JEE Mains Aieee 2011 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQelectrostatics

+4 / -1

The electrostatic potential inside a charged spherical ball is given by

\phi = a{r^2} + b

where

r

is the distance from the center and

a,b

are constants. Then the charge density inside the ball is:

A

- 6a{\varepsilon _0}r

B

- 24\pi a{\varepsilon _0}

C

- 6a{\varepsilon _0}

D

- 24\pi {\varepsilon _0}r

Q 2PhysicsSection A • MCQray optics

+4 / -1

Let

x

-

z

plane be the boundary between two transparent media. Medium

1

in

z \ge 0

has a refractive index of

\sqrt 2

and medium

2

with

z < 0

has a refractive index of

\sqrt 3 .

A ray of light in medium

1

given by the vector

\overrightarrow A = 6\sqrt 3 \widehat i + 8\sqrt 3 \widehat j - 10\widehat k

is incident on the plane of separation. The angle of refraction in medium

2

is:

A

{45^ \circ }

B

{60^ \circ }

C

{75^ \circ }

D

{30^ \circ }

Q 3PhysicsSection A • MCQheat and thermodynamics

+4 / -1

100g

of water is heated from

{30^ \circ }C

to

{50^ \circ }C

. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is

4184

J/kg/K

):

A

8.4

kJ

B

84

kJ

C

2.1

kJ

D

4.2

kJ

Q 4PhysicsSection A • MCQelectromagnetic induction

+4 / -1

A boat is moving due east in a region where the earth's magnetic fields is

5.0 \times {10^{ - 5}}

N{A^{ - 1}}\,{m^{ - 1}}

due north and horizontal. The best carries a vertical aerial

2

m

long. If the speed of the boat is

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

the magnitude of the induced

emf

in the wire of aerial is :

A

0.75

mV

B

0.50

mV

C

0.15

mV

D

1

mV

Q 5PhysicsSection A • MCQsimple harmonic motion

+4 / -1

Two particles are executing simple harmonic motion of the same amplitude

A

and frequency

\omega

along the

x

-axis. Their mean position is separated by distance

{X_0}\left( {{X_0} > A} \right)

. If the maximum separation between them is

\left( {{X_0} + A} \right),

the phase difference between their motion is:

A

{\pi \over 3}

B

{\pi \over 4}

C

{\pi \over 6}

D

{\pi \over 2}

Q 6PhysicsSection A • MCQsimple harmonic motion

+4 / -1

A mass

M,

attached to a horizontal spring, executes

S.H.M.

with amplitude

{A_1}.

When the mass

M

passes through its mean position then a smaller mass

m

is placed over it and both of them move together with amplitude

{A_2}.

The ratio of

\left( {{{{A_1}} \over {{A_2}}}} \right)

is :

A

{{M + m} \over M}

B

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

C

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

D

{M \over {M + m}}

Q 7PhysicsSection A • MCQmagnetics

+4 / -1

A current

I

flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius

R.

The magnitude of the magnetic induction along its axis is:

A

{{{\mu _0}I} \over {2{\pi ^2}R}}

B

{{{\mu _0}I} \over {2\pi R}}

C

{{{\mu _0}I} \over {4\pi R}}

D

{{{\mu _0}I} \over {{\pi ^2}R}}

Q 8PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A thermally insulated vessel contains an ideal gas of molecular mass

M

and ratio of specific heats

\gamma .

It is moving with speed

v

and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

A

{{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K

B

{{\gamma {M^2}v} \over {2R}}K

C

{{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K

D

{{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K

Q 9PhysicsSection A • MCQdual nature of radiation

+4 / -1

This question has Statement -

1

and Statement -

2

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

Statement - $1$ : A metallic surface is irradiated by a monochromatic light of frequency $v > {v_0}$ (the threshold frequency). The maximum kinetic energy and the stopping potential are ${K_{\max }}$ and ${V_0}$ respectively. If the frequency incident on the surface is doubled, both the ${K_{\max }}$ anmd ${V_0}$ are also doubled.
Statement - $2$ : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

A

Statement -

1

is true, Statement -

2

is true, Statement -

2

is the correct explanation of Statement -

1

.

B

Statement -

1

is true, Statement -

2

is true, Statement -

2

is not the correct explanation of Statement -

1

.

C

Statement -

1

is false, Statement -

2

is true.

D

Statement -

1

is true, Statement -

2

is false.

Q 10PhysicsSection A • MCQwave optics

+4 / -1

This question has a paragraph followed by two statements, Statement

-1

and Statement

-2

. Of the given four alternatives after the statements, choose the one that describes the statements.

A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plane. With monochromatic light, this film gives an interference pattern due to light, reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement - $1$ : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi .$

Statement - $2$ : The center of the interference pattern is dark.

A

Statement -

1

is true, Statement -

2

is true, Statement -

2

is the correct explanation of Statement -

1

B

Statement -

1

is true, Statement -

2

is true, Statement -

2

is not the correct explanation of Statement -

1

C

Statement -

1

is false, Statement -

2

is true

D

Statement -

1

is true, Statement -

2

is false.

Q 11PhysicsSection A • MCQheat and thermodynamics

+4 / -1

Three perfect gases at absolute temperatures

{T_1},\,{T_2}

and

{T_3}

are mixed. The masses of molecules are

{m_1},{m_2}

and

{m_3}

and the number of molecules are

{n_1},

{n_2}

and

{n_3}

respectively. Assuming no loss of energy, the final temperature of the mixture is:

A

{{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}

B

{{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}

C

{{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}

D

{{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}

Q 12PhysicsSection A • MCQcommunication systems

+4 / -1

This question has Statement -

1

and Statement -

2

. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - $1$ : Sky wave signals are used for long distance radio communication. These signals are in general, less stable then ground wave signals.
Statement - $2$ : The state of ionosphere varies from hour to hour, day to day and season to season.

A

Statement -

1

is true, Statement -

2

is true, Statement -

2

is the correct explanation of Statement -

1

.

B

Statement -

1

is true, Statement -

2

is true, Statement -

2

is not the correct explanation of Statement -

1

.

C

Statement -

1

is false, Statement -

2

is true

D

Statement -

1

is true, Statement -

2

is false.

Q 13PhysicsSection A • MCQcurrent electricity

+4 / -1

If a wire is stretched to make it

0.1\%

longer, its resistance will:

A

increase by

0.2\%

B

decrease by

0.2\%

C

decrease by

0.05\%

D

increase by

0.05\%

Q 14PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A Carnot engine operating between temperatures

{{T_1}}

and

{{T_2}}

has efficiency

{1 \over 6}

. When

{T_2}

is lowered by

62

K

its efficiency increases to

{1 \over 3}

. Then

{T_1}

and

{T_2}

are, respectively:

A

372

K

and

330

K

B

330

K

and

268

K

C

310

K

and

248

K

D

372

K

and

310

K

Q 15PhysicsSection A • MCQgravitation

+4 / -1

Two bodies of masses

m

and

4

m

are placed at a distance

r.

The gravitational potential at a point on the line joining them where the gravitational field is zero is:

A

- {{4Gm} \over r}

B

- {{6Gm} \over r}

C

- {{9Gm} \over r}

D

zero

Q 16PhysicsSection A • MCQatoms and nuclei

+4 / -1

The half life of a radioactive substance is

20

minutes. The approximate time interval

\left( {{t_2} - {t_1}} \right)

between the time

{{t_2}}

when

{2 \over 3}

of it had decayed and time

{{t_1}}

when

{1 \over 3}

of it had decayed is :

A

14

min

B

20

min

C

28

min

D

7

min

Q 17PhysicsSection A • MCQproperties of matter

+4 / -1

Work done in increasing the size of a soap bubble from a radius of

3

cm

to

5

cm

is nearly (Surface tension of soap solution

= 0.03N{m^{ - 1}},

A

0.2\pi mJ

B

2\pi mJ

C

0.4\pi mJ

D

4\pi mJ

Q 18PhysicsSection A • MCQrotational motion

+4 / -1

A mass

m

hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass

m

and radius

R.

Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass

m,

if the string does not slip on the pulley, is:

A

g

B

{2 \over 3}g

C

{g \over 3}

D

{3 \over 2}g

Q 19PhysicsSection A • MCQatoms and nuclei

+4 / -1

Energy required for the electron excitation in

L{i^{ + + }}

from the first to the third Bohr orbit is :

A

36.3

eV

B

108.8

eV

C

122.4

eV

D

12.1

eV

Q 20PhysicsSection A • MCQalternating current

+4 / -1

A fully charged capacitor

C

with initial charge

{q_0}

is connected to a coil of self inductance

L

at

t=0.

The time at which the energy is stored equally between the electric and the magnetic fields is :

A

{\pi \over 4}\sqrt {LC}

B

2\pi \sqrt {LC}

C

\sqrt {LC}

D

\pi \sqrt {LC}

Q 21PhysicsSection A • MCQray optics

+4 / -1

A car is fitted with a convex side-view mirror of focal length

20

cm

. A second car

2.8m

behind the first car is overtaking the first car at a relative speed of

15

m/s

. The speed of the image of the second car as seen in the mirror of the first one is :

A

{1 \over {15}}\,m/s

B

10\,m/s

C

15\,m/s

D

{1 \over {10}}\,m/s

Q 22PhysicsSection A • MCQmotion

+4 / -1

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :

{{dv} \over {dt}} = - 2.5\sqrt v

where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

A

2 s

B

4 s

C

8 s

D

1 s

Q 23PhysicsSection A • MCQunits and measurements

+4 / -1

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.
The diameter of wire from the above date is:

A

0.052 cm

B

0.026 cm

C

0.005 cm

D

0.52 cm

Q 24PhysicsSection A • MCQrotational motion

+4 / -1

A pulley of radius

2

m

is rotated about its axis by a force

F = \left( {20t - 5{t^2}} \right)

newton (where

t

is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is

10kg

-

{m^2}

the number of rotation made by the pulley before its direction of motion is reversed, is:

A

more than

3

but less than

6

B

more than

6

but less than

9

C

more than

9

D

less than

3

Q 25PhysicsSection A • MCQmotion

+4 / -1

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :

A

\pi {{{v^4}} \over {{g^2}}}

B

{\pi \over 2}{{{v^4}} \over {{g^2}}}

C

\pi {{{v^2}} \over {{g^2}}}

D

\pi {{{v^2}} \over g}

Q 26PhysicsSection A • MCQwaves

+4 / -1

The transverse displacement

y(x, t)

of a wave on a string is given by

y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.

This represents

a:

A

wave moving in

-x

direction with speed

\sqrt {{b \over a}}

B

standing wave of frequency

\sqrt b

C

standing wave of frequency

{1 \over {\sqrt b }}

D

wave moving in

+x

direction speed

\sqrt {{a \over b}}

Q 27PhysicsSection A • MCQelectrostatics

+4 / -1

Two identical charged spheres suspended from a common point by two massless strings of length

l

are initially a distance

d\left( {d < < 1} \right)

apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity

v

. Then as a function of distance

x

between them,

A

v\, \propto \,{x^{ - 1}}

B

y\, \propto \,{x^{{\raise0.5ex\hbox{

C

v\, \propto \,x

D

v\, \propto \,{x^{ - {\raise0.5ex\hbox{

Q 28PhysicsSection A • MCQproperties of matter

+4 / -1

Water is flowing continuously from a tap having an internal diameter

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

The water velocity as it leaves the tap is

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

. The diameter of the water stream at a distance

2 \times {10^{ - 1}}\,\,m

below the tap is close to :

A

7.5 \times {10^{ - 3}}m

B

9.6 \times {10^{ - 3}}m

C

3.6 \times {10^{ - 3}}m

D

5.0 \times {10^{ - 3}}m

Q 29PhysicsSection A • MCQrotational motion

+4 / -1

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.

A

continuously decreases

B

continuously increases

C

first increases and then decreases

D

remains unchanged

Q 30PhysicsSection A • MCQalternating current

+4 / -1

A resistor

'R'

and

2\mu F

capacitor in series is connected through a switch to

200

V

direct supply. Across the capacitor is a neon bulb that lights up at

120

V.

Calculate the value of

R

to make the bulb light up

5

s

after the switch has been closed.

\left( {{{\log }_{10}}2.5 = 0.4} \right)

A

1.7 \times {10^5}\,\Omega

B

2.7 \times {10^6}\,\Omega

C

3.3 \times {10^7}\,\Omega

D

1.3 \times {10^4}\,\Omega

Q 31ChemistrySection A • MCQbiomolecules

+4 / -1

The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

A

2^nd

B

3^rd

C

4^th

D

1^st

Q 32ChemistrySection A • MCQd and f block elements

+4 / -1

In context of the lanthanoids, which of the following statements is not correct?

A

All the members exhibit +3 oxidation state

B

Because of similar properties the separation of lanthanoids is not easy.

C

Availability of 4f electrons results in the formation of compounds in +4 state for all the members of the series.

D

There is a gradual decrease in the radii of the members with increasing atomic number in the series.

Q 33ChemistrySection A • MCQelectrochemistry

+4 / -1

The reduction potential of hydrogen half cell will be negative if :

A

p(H₂) = 1 atm and [H⁺] = 1.0 M

B

p(H₂) = 1 atm and [H⁺] = 2.0 M

C

p(H₂) = 2 atm and [H⁺] =1.0 M

D

p(H₂) = 2 atm and [H⁺] =2.0 M

Q 34ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

The rate of a chemical reaction doubles for every 10^oC rise of temperature. If the temperature is raised by 50^oC , the rate of the reaction increases by about :

A

24 times

B

32 times

C

64 times

D

10 times

Q 35ChemistrySection A • MCQcoordination compounds

+4 / -1

The magnetic moment (spin only) of [NiCl₄]²⁻ is

A

5.46 BM

B

2.82 BM

C

1.41 BM

D

1.82 BM

Q 36ChemistrySection A • MCQhydrocarbons

+4 / -1

Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :

A

a vinyl group

B

an isopropyl group

C

an acetylenic triple bond

D

two ethylenic double bonds

Q 37ChemistrySection A • MCQsolid state

+4 / -1

In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is :

A

AB₂

B

A₂B₃

C

A₂B₅

D

A₂B

Q 38ChemistrySection A • MCQsolutions

+4 / -1

Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6^oC will be : [K_f for water = 1.86 K kg mol⁻¹ , and molar mass of ethylene glycol = 62 g mol⁻¹ )

A

204.30 g

B

400.00 g

C

304.60 g

D

804.32 g

Q 39ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Outer electronic configuration of Gd (Atomic no : 64) is -

A

4f⁸5d⁰6s²

B

4f⁴5d⁴6s²

C

4f⁷5d¹6s²

D

4f³5d⁵6s²

Q 40ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

A 5.2 molal aqueous solution of methyl alcohol, CH₃OH, is supplied. What is the mole fraction of methyl alcohol in the solution ?

A

0.190

B

0.086

C

0.050

D

0.100

Q 41ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?

A

MgO < K₂O < Al₂O₃ < Na₂O

B

Al₂O₃ < MgO < Na₂O < K₂O

C

Na₂O < K₂O < MgO < Al₂O₃

D

K₂O < Na₂O < Al₂O₃ < MgO

Official Correct Answer:Option (B)

Step-by-Step Solution:

You should know that,

(1)

\,\,\,

In a period, from left to right the acidic strength increases that mean basic nature decreases.

(2)

\,\,\,

In a group, from top to bottom the basic nature increases that means acidic nature decreases.

Na, Mg, Al and K are present in periodic table like this : -

	Group 1	Group 2		Group 13
Period 3	Na	Mg	.....	Al
Period 4	K

So, you can see Na, Mg and Al are present in same period so the order of basic nature among Na, Mg and Al is Na > Mg > Al.

And Na and K are from same group so basic nature of K > Na.

So the correct order of oxides

Al₂O₃ < MgO < Na₂O < K₂O

Q 42ChemistrySection A • MCQgaseous state

+4 / -1

'a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because

A

a and b for Cl₂ < a and b for C₂H₆

B

a and b for Cl₂ > a and b for C₂H₆

C

a for Cl₂ > a for C₂H₆ and b Cl₂ < b for C₂H₆

D

a for Cl₂ < a for C₂H₆ and b Cl₂ > b for C₂H₆

Q 43ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Identify the compound that exhibits tautomerism.

A

Lactic acid

B

2-Pentanone

C

Pheno

D

2- Butene

Q 44ChemistrySection A • MCQchemical equilibrium

+4 / -1

A vessel at 1000 K contains CO₂ with a pressure of 0.5 atm. Some of the CO₂ is converted into CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is :

A

3 atm

B

0.3 atm

C

0.18 atm

D

1.8 atm

Q 45ChemistrySection A • MCQd and f block elements

+4 / -1

The outer electron configuration of

Gd

(Atomic No.

64

) is :

A

4{f^3}\,5{d^5}\,6{s^2}

B

4{f^8}\,5{d^0}\,6{s^2}

C

4{f^4}\,5{d^4}\,6{s^2}

D

4{f^7}\,5{d^1}\,6{s^2}

Q 46ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :

A

Trichloromethanol

B

2, 2, 2-Trichloropropanol

C

Chloroform

D

2, 2, 2-Trichloroethanol

Q 47ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

The strongest acid amongst the following compounds is :

A

HCOOH

B

CH₃CH₂CH(Cl)CO₂H

C

ClCH₂CH₂CH₂COOH

D

CH₃COOH

Q 48ChemistrySection A • MCQthermodynamics

+4 / -1

The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm³ to a volume of 100 dm³ at 27^oC is :

A

35.8 J mol^-1 K⁻¹

B

32.3 J mol^-1 K⁻¹

C

42.3 J mol^-1 K⁻¹

D

38.3 J mol^-1 K⁻¹

Q 49ChemistrySection A • MCQp block elements

+4 / -1

Boron cannot form which one of the following anions?

A

BH_4^-

B

BF_6^{3-}

C

B(OH)_4^-

D

BO_2^-

Q 50ChemistrySection A • MCQatomic structure

+4 / -1

A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

A

325 nm

B

743 nm

C

518 nm

D

1035 nm

Q 51ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The hybridization of orbitals of N atom in

NO_3^-

,

NO_2^+

and

NH_4^+

are respectively :

A

sp , sp², sp³

B

sp², sp , sp³

C

sp , sp³, sp²

D

sp², sp³, sp

Q 52ChemistrySection B • Numericalaldehydes ketones and carboxylic acids

+4 / -1

Silver Mirror test is given by which one of the following compounds ?

Q 53ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The structure of IF₇ is :

A

trigonal bipyramid

B

octahedral

C

pentagonal bipyramid

D

square pyramid

Q 54ChemistrySection A • MCQpractical organic chemistry

+4 / -1

Which of the following reagents may be used to distinguish between phenol and benzoic acid ?

A

Tollen’s reagent

B

Molisch reagent

C

Neutral FeCl₃

D

Aqueous NaOH

Q 55ChemistrySection A • MCQp block elements

+4 / -1

Which of the following statements regarding sulphur is incorrect?

A

The vapour at 200^oC consists mostly of S₈ rings

B

At 600^oC the gas mainly consists of S₂ molecules

C

The oxidation state of sulphur is never less than +4 in its compounds

D

S₂ molecule is paramagnetic.

Q 56ChemistrySection A • MCQp block elements

+4 / -1

Which of the following statement is wrong?

A

Nitrogen cannot form

d\pi - p\pi

bond.

B

Single N – N bond is weaker than the single P – P bond

C

N₂O₄ has two resonance structures

D

The stability of hydrides increases from NH₃ to BiH₃ in group 15 of the periodic table

Q 57ChemistrySection A • MCQcoordination compounds

+4 / -1

Which of the following facts about the complex [Cr (NH₃)₆ ]Cl₃ is wrong?

A

The complex is paramagnetic

B

The complex is an outer orbital complex

C

The complex gives white precipitate with silver nitrate solution

D

The complex involves d²sp³ hybridization and is octahedral in shape.

Q 58ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is

A

2-Butanone

B

Ethyl chloride

C

Ethyl ethanoate

D

Diethyl ether

Q 59ChemistrySection A • MCQsolutions

+4 / -1

The degree of dissociation (

\alpha

) of a weak electrolyte, A_xB_y is related to van’t Hoff factor (i) by the expression :

A

\alpha = {{i - 1} \over {x + y + 1}}

B

\alpha = {{x + y - 1} \over {i - 1}}

C

\alpha = {{x + y + 1} \over {i - 1}}

D

\alpha = {{i - 1} \over {(x + y - 1)}}

Q 60ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Phenol is heated with a solution of mixture of KBr and KBrO₃. The major product obtained in the above reaction is

A

3-Bromophenol

B

4-Bromophenol

C

2, 4, 6- Tribromophenol

D

2-Bromophenol

Q 61ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Among the following the maximum covalent character is shown by the compound :

A

SnCl₂

B

AlCl₃

C

MgCl₂

D

FeCl₂

Q 62MathematicsSection A • MCQcomplex numbers

+4 / -1

Let

\alpha \,,\beta

be real and z be a complex number. If

{z^2} + \alpha z + \beta = 0

has two distinct roots on the line Re z = 1, then it is necessary that :

A

\beta \, \in ( - 1,0)

B

\left| {\beta \,} \right| = 1

C

\beta \, \in (1,\infty )

D

\beta \, \in (0,1)

Q 63MathematicsSection A • MCQellipse

+4 / -1

Equation of the ellipse whose axes of coordinates and which passes through the point

(-3,1)

and has eccentricity

\sqrt {{2 \over 5}}

is :

A

5{x^2} + 3{y^2} - 48 = 0

B

3{x^2} + 5{y^2} - 15 = 0

C

5{x^2} + 3{y^2} - 32 = 0

D

3{x^2} + 5{y^2} - 32 = 0

Q 64MathematicsSection A • MCQ3d geometry

+4 / -1

Statement - 1 : The point

A(1,0,7)

is the mirror image of the point

B(1,6,3)

in the line :

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

Statement - 2 : The line

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

bisects the line

segment joining

A(1,0,7)

and

B(1, 6, 3)

A

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

B

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

C

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

D

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

Q 65MathematicsSection A • MCQsequences and series

+4 / -1

A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increases by ₹ 40 more than the saving of immediately previous month. His total saving from the start of service will be ₹ 11040 after

A

19 months

B

20 months

C

21 months

D

18 months

Q 66MathematicsSection A • MCQvector algebra

+4 / -1

The vectors

\overrightarrow a

and

\overrightarrow b

are not perpendicular and

\overrightarrow c

and

\overrightarrow d

are two vectors satisfying

\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d

and

\overrightarrow a .\overrightarrow d = 0\,\,.

Then the vector

\overrightarrow d

is equal to :

A

\overrightarrow c + \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b

B

\overrightarrow b + \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c

C

\overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b

D

\overrightarrow b - \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c

Q 67MathematicsSection A • MCQapplication of derivatives

+4 / -1

For

x \in \left( {0,{{5\pi } \over 2}} \right),

define

f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.}

Then

f

has

A

local minimum at

\pi

and

2\pi

B

local minimum at

\pi

and local maximum at

2\pi

C

local maximum at

\pi

and local minimum at

2\pi

D

local maximum at

\pi

and

2\pi

Q 68MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The lines

{L_1}:y - x = 0

and

{L_2}:2x + y = 0

intersect the line

{L_3}:y + 2 = 0

at

P

and

Q

respectively. The bisector of the acute angle between

{L_1}

and

{L_2}

intersects

{L_3}

at

R

.

Statement-1: The ratio $PR$ : $RQ$ equals $2\sqrt 2 :\sqrt 5$
Statement-2: In any triangle, bisector of an angle divide the triangle into two similar triangles.

A

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

B

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

C

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

D

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

Q 69MathematicsSection A • MCQarea under the curves

+4 / -1

The area of the region enclosed by the curves

y = x,x = e,y = {1 \over x}

and the positive

x

-axis is :

A

1

square unit

B

{3 \over 2}

square units

C

{5 \over 2}

square units

D

{1 \over 2}

square unit

Q 70MathematicsSection A • MCQdifferentiation

+4 / -1

{{{d^2}x} \over {d{y^2}}}

equals:

A

- {\left( {{{{d^2}y} \over {d{x^2}}}} \right)^{ - 1}}{\left( {{{dy} \over {dx}}} \right)^{ - 3}}

B

{\left( {{{{d^2}y} \over {d{x^2}}}} \right)^{}}{\left( {{{dy} \over {dx}}} \right)^{ - 2}}

C

- \left( {{{{d^2}y} \over {d{x^2}}}} \right){\left( {{{dy} \over {dx}}} \right)^{ - 3}}

D

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

Q 71MathematicsSection A • MCQcomplex numbers

+4 / -1

If

\omega ( \ne 1)

is a cube root of unity, and

{(1 + \omega )^7} = A + B\omega \,

. Then

(A,B)

equals :

A

(1 ,1)

B

(1, 0)

C

(- 1 ,1)

D

(0 ,1)

Q 72MathematicsSection A • MCQdifferential equations

+4 / -1

If

{{dy} \over {dx}} = y + 3 > 0\,\,

and

y(0)=2,

then

y\left( {\ln 2} \right)

is equal to :

A

5

B

13

C

-2

D

7

Q 73MathematicsSection A • MCQcircle

+4 / -1

The two circles x² + y² = ax, and x² + y² = c² (c > 0) touch each other if :

A

| a | = c

B

a = 2c

C

| a | = 2c

D

2 | a | = c

Q 74MathematicsSection A • MCQdifferential equations

+4 / -1

Let

I

be the purchase value of an equipment and

V(t)

be the value after it has been used for

t

years. The value

V(t)

depreciates at a rate given by differential equation

{{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),

where

k>0

is a constant and

T

is the total life in years of the equipment. Then the scrap value

V(T)

of the equipment is

A

I - {{k{T^2}} \over 2}

B

I - {{k{{\left( {T - t} \right)}^2}} \over 2}

C

{e^{ - kT}}

D

{T^2} - {1 \over k}

Q 75MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let

A

and

B

be two symmetric matrices of order

3

.

Statement - 1 :

A(BA)

and

(AB)

A

are symmetric matrices.

Statement - 2 :

AB

is symmetric matrix if matrix multiplication of

A

with

B

is commutative.

A

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

B

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

C

statement - 1 is false, statement -2 is true

D

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

Q 76MathematicsSection A • MCQfunctions

+4 / -1

The domain of the function f(x) =

{1 \over {\sqrt {\left| x \right| - x} }}

is

A

\left( {0,\infty } \right)

B

\left( { - \infty ,0} \right)

C

\left( { - \infty ,\infty } \right) - \left\{ 0 \right\}

D

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

Q 77MathematicsSection A • MCQpermutations and combinations

+4 / -1

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:

A

N \le 100

B

100 < N \le 140

C

140 < N \le 190\,

D

N > 190

Q 78MathematicsSection A • MCQprobability

+4 / -1

Consider

5

independent Bernoulli's trials each with probability of success

p.

If the probability of at least one failure is greater than or equal to

{{31} \over 32},

then

p

lies in the interval :

A

\left( {{3 \over 4},{{11} \over {12}}} \right]

B

\left[ {0,{1 \over 2}} \right]

C

\left( {{11 \over 12},1} \right]

D

\left( {{1 \over 2},{{3} \over {4}}} \right]

Q 79MathematicsSection A • MCQstatistics

+4 / -1

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

A

4

B

5

C

2

D

3

Q 80MathematicsSection A • MCQ3d geometry

+4 / -1

If the angle between the line

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

and the plane

x+2y+3z=4

is

{\cos ^{ - 1}}\left( {\sqrt {{5 \over {14}}} } \right),

then

\lambda

equals :

A

{3 \over 2}

B

{2 \over 5}

C

{5 \over 3}

D

{2 \over 3}

Q 81MathematicsSection A • MCQmathematical reasoning

+4 / -1

Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement,

“Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as :

A

\sim \left[ {Q \leftrightarrow \left( {P \wedge \sim R} \right)} \right]

B

\sim Q \leftrightarrow P \wedge R

C

\sim \left( {P \wedge \sim R} \right) \leftrightarrow Q

D

\sim P \wedge \left( {Q \leftrightarrow \sim R} \right)

Q 82MathematicsSection A • MCQprobability

+4 / -1

If

C

and

D

are two events such that

C \subset D

and

P\left( D \right) \ne 0,

then the correct statement among the following is :

A

P\left( {{C \over D}} \right)

\ge P\left( C \right)

B

P\left( {{C \over D}} \right)

< P\left( C \right)

C

P\left( {{C \over D}} \right)

= {{P\left( D \right)} \over {P\left( C \right)}}

D

P\left( {{C \over D}} \right)

= P\left( C \right)

Q 83MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of

p

and

q

for which the function

f\left( x \right) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{3/2}}}}} & {,x > 0} \cr } } \right.

is continuous for all

x

in R, are

A

p =

{5 \over 2}

,

q =

{1 \over 2}

B

p =

-{3 \over 2}

,

q =

{1 \over 2}

C

p =

{1 \over 2}

,

q =

{3 \over 2}

D

p =

{1 \over 2}

,

q =

-{3 \over 2}

Q 84MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

\mathop {\lim }\limits_{x \to 2} \left( {{{\sqrt {1 - \cos \left\{ {2(x - 2)} \right\}} } \over {x - 2}}} \right)

A

Equals

\sqrt 2

B

Equals

-\sqrt 2

C

Equals

{1 \over {\sqrt 2 }}

D

does not exist

Q 85MathematicsSection A • MCQvector algebra

+4 / -1

If

\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)

and

\overrightarrow b = {1 \over 7}\left( {2\widehat i + 3\widehat j - 6\widehat k} \right),

then the value

of

\left( {2\overrightarrow a - \overrightarrow b } \right)\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a + 2\overrightarrow b } \right)} \right]

is :

A

-3

B

5

C

3

D

-5

Q 86MathematicsSection A • MCQsets and relations

+4 / -1

Let

R

be the set of real numbers.

Statement I :

A=\{(x, y) \in R \times R: y-x

is an integer

\}

is an equivalence relation on

R

.

Statement II :

B=\{(x, y) \in R \times R: x=\alpha y

for some rational number

\alpha\}

is an equivalence relation on

R

.

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 (B)

Step-by-Step Solution:

An equivalence relation on a set must satisfy three properties: reflexivity (every element is related to itself), symmetry (if an element is related to a second, the second is related to the first), and transitivity (if a first element is related to a second, and the second is related to a third, then the first is related to the third).

Statement I : $A={(x, y) \in R \times R: }$ y-x is an integer .

Reflexivity : For all $x$ in $R$ , $x - x = 0$ which is an integer. So, every element is related to itself.

Symmetry : For all $x, y$ in $R$ , if $y - x$ is an integer, then $x - y = - (y - x)$ is also an integer. So, if $x$ is related to $y$ , then $y$ is related to $x$ .

Transitivity : For all $x, y, z$ in $R$ , if $y - x$ and $z - y$ are integers, then $(z - y) + (y - x) = z - x$ is also an integer. So, if $x$ is related to $y$ and $y$ is related to $z$ , then $x$ is related to $z$ .

Therefore, $A$ is an equivalence relation on $R$ .

Statement II : $B={(x, y) \in R \times R: x=\alpha y}$ for some rational number $\alpha$ .

Reflexivity : For all $x$ in $R$ , $x = 1x$ . Since 1 is a rational number, every element is related to itself.

Symmetry : For all $x, y$ in $R$ , if $x = \alpha y$ for some rational $\alpha$ , then $y = \frac{1}{\alpha}x$ . However, if $\alpha = 0$ , then $\frac{1}{\alpha}$ is undefined, and therefore, $B$ doesn't satisfy symmetry.

Transitivity : If $x = \alpha y$ and $y = \beta z$ for some rational numbers $\alpha$ and $\beta$ , then $x = (\alpha \beta)z$ . Since the product of rational numbers is rational, if $x$ is related to $y$ and $y$ is related to $z$ , then $x$ is related to $z$ .

Therefore, $B$ is not an equivalence relation on $R$ since it does not satisfy the symmetry property.

In conclusion, the correct answer is

Option B : Statement I is true, Statement II is false.

Q 87MathematicsSection A • MCQpermutations and combinations

+4 / -1

Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is

{}^9{C_3}

.
Statement - 2: The number of ways of choosing any 3 places from 9 different places is

{}^9{C_3}

.

A

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

B

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

C

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

D

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

Q 88MathematicsSection A • MCQbinomial theorem

+4 / -1

The coefficient of

{x^7}

in the expansion of

{\left( {1 - x - {x^2} + {x^3}} \right)^6}

is

A

-132

B

-144

C

132

D

144

Q 89MathematicsSection A • MCQdefinite integration

+4 / -1

The value of

\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx

is

A

{\pi \over 8}\log 2

B

{\pi \over 2}\log 2

C

\log 2

D

\pi \log 2

Q 90MathematicsSection A • MCQmatrices and determinants

+4 / -1

The number of values of

k

for which the linear equations

4x + ky + 2z = 0,kx + 4y + z = 0

and

2x+2y+z=0

possess a non-zero solution is :

A

2

B

1

C

zero

D

3

Q 91MathematicsSection A • MCQapplication of derivatives

+4 / -1

The shortest distance between line

y-x=1

and curve

x = {y^2}

is

A

{{3\sqrt 2 } \over 8}

B

{8 \over {3\sqrt 2 }}

C

{4 \over {\sqrt 3 }}

D

{{\sqrt 3 } \over 4}

Q 92MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

If

A = {\sin ^2}x + {\cos ^4}x,

then for all real

x

:

A

{{13} \over {16}} \le A \le 1

B

1 \le A \le 2

C

{3 \over 4} \le A \le {{13} \over {16}}

D

{{3} \over {4}} \le A \le 1

Q 93MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a

,

\overrightarrow b

,

\overrightarrow c

be three non-zero vectors which are pairwise non-collinear. If

\overrightarrow a+3 \overrightarrow b

is collinear with

\overrightarrow c

and

\overrightarrow b+2 \overrightarrow c

is collinear with

\overrightarrow a

, then

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

is :

A

\overrightarrow a+\overrightarrow c

B

\overrightarrow c

C

\overrightarrow a

D

\overrightarrow 0

Official Correct Answer:Option (D)

Step-by-Step Solution:

We are given that $\overrightarrow a + 3 \overrightarrow b$ is collinear with $\overrightarrow c$ , and $\overrightarrow b + 2 \overrightarrow c$ is collinear with $\overrightarrow a$ . This means we can write:

$\overrightarrow a + 3 \overrightarrow b = \lambda \overrightarrow c \quad ...(i)$
$\overrightarrow b + 2 \overrightarrow c = \mu \overrightarrow a \quad ...(ii)$

for some scalars $\lambda$ and $\mu$ .

We are trying to find $\overrightarrow a + \overrightarrow b + 6\overrightarrow c$ in terms of $\overrightarrow a$ , $\overrightarrow b$ , and $\overrightarrow c$ . We can also express this as :

$\overrightarrow a + 3 \overrightarrow b + 6\overrightarrow c = (\lambda + 6) \overrightarrow c \quad ...(iii)$

by adding $6\overrightarrow c$ to both sides of equation (i).

Now, from equation (ii), multiplying by 3 gives us :

$3\overrightarrow b + 6 \overrightarrow c = 3\mu \overrightarrow a \quad ...(iv)$

Adding $\overrightarrow a$ to both sides of equation (iv) gives :

$\overrightarrow a + 3 \overrightarrow b + 6\overrightarrow c = (1 + 3\mu) \overrightarrow a \quad ...(v)$

Now, we have two expressions for $\overrightarrow a + 3 \overrightarrow b + 6\overrightarrow c$ , one in terms of $\overrightarrow c$ (from equation iii) and one in terms of $\overrightarrow a$ (from equation v). Setting these equal to each other gives :

$(\lambda + 6) \overrightarrow c = (1 + 3\mu) \overrightarrow a \quad ...(vi)$

Since $\overrightarrow a$ and $\overrightarrow c$ are not collinear, this equation can only hold if the coefficients on both sides are zero, hence :

$\lambda + 6 = 0$ and $1 + 3\mu = 0$

This gives $\lambda = -6$ and $\mu = -\frac{1}{3}$ .

Finally, substituting $\lambda = -6$ into equation (iii) gives :

$\overrightarrow a + 3 \overrightarrow b + 6\overrightarrow c = 0$

So, $\overrightarrow a + \overrightarrow b + 6\overrightarrow c = \overrightarrow 0$ .

Therefore, the correct answer is Option D : $\overrightarrow 0$ .

AIEEE 2011 Question Paper with Solutions