JEE Main 2013 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQproperties of matter

+4 / -1

A uniform cylinder of length

L

and mass

M

having cross-sectional area

A

is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density

\sigma

at equilibrium position. The extension

{x_0}

of the spring when it is in equilibrium is:

A

{{Mg} \over k}

B

{{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)

C

{{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)

D

{{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)

Q 2PhysicsSection A • MCQsimple harmonic motion

+4 / -1

The amplitude of a damped oscillator decreases to

0.9

times its original magnitude in

5s

. In another

10s

it will decrease to

\alpha

times its original magnitude, where

\alpha

equals

A

0.7

B

0.81

C

0.729

D

0.6

Q 3PhysicsSection A • MCQalternating current

+4 / -1

In an

LCR

circuit as shown below both switches are open initially. Now switch

{S_1}

is closed,

{S_2}

kept open. (

q

is charge on the capacitor and

\tau

=RC

is Capacitance time constant). Which of the following statement is correct ? qImage-growth-and-decay-of-current-alternating-current-electricity-Jeemate

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

A

Work done by the battery is half of the energy dissipated in the resistor

B

t = \,\tau ,\,q = CV/2

C

At

t = \,2\tau ,\,q = CV\left( {1 - {e^{ - 2}}} \right)

D

At

t = \,2\tau ,\,q = CV\left( {1 - {e^{ - 1}}} \right)

Q 4PhysicsSection A • MCQcenter of mass

+4 / -1

This question has statement

{\rm I}

and statement

{\rm I}

{\rm I}

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

Statement - ${\rm I}$ : A point particle of mass $m$ moving with speed $\upsilon$ collides with stationary point particle of mass $M.$ If the maximum energy loss possible is given as $f\left( {{1 \over 2}m{v^2}} \right)$ , then $f = \left( {{m \over {M + m}}} \right).$

Statement - ${\rm II}$ : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A

Statement -

{\rm I}

is true, Statement -

{\rm II}

is true; Statement -

{\rm II}

is the correct explanation of Statement -

{\rm I}

.

B

Statement -

{\rm I}

is true, Statement -

{\rm II}

is true; Statement -

{\rm II}

is not the correct explanation of Statement -

{\rm I}

.

C

Statement -

{\rm I}

is true, Statement -

{\rm II}

is false

D

Statement -

{\rm I}

is false, Statement -

{\rm II}

true.

Q 5PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

Two short bar magnets of length

1

cm

each have magnetic moments

1.20

A{m^2}

and

1.00

A{m^2}

respectively. They are placed on a horizontal table parallel to each other with their

N

poles pointing towards the South. They have a common magnetic equator and are separated by a distance of

20.0

cm.

The value of the resultant horizontal magnetic induction at the mid-point

O

of the line joining their centres is close to

\left( \, \right.

Horizontal component of earth's magnetic induction is

3.6 \times 10.5Wb/{m^2})

A

3.6 \times 10.5\,\,Wb/{m^2}

B

2.56 \times 10.4\,\,Wb/{m^2}

C

3.50 \times 10.4\,\,Wb/{m^2}

D

5.80 \times 10.4\,Wb/{m^2}

Q 6PhysicsSection A • MCQelectrostatics

+4 / -1

Two charges, each equals to

q,

are kept at

x=-a

and

x=a

on the

x

-axis. A particle of mass

m

and charge

{q_0} = {q \over 2}

is placed at the origin. If charge

{q_0}

is given a small displacement

\left( {y < < a} \right)

along the

y

-axis, the net force acting on the particle is proportional to

A

y

B

-y

C

{1 \over y}

D

-{1 \over y}

Q 7PhysicsSection A • MCQrotational motion

+4 / -1

A hoop of radius

r

and mass

m

rotating with an angular velocity

{\omega _0}

is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?

A

{{r{\omega _0}} \over 4}

B

{{r{\omega _0}} \over 3}

C

{{r{\omega _0}} \over 2}

D

{r{\omega _0}}

Q 8PhysicsSection A • MCQelectrostatics

+4 / -1

A charge

Q

is uniformly distributed over a long rod

AB

of length

L

as shown in the figure. The electric potential at the point

O

lying at distance

L

from the end

A

is

qImage-electric-potential-energy-and-electric-potential-electrostatics-electricity-Jeemate

A

{Q \over {8\pi {\varepsilon _0}L}}

B

{{3Q} \over {4\pi {\varepsilon _0}L}}

C

{Q \over {4\pi {\varepsilon _0}L\,\ln \,2}}

D

{{Q\ln \,2} \over {4\pi {\varepsilon _0}L\,{}^s}}

Q 9PhysicsSection A • MCQwave optics

+4 / -1

Two coherent point sources

{S_1}

and

{S_2}

are separated by a small distance

'd'

as shown. The fringes obtained on the screen will be

qImage-huygens-principle-and-interference-of-light-wave-optics-optics-Jeemate

A

points

B

straight lines

C

semi-circles

D

concentric circles

Q 10PhysicsSection A • MCQelectronic devices

+4 / -1

A diode detector is used to detect an amplitude modulated wave of

60\%

modulation by using a condenser of capacity

250

picofarad in parallel with a load resistance

100

kilo

ohm.

Find the maximum modulated frequency which could be detected by it. qImage-digital-circuits-electronic-devices-modern-physics-Jeemate

A

10.62

MHz

B

10.62

kHz

C

5.31

MHz

D

5.31

kHz

Q 11PhysicsSection A • MCQdual nature of radiation

+4 / -1

The anode voltage of a photocell is kept fixed. The wavelength

\lambda

of the light falling on the cathode is gradually changed. The plate current

I

of the photocell varies as follows :

A

qImage-photoelectric-effect-dual-nature-of-radiation-modern-physics-Jeemate

B

C

D

Q 12PhysicsSection A • MCQelectronic devices

+4 / -1

The

{\rm I}

-

V

characteristic of an

LED

is

A

qImage-semiconductor-and-p-n-junction-diode-electronic-devices-modern-physics-Jeemate

B

C

D

Q 13PhysicsSection A • MCQunits and measurements

+4 / -1

Let [

{\varepsilon _0}

] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:

A

{\varepsilon _0} = \left[ {{M^{ - 1}}{L^{ - 3}}{T^2}A} \right]

B

{\varepsilon _0} =

\left[ {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}} \right]

C

{\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}{A^2}} \right]

D

{\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}A} \right]

Q 14PhysicsSection A • MCQmotion

+4 / -1

A projectile is given an initial velocity of

\left( {\widehat i + 2\widehat j} \right)

m/s, where

{\widehat i}

is along the ground and

{\widehat j}

is along the vertical. If g = 10 m/s², the equation of its trajectory is:

A

y = x - 5x²

B

y = 2x - 5x²

C

4y = 2x - 5x²

D

4y = 2x - 25x²

Q 15PhysicsSection A • MCQwaves

+4 / -1

A sonometer wire of length

1.5

m

is made of steel. The tension in it produces an elastic strain of

1\%

. What is the fundamental frequency of steel if density and elasticity of steel are

7.7 \times {10^3}\,kg/{m^3}

and

2.2 \times {10^{11}}\,N/{m^2}

respectively ?

A

188.5

Hz

B

178.2

Hz

C

200.5

Hz

D

770

Hz

Q 16PhysicsSection A • MCQproperties of matter

+4 / -1

If a piece of metal is heated to temperature

\theta

and then allowed to cool in a room which is at temperature

{\theta _0},

the graph between the temperature

T

of the metal and time

t

will be closest to

A

qImage-newtons-law-of-cooling-properties-of-matter-mechanics-Jeemate

B

C

D

Q 17PhysicsSection A • MCQheat and thermodynamics

+4 / -1

qImage-thermodynamics-process-heat-and-thermodynamics-mechanics-Jeemate

The above $p$ - $v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

A

{p_0}{v_0}

B

\left( {{{13} \over 2}} \right){p_0}{v_0}

C

\left( {{{11} \over 2}} \right){p_0}{v_0}

D

4{p_0}{v_0}

Q 18PhysicsSection A • MCQcapacitor

+4 / -1

Two capacitors

{C_1}

and

{C_2}

are charged to

120

V

and

200

V

respectively. It is found that connecting them together the potential on each one can be made zero. Then

A

5{C_1} = 3{C_2}

B

3{C_1} = 5{C_2}

C

3{C_1} + 5{C_2} = 0

D

9{C_1} = 4{C_2}

Q 19PhysicsSection A • MCQelectromagnetic waves

+4 / -1

The magnetic field in a travelling electromagnetic wave has a peak value of

20

n

T

. The peak value of electric field strength is :

A

3V/m

B

6V/m

C

9V/m

D

12V/m

Q 20PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A metallic rod of length

'\ell '

is tied to a string of length

2

\ell

and made to rotate with angular speed

w

on a horizontal table with one end of the string fixed. If there is a vertical magnetic field

'B'

in the region, the

e.m.f

induced across the ends of the rod is qImage-motional-emf-and-eddy-current-electromagnetic-induction-electricity-Jeemate

A

{{2B\omega \ell } \over 2}

B

{{3B\omega \ell } \over 2}

C

{{4B\omega {\ell ^2}} \over 2}

D

{{5B\omega {\ell ^2}} \over 2}

Q 21PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A circular loop of radius

0.3

cm

lies center of the small loop is on the axis of the bigger loop. The distance between their centers is

15

cm.

If a current of

2.0

A

flows through the smaller loop, than the flux linked with bigger loop is

A

9.1 \times {10^{ - 11}}\,

weber

B

6 \times {10^{ - 11}}\,

weber

C

3.3 \times {10^{ - 11}}\,

weber

D

6.6 \times {10^{ - 9}}\,

weber

Q 22PhysicsSection A • MCQray optics

+4 / -1

The graph between angle of deviation

\left( \delta \right)

and angle of incidence

(i)

for a triangular prism is represented by

A

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

B

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

C

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

D

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

Q 23PhysicsSection A • MCQgravitation

+4 / -1

What is the minimum energy required to launch a satellite of mass

m

from the surface of a planet of mass

M

and radius

R

in a circular orbit at an altitude of

2R

?

A

{{5GmM} \over {6R}}

B

{{2GmM} \over {3R}}

C

{{GmM} \over {2R}}

D

{{GmM} \over {3R}}

Q 24PhysicsSection A • MCQwave optics

+4 / -1

A beam of unpolarised light of intensity

{{\rm I}_0}

is passed through a polaroid

A

and then through another polaroid

B

which is oriented so that its principal plane makes an angle of

{45^ \circ }

relative to that of

A

. The intensity of the emergent light is

A

{{\rm I}_0}

B

{{{I_0}} \over 2}

C

{{{I_0}} \over 4}

D

{{{I_0}} \over 8}

Q 25PhysicsSection A • MCQcurrent electricity

+4 / -1

The supply voltage to room is

120V.

The resistance of the lead wires is

6\Omega

. A

60

W

bulb is already switched on. What is the decrease of voltage across the bulb, when a

240

W

heater is switched on in parallel to the bulb?

A

zero

B

2.9

Volt

C

13.3

Volt

D

10.04

Volt

Q 26PhysicsSection A • MCQcurrent electricity

+4 / -1

This questions has Statement -

{\rm I}

and Statement -

{\rm I}

{\rm I}

. Of the four choices given after the Statements, choose the one that best describes into two Statements.

Statement - ${\rm I}$ : Higher the range, greater is the resistance of ammeter.
Statement - ${\rm I}$ ${\rm I}$ : To increase the range of ammeter, additional shunt needs to be used across it.

A

Statement -

{\rm I}

is true, Statement -

{\rm II}

is true, Statement -

{\rm II}

is the correct explanation of statement -

{\rm I}

.

B

Statement -

{\rm I}

is true, Statement -

{\rm II}

is true, Statement -

{\rm II}

is not the correct explanation of statement -

{\rm I}

.

C

Statement -

{\rm I}

is true, Statement -

{\rm II}

is false

D

Statement -

{\rm I}

is false, Statement -

{\rm II}

is true

Q 27PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is

T,

density of liquid is

\rho

and

L

is its latent heat of vaporization.

A

\rho L/T

B

\sqrt {T/\rho L}

C

T/\rho L

D

2T/\rho L

Q 28PhysicsSection A • MCQray optics

+4 / -1

Diameter of a plano-convex lens is

6

cm

and thickness at the center is

3mm

. If speed of light in material of lens is

2 \times {10^8}\,m/s,

the focal length of the lens is

A

15

cm

B

20

cm

C

30

cm

D

10

cm

Q 29PhysicsSection A • MCQsimple harmonic motion

+4 / -1

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass

M.

The piston and the cylinder have equal cross sectional area

A

. When the piston is in equilibrium, the volume of the gas is

{V_0}

and its pressure is

{P_0}.

The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency

A

{1 \over {2\pi }}\,{{A\gamma {P_0}} \over {{V_0}M}}

B

{1 \over {2\pi }}\,{{{V_0}M{P_0}} \over {{A^2}\gamma }}

C

{1 \over {2\pi }}\,\sqrt {{{A\gamma {P_0}} \over {{V_0}M}}}

D

{1 \over {2\pi }}\,\sqrt {{{M{V_0}} \over {A\gamma {P_0}}}}

Q 30PhysicsSection A • MCQatoms and nuclei

+4 / -1

In a hydrogen like atom electron make transition from an energy level with quantum number

n

to another with quantum number

\left( {n - 1} \right)

. If

n > > 1,

the frequency of radiation emitted is proportional to :

A

{1 \over n}

B

{1 \over {{n^2}}}

C

{1 \over {{n^{{3 \over 2}}}}}

D

{1 \over {{n^3}}}

Q 31ChemistrySection A • MCQelectrochemistry

+4 / -1

Given

E_{C{r^{2 + }}/Cr}^o

= -0.74 V;

E_{MnO_4^ - /M{n^{2 + }}}^o

= 1.51 V

E_{C{r_2}O_7^{2 - }/C{r^{3 + }}}^o

= 1.33 V;

E_{Cl/C{l^ - }}^o

= 1.36 V

Based on the data given above, strongest oxidising agent will be :

A

Cr³⁺

B

Mn²⁺

C

MnO_4^ -

D

Cl^-

Q 32ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

A

Methylamine

B

Ammonia

C

Phosgene

D

Methyl isocyanate

Q 33ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Arrange the following compounds in order of decreasing acidity :

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

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

A

{\rm I}{\rm I} > {\rm I}V > {\rm I} > {\rm I}{\rm I}{\rm I}

B

{\rm I} > {\rm I}{\rm I} > {\rm I}{\rm I}{\rm I} > {\rm I}V

C

{\rm I}{\rm I}{\rm I} > {\rm I} > {\rm I}{\rm I} > {\rm I}V

D

{\rm I}V > {\rm I}{\rm I}{\rm I} > {\rm I} > {\rm I}{\rm I}

Q 34ChemistrySection A • MCQd and f block elements

+4 / -1

Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest

E_{{M^{3 + }}/{M^{2 + }}}^0

value?

A

Mn (Z = 25)

B

Fe (Z = 26)

C

Co (Z = 27)

D

Cr (Z = 24)

Q 35ChemistrySection A • MCQperiodic classification of elements

+4 / -1

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be:

A

– 5.1 eV

B

–10.2 eV

C

+ 2.55 eV

D

– 2.55 eV

Q 36ChemistrySection A • MCQcoordination compounds

+4 / -1

Which of the following complex species is not expected to exhibit optical isomerism?

A

[Co (en)₂ Cl₂]^-

B

[Co (NH₃)₃ Cl₃]

C

[Co (en) (NH₃)₂ Cl₂]⁺

D

[Co (en)₃]³⁺

Q 37ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:

A

1.00 M

B

1. 75 M

C

0.975 M

D

0.875 M

Q 38ChemistrySection A • MCQgaseous state

+4 / -1

For gaseous state, if most probable speed is denoted by C*, average speed by

\mathop C\limits^{\_\_}

and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

A

C*:

\mathop C\limits^{\_\_}

: C = 1.128 : 1.225 : 1

B

C*:

\mathop C\limits^{\_\_}

: C = 1.225 : 1.128 : 1

C

C*:

\mathop C\limits^{\_\_}

: C = 1 : 1.225 : 1.128

D

C*:

\mathop C\limits^{\_\_}

: C = 1 : 1.128 : 1.225

Q 39ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be:(R = 8.314 JK^–1 mol^–1 and log 2 = 0.301)

A

48.6 kJ mol^–1

B

58.5 kJ mol^–1

C

60.5 kJ mol^–1

D

53.6 kJ mol^–1

Q 40ChemistrySection B • Numericalp block elements

+4 / -1

Which of the following is the wrong statement?

Q 41ChemistrySection A • MCQatomic structure

+4 / -1

Energy of an electron is given by

E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)

. Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be
(h = 6.62 × 10⁻³⁴ Js and c = 3.0 × 10⁸ ms⁻¹)

A

2.816 × 10⁻⁷ m

B

6.500 × 10⁻⁷ m

C

8.500 × 10⁻⁷ m

D

1.214 × 10⁻⁷ m

Q 42ChemistrySection A • MCQredox reactions

+4 / -1

Consider the following reaction:

xMnO_4^- + yC_2O_4^{2-}

+ zH⁺

\to

xMn²⁺ + 2yCO₂ +

{z \over 2}{H_2}O

The value's of x, y and z in the reaction are, respectively :

A

5, 2 and 16

B

2, 5 and 8

C

2, 5 and 16

D

5, 2 and 8

Q 43ChemistrySection A • MCQthermodynamics

+4 / -1

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0^oC. As it does so, it absorbs 208J of heat. The values of q and w for the process will be :
(R = 8.314 J/mol K) ( l n 7.5 = 2.01)

A

q = – 208 J, w = – 208 J

B

q = – 208 J, w = + 208 J

C

q = + 208 J, w = + 208 J

D

q = + 208 J, w = – 208 J

Q 44ChemistrySection B • Numericalchemical bonding and molecular structure

+4 / -1

Which one of the following molecules is expected to exhibit diamagnetic behaviour?

Q 45ChemistrySection A • MCQionic equilibrium

+4 / -1

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?

A

0.1 L

B

0.9 L

C

2.0 L

D

9.0 L

Q 46ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

A compound with molecular mass 180 is acylated with CH₃COCl to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:

A

2

B

5

C

4

D

6

Q 47ChemistrySection A • MCQsurface chemistry

+4 / -1

The coagulating power of electrolytes having ions Na⁺, Al³⁺ and Ba²⁺ for arsenic sulphide sol increases in the order:

A

Na⁺ < Ba²⁺ < Al³⁺

B

Al³⁺ < Ba²⁺ < Na⁺

C

Ba²⁺ < Na⁺ < Al³⁺

D

Al³⁺ < Na⁺ < Ba²⁺

Q 48ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

In which of the following pairs of molecules/ions, both the species are not likely to exist?

A

H_2^+

,

He_2^{2-}

B

H_2^-

,

He_2^{2-}

C

H_2^{2+}

,

He_2

D

H_2^-

,

He_2^{2+}

Q 49ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The order of stability of the following carbocations :

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

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

A

{\rm I}{\rm I}{\rm I} > {\rm I}{\rm I} > {\rm I}

B

{\rm I}{\rm I} > {\rm I}{\rm I}{\rm I} > {\rm I}

C

{\rm I} > {\rm I}{\rm I} > {\rm I}{\rm I}{\rm I}

D

{\rm I}{\rm I}{\rm I} > {\rm I} > {\rm I}{\rm I}

Q 50ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

A

tertiary alcohol by S_N1

B

secondary alcohol by S_N2

C

tertiary alcohol by S_N2

D

secondary alcohol by S_N1

Q 51ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO₂. The empirical formula of the hydrocarbon is

A

C₂H₄

B

C₃H₄

C

C₆H₅

D

C₇H₈

Q 52ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Compound

\left( A \right),\,{C_8}{H_9}Br,\,\,\,

gives a white precipitate when warmed with alcoholic

AgN{O_3}.

Oxidation of

(A)

gives an acid

\left( B \right),

{C_8}{H_6}{O_4}.\,\,\left( B \right)

easily forms anhydride on heating. Identify the compound

(A).

A

qImage-haloalkanes-haloalkanes-and-haloarenes-organic-chemistry-Jeemate

B

C

D

Q 53ChemistrySection A • MCQd and f block elements

+4 / -1

Which of the following arrangements does not represent the correct order of the property stated against it?

A

Ni²⁺ < Co²⁺ < Fe²⁺ < Mn²⁺ : ionic size

B

Co³⁺ < Fe³⁺ < Cr³⁺ < Sc³⁺ : stability in aqueous solution

C

Sc < Ti < Cr < Mn : number of oxidation states

D

V²⁺ < Cr²⁺ < Mn²⁺ < Fe²⁺ : paramagnetic behaviour

Official Correct Answer:Option (D)

Step-by-Step Solution:

(1)

V = 3d³4s²	V²⁺ = 3d³	= 3 unpaired electron
Cr = 3d⁵4s¹	Cr²⁺ = 3d⁴	= 4 unpaired electron
Mn = 3d⁵4s²	Mn²⁺ = 3d⁵	= 5 unpaired electron
Fe = 3d⁶4s²	Fe²⁺ = 3d⁶	= 4 unpaired electron

hence the correct order of paramagnetic behaviour

{V^{2 + }} < Cr{}^{2 + } = F{e^{2 + }} < M{n^{2 + }}

(2)

\,\,\,\,

For the same oxidation state, the-ionic radii generally

dc

-creases as the atomic number increases in a particular transition series.

Hence the order is

M{n^{ + + }} > F{e^{ + + }} > C{o^{ + + }} > N{i^{ + + }}

(3)

In solution, the stability of the compounds depends upon electrode potentials,

SEP

of the transitions metal ions are given as

C{o^{3 + }}/Co = + 1.97,\,\,\,F{e^{3 + }}/Fe = + 0.77;

C{r^{3 + }}/C{r^{2 + }} = - 0.41,\,\,S{c^{3 + }}

is highly stable as it does not show

+2

O.

S.

(4)

Sc - \left( { + 2} \right),\left( { + 3} \right)

Ti - \left( { + 2} \right),\left( { + 3} \right),\left( { + 4} \right)

Cr - \left( { + 1} \right),\left( { + 2} \right),\left( { + 3} \right),\left( { + 4} \right),\left( { + 5} \right),\left( { + 6} \right)

Mn - \left( { + 2} \right),\left( { + 3} \right),\left( { + 4} \right),\left( { + 5} \right),\left( { + 6} \right),\left( { + 7} \right)

i.e.\,Sc < Ti < Cr = Mn

{E_a} = 53598.6J/mol

= 53.6\,kJ/mol.

Q 54ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?

A

S < Se < Ca < Ba < Ar

B

Ba < Ca < Se < S < Ar

C

Ca < Ba < S < Se < Ar

D

Ca < S < Ba < Se < Ar

Official Correct Answer:Option (B)

Step-by-Step Solution:

Those elements are present in periodic table like this -

	Group 2		Group 16		Group 18
Period 3	Ca	..........	S	.........	Ar
Period 4			Sc
Period 5	Ba

In periodic table,

1. From left to right ionization energy increases.

2. From top to bottom ionization energy decreases.

\therefore

Ba < Ca and Se < S and S < Ar

\therefore

Correct order is -
Ba < Ca < Sc < S < Ar

Q 55ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

An organic compound A upon reacting with

N{H_3}

gives

B.

On heating

B

gives

C.

C

in presence of

KOH

reacts with

B{r_2}

to given

C{H_3}C{H_2}N{H_2}2.

A

is :

A

C{H_3}COOH

B

C{H_3}C{H_2}C{H_2}COOH

C

qImage-aliphatic-amines-compounds-containing-nitrogen-organic-chemistry-Jeemate

D

C{H_3}C{H_2}COOH

Q 56ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

A solution of (–

l

) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small amount of SbCl₅, due to the formation of :

A

carbene

B

carbocation

C

free radical

D

carbanion

Q 57ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Stability of the species Li₂,

Li_2^−

and

Li_2^+

increases in the order of:

A

Li₂ <

Li_2^+

<

Li_2^-

B

Li_2^+

<

Li_2^-

< Li₂

C

Li_2^-

<

Li_2^+

< Li₂

D

Li_2^-

< Li₂ <

Li_2^+

Q 58ChemistrySection A • MCQbiomolecules

+4 / -1

Synthesis of each molecule of glucose in photosynthesis involves:

A

10 molecules of ATP

B

8 molecules of ATP

C

6 molecules of ATP

D

18 molecules of ATP

Q 59ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

Experimentally it was found that a metal oxide has formula M_0.98O. Metal M, present as M²⁺ and M³⁺ in its oxide. Fraction of the metal which exists as M³⁺ would be

A

7.01%

B

4.08%

C

6.05%

D

5.08%

Q 60ChemistrySection A • MCQsolid state

+4 / -1

Which of the following exists as covalent crystals in the solid state?

A

Silicon

B

Sulphur

C

Phosphorous

D

Iodine

Q 61MathematicsSection A • MCQpermutations and combinations

+4 / -1

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A

\times

B having 3 or more elements is :

A

219

B

211

C

256

D

220

Q 62MathematicsSection A • MCQapplication of derivatives

+4 / -1

The intercepts on

x

-axis made by tangents to the curve,

y = \int\limits_0^x {\left| t \right|dt,x \in R,}

which are parallel to the line

y=2x

, are equal to :

A

\pm 1

B

\pm 2

C

\pm 3

D

\pm 4

Q 63MathematicsSection A • MCQbinomial theorem

+4 / -1

The term independent of

x

in expansion of

{\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right)^{10}}

is

A

4

B

120

C

210

D

310

Q 64MathematicsSection A • MCQcircle

+4 / -1

The circle passing through

(1, -2)

and touching the axis of

x

at

(3, 0)

also passes through the point :

A

\left( { - 5,\,2} \right)

B

\left( { 2,\,-5} \right)

C

\left( { 5,\,-2} \right)

D

\left( { - 2,\,5} \right)

Q 65MathematicsSection A • MCQ3d geometry

+4 / -1

If the lines

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

and

{{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}

are coplanar, then

k

can have :

A

any value

B

exactly one value

C

exactly two values

D

exactly three values

Q 66MathematicsSection A • MCQheight and distance

+4 / -1

ABCD

is a trapezium such that

AB

and

CD

are parallel and

BC \bot CD.

If

\angle ADB = \theta ,\,BC = p

and

CD = q,

then AB is equal to:

A

{{\left( {{p^2} + {q^2}} \right)\sin \theta } \over {p\cos \theta + q\sin \theta }}

B

{{{p^2} + {q^2}\cos \theta } \over {p\cos \theta + q\sin \theta }}

C

{{{p^2} + {q^2}} \over {{p^2}\cos \theta + {q^2}\sin \theta }}

D

{{\left( {{p^2} + {q^2}} \right)\sin \theta } \over {{{\left( {p\cos \theta + q\sin \theta } \right)}^2}}}

Q 67MathematicsSection A • MCQsequences and series

+4 / -1

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is

A

{7 \over {81}}\left( {179 - {{10}^{ - 20}}} \right)

B

\,{7 \over 9}\left( {99 - {{10}^{ - 20}}} \right)

C

{7 \over {81}}\left( {179 + {{10}^{ - 20}}} \right)

D

{7 \over 9}\left( {99 + {{10}^{ - 20}}} \right)

Q 68MathematicsSection A • MCQmatrices and determinants

+4 / -1

The number of values of

k

, for which the system of equations :

&#x27; in math mode at position 1:

̲\matrix{ {\l…" style="color:#cc0000">$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr }$
has no solution, is

A

infinite

B

1

C

2

D

3

Q 69MathematicsSection A • MCQvector algebra

+4 / -1

If the vectors

\overrightarrow {AB} = 3\widehat i + 4\widehat k

and

\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k

are the sides of a triangle

ABC,

then the length of the median through

A

is :

A

\sqrt {18}

B

\sqrt {72}

C

\sqrt {33}

D

\sqrt {45}

Q 70MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

The expression

{{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}

can be written as:

A

\sin {\rm A}\,\cos {\rm A} + 1

B

\,\sec {\rm A}\,\cos ec{\rm A} + 1

C

\tan {\rm A} + \cot {\rm A}

D

\sec {\rm A} + \cos ec{\rm A}

Q 71MathematicsSection 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

- {1 \over 4}

B

{1 \over 2}

C

1

D

2

Q 72MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

A ray of light along

x + \sqrt 3 y = \sqrt 3

gets reflected upon reaching

X

-axis, the equation of the reflected ray is :

A

y = x + \sqrt 3

B

\sqrt 3 y = x - \sqrt 3

C

y = \sqrt 3 x - \sqrt 3

D

\sqrt 3 y = x - 1

Q 73MathematicsSection A • MCQmathematical reasoning

+4 / -1

Consider :
Statement − I :

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

is a fallacy.
Statement − II :

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

is a tautology.

A

Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

B

Statement -I is True; Statement -II is False.

C

Statement -I is False; Statement -II is True

D

Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Official Correct Answer:Option (A)

Step-by-Step Solution:

Statement - I : $(p \wedge \sim q) \wedge ( \sim p \wedge q)$

p	q	$\sim p$	$\sim q$	$p \wedge \sim q$	$\sim p \wedge q$	$(p \wedge \sim q) \wedge ( \sim p \wedge q)$
T	T	F	F	F	F	F
T	F	F	T	T	F	F
F	T	T	F	F	T	F
F	F	T	T	F	F	F

Hence, statement-I is a fallacy.

Statement - II : $(p \to q) \leftrightarrow ( \sim q \to \sim p)$

p	q	$\sim p$	$\sim q$	$p \to q$	$\sim q \to \sim p$	$(p \to q) \leftrightarrow ( \sim q \to \sim p)$
T	T	F	F	T	T	T
T	F	F	T	F	F	T
F	T	T	F	T	T	T
F	F	T	T	T	T	T

Hence, statement - II is a tautology.

Now, statement-II does not depend on statement-I.

Q 74MathematicsSection A • MCQprobability

+4 / -1

A multiple choice examination has

5

questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get

4

or more correct answers just by guessing is :

A

{{17} \over {{3^5}}}

B

{{13} \over {{3^5}}}

C

{{11} \over {{3^5}}}

D

{{10} \over {{3^5}}}

Q 75MathematicsSection A • MCQellipse

+4 / -1

The equation of the circle passing through the foci of the ellipse

{{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1

, and having centre at

(0,3)

is :

A

{x^2} + {y^2} - 6y - 7 = 0

B

{x^2} + {y^2} - 6y + 7 = 0

C

{x^2} + {y^2} - 6y - 5 = 0

D

{x^2} + {y^2} - 6y + 5 = 0

Q 76MathematicsSection A • MCQ3d geometry

+4 / -1

Distance between two parallel planes

2x+y+2z=8

and

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

is :

A

{3 \over 2}

B

{5 \over 2}

C

{7 \over 2}

D

{9 \over 2}

Q 77MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The

x

-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as

(0, 1) (1, 1)

and

(1, 0)

is :

A

2 + \sqrt 2

B

2 - \sqrt 2

C

1 + \sqrt 2

D

1 - \sqrt 2

Q 78MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

If

x, y, z

are in A.P. and

{\tan ^{ - 1}}x,{\tan ^{ - 1}}y

and

{\tan ^{ - 1}}z

are also in A.P., then :

A

x=y=z

B

2x=3y=6z

C

6x=3y=2z

D

6x=4y=3z

Q 79MathematicsSection A • MCQapplication of derivatives

+4 / -1

The real number

k

for which the equation,

2{x^3} + 3x + k = 0

has two distinct real roots in

\left[ {0,\,1} \right]

A

lies between 1 and 2

B

lies between 2 and 3

C

lies between

- 1

and 0

D

does not exist.

Q 80MathematicsSection A • MCQindefinite integration

+4 / -1

If

\int {f\left( x \right)dx = \psi \left( x \right),}

then

\int {{x^5}f\left( {{x^3}} \right)dx}

is equal to

A

{1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C

B

{1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C

C

{1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C

D

{1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C

Q 81MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

P = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]

is the adjoint of a

3 \times 3

matrix

A

and

\left| A \right| = 4,

then

\alpha

is equal to :

A

4

B

11

C

5

D

0

Q 82MathematicsSection A • MCQdifferentiation

+4 / -1

If

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

then

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

at

x=1

is equal to :

A

{1 \over {\sqrt 2 }}

B

{1 \over 2}

C

1

D

\sqrt 2

Q 83MathematicsSection A • MCQparabola

+4 / -1

Given : A circle,

2{x^2} + 2{y^2} = 5

and a parabola,

{y^2} = 4\sqrt 5 x

.
Statement-1 : An equation of a common tangent to these curves is

y = x + \sqrt 5

.

Statement-2 : If the line, $y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)$ is their common tangent, then $m$ satiesfies ${m^4} - 3{m^2} + 2 = 0$ .

A

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

B

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

C

Statement-1 is true; Statement-2 is false.

D

Statement-1 is false Statement-2 is true.

Q 84MathematicsSection A • MCQpermutations and combinations

+4 / -1

Let

{T_n}

be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If

{T_{n + 1}} - {T_n}

= 10, then the value of n is :

A

7

B

5

C

10

D

8

Q 85MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If the equations

{x^2} + 2x + 3 = 0

and

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

a,\,b,\,c\, \in \,R,

have a common root, then

a\,:b\,:c\,

is

A

1:2:3

B

3:2:1

C

1:3:2

D

3:1:2

Q 86MathematicsSection A • MCQstatistics

+4 / -1

All the students of a class performed poorly in maths. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

A

median

B

mode

C

variance

D

mean

Q 87MathematicsSection A • MCQdefinite integration

+4 / -1

Statement-1 : The value of the integral

\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}}

is equal to

\pi /6

Statement-2 : $\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.$

A

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

B

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

C

Statement- 1 is true; Statement-2 is False.

D

Statement-1 is false; Statement-2 is true.

Q 88MathematicsSection A • MCQdifferential equations

+4 / -1

At present, a firm is manufacturing

2000

items. It is estimated that the rate of change of production P w.r.t. additional number of workers

x

is given by

{{dp} \over {dx}} = 100 - 12\sqrt x .

If the firm employs

25

more workers, then the new level of production of items is

A

2500

B

3000

C

3500

D

4500

Q 89MathematicsSection A • MCQarea under the curves

+4 / -1

The area (in square units) bounded by the curves

y = \sqrt {x,}

2y - x + 3 = 0,

x

-axis, and lying in the first quadrant is :

A

9

B

36

C

18

D

{{27} \over 4}

Q 90MathematicsSection A • MCQcomplex numbers

+4 / -1

If z is a complex number of unit modulus and argument

\theta

, then arg

\left( {{{1 + z} \over {1 + \overline z }}} \right)

equals :

A

- \theta \,\,

B

{\pi \over 2} - \theta \,

C

\theta \,

D

\,\pi - \theta \,\,

JEE Main 2013 Question Paper with Solutions