{\log \,{x^2}} \over {\log {x^2} + \log \left( {36 - 12x + {x^2}} \right)}}dx}

is equal to :

A

1

B

6

C

2

D

4

Q 64MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

If the function.

g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.

is differentiable, then the value of

k+m

is :

A

{{10} \over 3}

B

4

C

2

D

{{16} \over 5}

Q 65MathematicsSection A • MCQarea under the curves

+4 / -1

The area (in sq. units) of the region described by

\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.

and

\left. {y \ge 4x - 1} \right\}

is :

A

{{15} \over {64}}

B

{{9} \over {32}}

C

{{7} \over {32}}

D

{{5} \over {64}}

Q 66MathematicsSection A • MCQsets and relations

+4 / -1

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A

\times

B , each having atleast three elements are

A

219

B

256

C

275

D

510

Q 67MathematicsSection A • MCQindefinite integration

+4 / -1

The integral

\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}}

equals :

A

- {\left( {{x^4} + 1} \right)^{{1 \over 4}}} + c

B

- {\left( {{{{x^4} + 1} \over {{x^4}}}} \right)^{{1 \over 4}}} + c

C

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

D

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

Q 68MathematicsSection A • MCQprobability

+4 / -1

If

12

different balls are to be placed in

3

identical boxes, then the probability that one of the boxes contains exactly

3

balls is :

A

220{\left( {{1 \over 3}} \right)^{12}}

B

22{\left( {{1 \over 3}} \right)^{11}}

C

{{55} \over 3}{\left( {{2 \over 3}} \right)^{11}}

D

55{\left( {{2 \over 3}} \right)^{10}}

Q 69MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let

f(x)

be a polynomial of degree four having extreme values
at

x=1

and

x=2

. If

\mathop {\lim }\limits_{x \to 0} \left[ {1 + {{f\left( x \right)} \over {{x^2}}}} \right] = 3

, then f

(2)

is equal to :

A

0

B

4

C

-8

D

-4

Q 70MathematicsSection A • MCQstatistics

+4 / -1

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

A

15.8

B

14.0

C

16.8

D

16.0

Q 71MathematicsSection A • MCQ3d geometry

+4 / -1

The distance of the point

(1, 0, 2)

from the point of intersection of the line

{{x - 2} \over 3} = {{y + 1} \over 4} = {{z - 2} \over {12}}

and the plane

x - y + z = 16,

is :

A

3\sqrt {21}

B

13

C

2\sqrt {14}

D

8

Q 72MathematicsSection A • MCQdifferential equations

+4 / -1

Let

y(x)

be the solution of the differential equation

\left( {x\,\log x} \right){{dy} \over {dx}} + y = 2x\,\log x,\left( {x \ge 1} \right).

Then

y(e)

is equal to :

A

2

B

2e

C

e

D

0

Q 73MathematicsSection A • MCQmatrices and determinants

+4 / -1

The set of all values of

\lambda

for which the system of linear equations:

\matrix{ {2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}} \cr {2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}} \cr { - {x_1} + 2{x_2} = \lambda {x_3}} \cr }

has a non-trivial solution

A

contains two elements

B

contains more than two elements

C

in an empty set

D

is a singleton

Q 74MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)} \over {x\tan 4x}}

is equal to

A

2

B

{1 \over 2}

C

4

D

3

Q 75MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a ,\overrightarrow b

and

\overrightarrow c

be three non-zero vectors such that no two of them are collinear and

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

If

\theta

is the angle between vectors

\overrightarrow b

and

{\overrightarrow c }

, then a value of sin

\theta

is :

A

{2 \over 3}

B

{{ - 2\sqrt 3 } \over 3}

C

{{ 2\sqrt 2 } \over 3}

D

{{ - \sqrt 2 } \over 3}

Q 76MathematicsSection A • MCQ3d geometry

+4 / -1

The equation of the plane containing the line

2x-5y+z=3; x+y+4z=5,

and parallel to the plane,

x+3y+6z=1,

is :

A

x+3y+6z=7

B

2x+6y+12z=-13

C

2x+6y+12z=13

D

x+3y+6z=-7

Q 77MathematicsSection A • MCQellipse

+4 / -1

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse

{{{x^2}} \over 9} + {{{y^2}} \over 5} = 1

, is :

A

{{27 \over 2}}

B

27

C

{{27 \over 4}}

D

18

Q 78MathematicsSection A • MCQparabola

+4 / -1

Let

O

be the vertex and

Q

be any point on the parabola,

{{x^2} = 8y}

. If the point

P

divides the line segment

OQ

internally in the ratio

1:3

, then locus of

P

is :

A

{y^2} = 2x

B

{{x^2} = 2y}

C

{{x^2} = y}

D

{y^2} = x

Q 79MathematicsSection A • MCQcomplex numbers

+4 / -1

A complex number z is said to be unimodular if

\,\left| z \right| = 1

. Suppose

{z_1}

and

{z_2}

are complex numbers such that

{{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}

is unimodular and

{z_2}

is not unimodular. Then the point

{z_1}

lies on a :

A

circle of radius 2.

B

circle of radius

{\sqrt 2 }

.

C

straight line parallel to x-axis

D

straight line parallel to y-axis.

Q 80MathematicsSection A • MCQcircle

+4 / -1

The number of common tangents to the circles

{x^2} + {y^2} - 4x - 6x - 12 = 0

and

{x^2} + {y^2} + 6x + 18y + 26 = 0,

is :

A

3

B

4

C

1

D

2

Q 81MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

Let

{\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),

where

\left| x \right| < {1 \over {\sqrt 3 }}.

Then a value of

y

is :

A

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

B

{{3x + {x^3}} \over {1 + 3{x^2}}}

C

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

D

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

Q 82MathematicsSection A • MCQbinomial theorem

+4 / -1

The sum of coefficients of integral power of

x

in the binomial expansion

{\left( {1 - 2\sqrt x } \right)^{50}}

is :

A

{1 \over 2}\left( {{3^{50}} - 1} \right)

B

{1 \over 2}\left( {{2^{50}} + 1} \right)

C

{1 \over 2}\left( {{3^{50}} + 1} \right)

D

{1 \over 2}\left( {{3^{50}}} \right)

Q 83MathematicsSection A • MCQsequences and series

+4 / -1

If m is the A.M. of two distinct real numbers l and n

(l,n > 1)

and

{G_1},{G_2}

and

{G_3}

are three geometric means between

l

and n, then

G_1^4\, + 2G_2^4\, + G_3^4

equals:

A

4\,lm{n^2}

B

4\,{l^2}{m^2}{n^2}

C

4\,{l^2}m\,n

D

4\,l\,{m^2}n

Q 84MathematicsSection A • MCQpermutations and combinations

+4 / -1

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

A

120

B

72

C

216

D

192

Q 85MathematicsSection A • MCQheight and distance

+4 / -1

If the angles of elevation of the top of a tower from three collinear points

A, B

and

C,

on a line leading to the foot of the tower, are

{30^ \circ }

,

{45^ \circ }

and

{60^ \circ }

respectively, then the ratio,

AB:BC,

is :

A

1:\sqrt 3

B

2:3

C

\sqrt 3 :1

D

\sqrt 3 :\sqrt 2

Q 86MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices

(0, 0)

(0, 41)

and

(41, 0)

is :

A

820

B

780

C

901

D

861

Q 87MathematicsSection A • MCQcircle

+4 / -1

Locus of the image of the point

(2, 3)

in the line

\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,\,k \in R,

is a :

A

circle of radius

\sqrt 2

.

B

circle of radius

\sqrt 3

.

C

straight line parallel to

x

-axis

D

straight line parallel to

y

-axis

Q 88MathematicsSection A • MCQapplication of derivatives

+4 / -1

The normal to the curve,

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

, at

(1,1)

A

meets the curve again in the third quadrant.

B

meets the curve again in the fourth quadrant.

C

does not meet the curve again.

D

meets the curve again in the second quadrant.

Q 89MathematicsSection A • MCQsequences and series

+4 / -1

The sum of first 9 terms of the series.

{{{1^3}} \over 1} + {{{1^3} + {2^3}} \over {1 + 3}} + {{{1^3} + {2^3} + {3^3}} \over {1 + 3 + 5}} + ......

A

142

B

192

C

71

D

96

Q 90MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

Let

\alpha

and

\beta

be the roots of equation

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

. If

{a_n} = {\alpha ^n} - {\beta ^n},

for

n \ge 1,

then the value of

{{{a_{10}} - 2{a_8}} \over {2{a_9}}}

is equal to :

A

3

B

- 3

C

6

D

- 6

JEE Main 2015 Question Paper with Solutions