JEE Main 2016 Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQelectromagnetic waves

+4 / -1

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :

A : Blue light B : Yellow light

C : X-ray D : Radiowave.

A

C, A, B, D

B

B, A, D, C

C

D, B, A, C

D

A, B, D, C

Q 2PhysicsSection A • MCQelectronic devices

+4 / -1

If

a, b, c, d

are inputs to a gate and

x

is its output, then, as per the following time graph, the gate is :

qImage-digital-circuits-electronic-devices-modern-physics-Jeemate

A

OR

B

NAND

C

NOT

D

AND

Q 3PhysicsSection A • MCQwork power and energy

+4 / -1

A person trying to lose weight by burning fat lifts a mass of

10

kg

upto a height of

1

m

1000

times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies

3.8 \times {10^7}J

of energy per

kg

which is converted to mechanical energy with a

20\%

efficiency rate. Take

g = 9.8\,m{s^{ - 2}}

:

A

9.89 \times {10^{ - 3}}\,\,kg

B

12.89 \times {10^{ - 3}}\,kg

C

2.45 \times {10^{ - 3}}\,\,kg

D

6.45 \times {10^{ - 3}}\,\,kg

Q 4PhysicsSection A • MCQheat and thermodynamics

+4 / -1

'n'

moles of an ideal gas undergoes a process

A

\to

B

as shown in the figure. The maximum temperature of the gas during the process will be :

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

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

A

{{9{P_0}{V_0}} \over {2nR}}

B

{{9{P_0}{V_0}} \over {nR}}

C

{{9{P_0}{V_0}} \over {4nR}}

D

{{3{P_0}{V_0}} \over {2nR}}

Q 5PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

Hysteresis loops for two magnetic materials

A

and

B

are given below : qImage-magnetic-properties-of-matter-magnetic-properties-of-matter-electricity-Jeemate

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

A

A

for transformers and

B

for electric generators.

B

B

for electromagnets and transformers.

C

A

for electric generators and transformers.

D

A

for electromagnets and

B

for electric generators.

Q 6PhysicsSection A • MCQelectrostatics

+4 / -1

The region between two concentric spheres of radii

'a'

and

'b',

respectively (see figure), have volume charge density

\rho = {A \over r},

where

A

is a constant and

r

is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :

qImage-electric-flux-and-gauss-law-electrostatics-electricity-Jeemate

qImage-electric-flux-and-gauss-law-electrostatics-electricity-Jeemate

A

{{2Q} \over {\pi \left( {{a^2} - {b^2}} \right)}}

B

{{2Q} \over {\pi \,{a^2}}}

C

{Q \over {2\pi \,{a^2}}}

D

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

Q 7PhysicsSection A • MCQcurrent electricity

+4 / -1

A galvanometer having a coil resistance of

100\,\Omega

gives a full scale deflection, when a currect of

1

mA

is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of

10

A,

is :

A

0.1\,\Omega

B

3\,\Omega

C

0.01\,\Omega

D

2\,\Omega

Q 8PhysicsSection A • MCQelectronic devices

+4 / -1

The temperature dependence of resistance of

Cu

and undoped

Si

in the temperature range

300-400

K,

is best described by :

A

Linear increases for

Cu,

exponential decrease of

Si.

B

Linear decrease for

Cu,

linear decrease for

Si

C

Linear increase for

Cu,

linear increase for

Si.

D

Linear increase for

Cu,

exponential increase for

Si

Q 9PhysicsSection A • MCQunits and measurements

+4 / -1

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45^th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25^th division coincides with the main scale line?

A

0.70 mm

B

0.50 mm

C

0.75 mm

D

0.80 mm

Q 10PhysicsSection A • MCQsimple harmonic motion

+4 / -1

A particle performs simple harmonic motion with amplitude

A.

Its speed is trebled at the instant that it is at a distance

{{2A} \over 3}

from equilibrium position. The new amplitude of the motion is:

A

A\sqrt 3

B

{{7A} \over 3}

C

{A \over 3}\sqrt {41}

D

3A

Q 11PhysicsSection A • MCQgravitation

+4 / -1

A satellite is revolving in a circular orbit at a height

'h'

from the earth's surface (radius of earth

R;h < < R

). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)

A

\sqrt{2 g R}

B

\sqrt{g R}

C

\sqrt{g R / 2}

D

\sqrt{g R}(\sqrt{2}-1)

Q 12PhysicsSection A • MCQwork power and energy

+4 / -1

A point particle of mass

m,

moves long the uniformly rough track

PQR

as shown in the figure. The coefficient of friction, between the particle and the rough track equals

\mu .

The particle is released, from rest from the point

P

and it comes to rest at point

R.

The energies, lost by the ball, over the parts,

PQ

and

QR

, of the track, are equal to each other , and no energy is lost when particle changes direction from

PQ

to

QR

.

The value of the coefficient of friction $\mu$ and the distance $x$ $(=QR),$ are, respectively close to:

qImage-energy-work-power-and-energy-mechanics-Jeemate

A

0.29

and

3.5

m

B

0.29

and

6.5

m

C

0.2

and

6.5

m

D

0.2

and

3.5

m

Q 13PhysicsSection A • MCQwave optics

+4 / -1

The box of a pin hole camera, of length

L,

has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength

\lambda

the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say

{b_{\min }}

) when :

A

a = \sqrt {\lambda L} \,

and

{b_{\min }} = \sqrt {4\lambda L}

B

a = {{{\lambda ^2}} \over L}

and

{b_{\min }} = \sqrt {4\lambda L}

C

a = {{{\lambda ^2}} \over L}

and

{b_{\min }} = \left( {{{2{\lambda ^2}} \over L}} \right)

D

a = \sqrt {\lambda L}

and

{b_{\min }} = \left( {{{2{\lambda ^2}} \over L}} \right)

Q 14PhysicsSection A • MCQray optics

+4 / -1

In an experiment for determination of refractive index of glass of a prism by

i - \delta ,

plot it was found thata ray incident at angle

{35^ \circ }

, suffers a deviation of

{40^ \circ }

and that it emerges at angle

{79^ \circ }.

In that case which of the following is closest to the maximum possible value of the refractive index?

A

1.7

B

1.8

C

1.5

D

1.6

Q 15PhysicsSection A • MCQray optics

+4 / -1

An observer looks at a distant tree of height

10

m

with a telescope of magnifying power of

20.

To the observer the tree appears:

A

20

times taller

B

20

times nearer

C

10

times taller

D

10

times nearer

Q 16PhysicsSection A • MCQwaves

+4 / -1

A uniform string of length

20

m

is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take

{\,\,g = 10m{s^{ - 2}}}

)

A

2\sqrt 2 s

B

2\pi \sqrt 2 s

C

2\pi \sqrt 2 s

D

2

s

Q 17PhysicsSection B • Numericalelectronic devices

+4 / -1

For a common emitter configuration, if

\alpha

and

\beta

have their usual meanings, the incorrect relationship between

\alpha

and

\beta

is :

Q 18PhysicsSection A • MCQwaves

+4 / -1

A pipe open at both ends has a fundamental frequency

f

in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

A

2f

B

f

C

{f \over 2}

D

{3f \over 4}

Q 19PhysicsSection A • MCQmagnetics

+4 / -1

Two identical wires

A

and

B,

each of length

'l'

, carry the same current

I

. Wire

A

is bent into a circle of radius

R

and wire

B

is bent to form a square of side

'a'

. If

{B_A}

and

{B_B}

are the values of magnetic fields at the centres of the circle and square respectively, then the ratio

{{{B_A}} \over {{B_B}}}

is:

A

{{{\pi ^2}} \over {16}}

B

{{{\pi ^2}} \over {8\sqrt 2 }}

C

{{{\pi ^2}} \over {8}}

D

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

Q 20PhysicsSection A • MCQdual nature of radiation

+4 / -1

Radiation of wavelength

\lambda ,

is incident on a photocell. The fastest emitted electron has speed

v.

If the wavelength is changed to

{{3\lambda } \over 4},

the speed of the fastest emitted electron will be:

A

= v{\left( {{4 \over 3}} \right)^{{1 \over 2}}}

B

= v{\left( {{3 \over 4}} \right)^{{1 \over 2}}}

C

> v{\left( {{4 \over 3}} \right)^{{1 \over 2}}}

D

< v{\left( {{4 \over 3}} \right)^{{1 \over 2}}}

Q 21PhysicsSection A • MCQrotational motion

+4 / -1

A roller is made by joining together two cones at their vertices

0

. It is kept on two rails

AB

and

CD

, which are placed asymmetrically (see figure), with its axis perpendicular to

CD

and its center

O

at the center of line joining

AB

and

CD

(see figure). It is given a light push so that it starts rolling with its center

O

moving parallel to

CD

in the direction shown. As it moves, the roller will tend to : qImage-torque-rotational-motion-mechanics-Jeemate

A

go straight

B

turn left and right alternately

C

turn left

D

turn right

Q 22PhysicsSection A • MCQcapacitor

+4 / -1

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge

Q

(having a charge equal to the sum of the charges on the

4

\mu \,F

and

9

\mu \,F

capacitors), at a point distance

30

m

from it, would equal :

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

A

420N/C

B

480N/C

C

240N/C

D

360N/C

Q 23PhysicsSection A • MCQunits and measurements

+4 / -1

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

A

92

\pm

1.8 s

B

92

\pm

3 s

C

92

\pm

2 s

D

92

\pm

5.0 s

Q 24PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A pendulum clock loses

12

s

a day if the temperature is

{40^ \circ }C

and gains

4

s

a day if the temperature is

{20^ \circ }C.

The temperature at which the clock will show correct time, and the co-efficient of linear expansion

\left( \alpha \right)

of the metal of the pendulum shaft are respectively :

A

{30^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 3}}/{}^ \circ C

B

{55^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 2}}/{}^ \circ C

C

{25^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 5}}/{}^ \circ C

D

{60^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 4}}/{}^ \circ C

Q 25PhysicsSection B • Numericalrotational motion

+4 / -1

A particle of mass m is moving along the side of a square of side ‘a’, with a uniform speed v in the x-y plane as shown in the figure :

qImage-angular-momentum-rotational-motion-mechanics-Jeemate

qImage-angular-momentum-rotational-motion-mechanics-Jeemate

Which of the following statements is false for the angular momentum

\overrightarrow L

about the origin ?

Q 26PhysicsSection A • MCQalternating current

+4 / -1

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

A

0.044 H

B

0.065 H

C

80 H

D

0.08 H

Q 27PhysicsSection A • MCQatoms and nuclei

+4 / -1

Half-lives of two radioactive elements

A

and

B

are

20

minutes and

40

minutes, respectively. Initially, the samples have equal number of nuclei. After

80

minutes, the ratio of decayed number of

A

and

B

nuclei will be:

A

1:4

B

5:4

C

1:16

D

4:1

Q 28PhysicsSection A • MCQcommunication systems

+4 / -1

Choose the correct statement :

A

In amplitude modulation the amplitude of the high frequency carrier wave is make to vary in proportion to the amplitude of the audio signal.

B

In amplitude modulation the frequency of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.

C

In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.

D

In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the frequency of the audio signal.

Q 29PhysicsSection A • MCQheat and thermodynamics

+4 / -1

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity

C

remains constant. If during this process the relation of pressure

P

and volume

V

is given by

P{V^n} =

constant, then

n

is given by (Here

{C_p}

and

{C_v}

are molar specific heat at constant pressure and constant volume, respectively:

A

n = {{{C_p} - C} \over {C - {C_v}}}

B

n = {{C - {C_v}} \over {C - {C_p}}}

C

n = {{{C_p}} \over {{C_v}}}

D

n = {{C - {C_p}} \over {C - {C_v}}}

Q 30PhysicsSection A • MCQelectronic devices

+4 / -1

Identify the semiconductor devices whose characteristics are given below, in the order

(a), (b), (c), (d)

:

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

A

Simple diode, Zener diode, Solar cell, Light dependent resistance

B

Zener diode, Simple diode, Light dependent resistance, Solar cell

C

Solar cell, Light dependent resistance, Zener diode, simple diode

D

Zener diode, Solar cell, simple diode, Light dependent resistance

Q 31ChemistrySection A • MCQd and f block elements

+4 / -1

Which of the following compounds is metallic and ferromagnetic ?

A

CrO₂

B

VO₂

C

MnO₂

D

TiO₂

Q 32ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

2

-chloro-

2

-methylpentane on reaction with sodium methoxide in methanol yields:

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

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

A

All of these

B

(a)

and

(c)

C

(c)

only

D

(a)

and

(b)

Q 33ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The absolute configuration of

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

is :

A

(2S, 3S)

B

(2R, 3R)

C

(2R, 3S)

D

(2S, 3R)

Q 34ChemistrySection A • MCQgaseous state

+4 / -1

Two closed bulbs of equal volume

(V)

containing an ideal gas initially at pressure

{p_i}

and temperature

{T_1}

are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to

{T_2}.

The final pressure

{p_f}

is :

qImage-real-gas-and-van-der-walls-equation-gaseous-state-physical-chemistry-Jeemate

A

2{p_i}\left( {{{{T_2}} \over {{T_1} + {T_2}}}} \right)

B

2{p_i}\left( {{{{T_1}{T_2}} \over {{T_1} + {T_2}}}} \right)

C

{p_i}\left( {{{{T_1}{T_2}} \over {{T_1} + {T_2}}}} \right)

D

2{p_i}\left( {{{{T_1}} \over {{T_1} + {T_2}}}} \right)

Q 35ChemistrySection A • MCQisolation of elements

+4 / -1

Which one of the following ores is best concentrated by froth floatation method?

A

Siderite

B

Galena

C

Malachite

D

Magnetite

Q 36ChemistrySection A • MCQd and f block elements

+4 / -1

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

A

NO₂ and NO

B

NO and N₂O

C

NO₂ and N₂O

D

N₂O and NO₂

Q 37ChemistrySection A • MCQcoordination compounds

+4 / -1

The pair having the same magnetic moment is :
[At. No.: Cr = 24, Mn = 25, Fe = 26, Co = 27]

A

[Cr(H₂O)₆]²⁺ and [Fe(H₂O)₆]²⁺

B

[Mn(H₂O)₆]²⁺ and [Cr(H₂O)₆]²⁺

C

[CoCl₄]^2– and [Fe(H₂O)₆]²⁺

D

[Cr(H₂O)₆]²⁺ and [CoCl₄]^2–

Q 38ChemistrySection A • MCQchemical equilibrium

+4 / -1

The equilibrium constant at 298 K for a reaction A + B

\leftrightharpoons

C + D is 100. If the initial concentration of all the four species were 1M each, then equilibrium concentration of D (in mol L^–1) will be:

A

0.818

B

1.818

C

1.182

D

0.182

Q 39ChemistrySection A • MCQs block elements

+4 / -1

The main oxides formed on combustion of Li, Na and K in excess of air are, respectively :

A

LiO₂, Na₂O₂ and K₂O

B

Li₂O₂, Na₂O₂ and KO₂

C

Li₂O, Na₂O₂ and KO₂

D

Li₂O, Na₂O and KO₂

Q 40ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Which of the following is an anionic detergent ?

A

Sodium stearate

B

Sodium lauryl sulphate

C

Cetyltrimethyl ammonium bromide

D

Glyceryl oleate

Q 41ChemistrySection A • MCQp block elements

+4 / -1

The pair in which phosphorous atoms have a formal oxidation state of +3 is :

A

Orthophosphorous and pyrophosphorous acids

B

Pyrophosphorous and hypophosphoric acids

C

Orthophosphorus and hypophosphoric acids

D

Pyrophosphorous and pyrophosphoric acids

Official Correct Answer:Option (A)

Step-by-Step Solution:

Phosphorous acids contain

P

in

+3

oxidation state.

Acid	Formula	Oxidation state of Phosphorous
Pyrophosphorous acid	H₄P₂O₅	+3
Pyrophophoric acid	H₄P₂O₇	+5
Orthophosphorous acid	H₃PO₃	+3
Hypophosphoric acid	H₄P₂O₆	+4

Q 42ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The species in which the

\mathrm{N}

atom is in a state of

s p

hybridization is :

A

\mathrm{NO}_2^{+}

B

\mathrm{NO}_2^{-}

C

\mathrm{NO}_3^{-}

D

\mathrm{NO}_3^{-}

Q 43ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

A

Simple distillation

B

Fractional distillation

C

Steam distillation

D

Distillation under reduced pressure

Q 44ChemistrySection A • MCQs block elements

+4 / -1

The hottest region of Bunsen flame shown in the figure below is :

qImage-physiochemical-trends-in-alkali-metals-s-block-elements-inorganic-chemistry-Jeemate

qImage-physiochemical-trends-in-alkali-metals-s-block-elements-inorganic-chemistry-Jeemate

A

region

1

B

region

2

C

region

3

D

region

4

Q 45ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

The product of the reaction given below is :

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

B

C

D

Q 46ChemistrySection A • MCQsurface chemistry

+4 / -1

For a linear plot of log (x/m) versus log p in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are constants)

A

Both k and 1/n appear in the slope term.

B

1/n appears as the intercept.

C

Only 1/n appears as the slope

D

log (1/n) appears as the intercept.

Q 47ChemistrySection A • MCQhydrogen

+4 / -1

Which one of the following statements about water is FALSE?

A

Water is oxidized to oxygen during photosynthesis

B

Water can act both as an acid and as a base.

C

There is extensive intramolecular hydrogen bonding in the condensed phase.

D

Ice formed by heavy water sinks in normal water

Q 48ChemistrySection A • MCQsolutions

+4 / -1

18 g glucose (C₆H₁₂O₆) is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueous solution is :

A

76.0

B

752.4

C

759.0

D

7.6

Q 49ChemistrySection A • MCQhydrocarbons

+4 / -1

The reaction of propene with HOCl (Cl₂ + H₂O) proceeds through the intermediate:

A

\mathrm{CH}_{3}-\mathrm{CH}^{+}-\mathrm{CH}_{2}-\mathrm{OH}

B

\mathrm{CH}_{3}-\mathrm{CHCl}-\mathrm{CH}_{2}^{+}

C

CH₃ - CH⁺ - CH₂ - OH

D

\mathrm{CH}_{3}-\mathrm{CH}^{+}-\mathrm{CH}_{2}-\mathrm{Cl}

Q 50ChemistrySection A • MCQelectrochemistry

+4 / -1

Galvanization is applying a coating of :

A

Cr

B

Cu

C

Zn

D

Pb

Q 51ChemistrySection A • MCQatomic structure

+4 / -1

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h /

\lambda

(where

\lambda

is wavelength associated with electron wave) is given by :

A

2meV

B

\sqrt {meV}

C

\sqrt {2meV}

D

meV

Q 52ChemistrySection A • MCQbiomolecules

+4 / -1

Thiol group is present in :

A

Cytosine

B

Cystine

C

Cysteine

D

Methionine

Q 53ChemistrySection A • MCQpolymers

+4 / -1

Which of the following statements about low density polythene is FALSE ?

A

Its synthesis requires high pressure.

B

It is a poor conductor of electricity.

C

Its synthesis requires dioxygen or a peroxide initiator as a catalyst.

D

It is used in the manufacture of buckets, dust-bins etc.

Q 54ChemistrySection A • MCQchemical kinetics and nuclear chemistry

+4 / -1

Decomposition of H₂O₂ follows a first order reaction. In fifty minutes the concentration of H₂O₂ decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of H₂O₂ reaches 0.05 M, the rate of formation of O₂ will be :

A

6.93

\times

10^-4 mol min^-1

B

6.96

\times

10^-2 mol min^-1

C

1.34

\times

10^-2 mol min^-1

D

2.66 L min^–1 at STP

Q 55ChemistrySection A • MCQhydrocarbons

+4 / -1

At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% O₂ by volume for complete combustion. After combustion the gases occupy 345 mL. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is:

A

C₃H₈

B

C₄H₈

C

C₄H₁₀

D

C₃H₆

Q 56ChemistrySection A • MCQenvironmental chemistry

+4 / -1

The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :

A

Lead

B

Nitrate

C

Iron

D

Fluoride

Q 57ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

In the Hofmann bromamide degradation reaction, the number of moles of NaOH and Br₂ used per mole of amine produced are:

A

Four moles of NaOH and two moles of Br₂.

B

Two moles of NaOH and two moles of Br₂

C

Four moles of NaOH and one mole of Br₂

D

One mole of NaOH and one mole of Br₂

Q 58ChemistrySection A • MCQs block elements

+4 / -1

Which of the following atoms has the highest first ionization energy?

A

Na

B

K

C

Sc

D

Rb

Q 59ChemistrySection A • MCQthermodynamics

+4 / -1

The heats of combustion of carbon and carbon monoxide are –393.5 and –283.5 kJ mol^–1, respectively. The heat of formation (in kJ) of carbon monoxide per mole is :

A

676.5

B

-676.5

C

–110

D

110.5

Q 60ChemistrySection A • MCQcoordination compounds

+4 / -1

Which one of the following complexes shows optical isomerism?
(en = ethylenediamine)

A

cis[Co(en)₂Cl₂]Cl

B

trans[Co(en)₂Cl₂]Cl

C

[Co(NH₃)₄Cl₂]Cl

D

[Co(NH₃)₃Cl₃]

Q 61MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

The sum of all real values of

x

satisfying the equation

{\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}}\, = 1

is :

A

6

B

5

C

3

D

-4

Q 62MathematicsSection A • MCQdifferential equations

+4 / -1

If a curve

y=f(x)

passes through the point

(1,-1)

and satisfies the differential equation,

y(1+xy) dx=x

dy

, then

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

is equal to :

A

{2 \over 5}

B

{4 \over 5}

C

-{2 \over 5}

D

-{4 \over 5}

Q 63MathematicsSection A • MCQarea under the curves

+4 / -1

The area (in sq. units) of the region

\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}

is :

A

\pi - {{4\sqrt 2 } \over 3}

B

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

C

\pi - {4 \over 3}

D

\pi - {8 \over 3}

Q 64MathematicsSection A • MCQpermutations and combinations

+4 / -1

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :

A

{46^{th}}

B

{59^{th}}

C

{52^{nd}}

D

{58^{th}}

Q 65MathematicsSection A • MCQdefinite integration

+4 / -1

\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}

is equal to:

A

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

B

3\,\log \,3 - 2

C

{{18} \over {{e^4}}}

D

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

Q 66MathematicsSection A • MCQindefinite integration

+4 / -1

The integral

\int {{{2{x^{12}} + 5{x^9}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}} dx

is equal to :

A

{{{x^5}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C

B

{{ - {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C

C

{{{-x^5}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C

D

{{ {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C

Q 67MathematicsSection A • MCQparabola

+4 / -1

Let

P

be the point on the parabola,

{{y^2} = 8x}

which is at a minimum distance from the centre

C

of the circle,

{x^2} + {\left( {y + 6} \right)^2} = 1

. Then the equation of the circle, passing through

C

and having its centre at

P

is:

A

{{x^2} + {y^2} - {x \over 4} + 2y - 24 = 0}

B

{{x^2} + {y^2} - 4x + 9y + 18 = 0}

C

{{x^2} + {y^2} - 4x + 8y + 12 = 0}

D

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

Q 68MathematicsSection A • MCQprobability

+4 / -1

Let two fair six-faced dice

A

and

B

be thrown simultaneously. If

{E_1}

is the event that die

A

shows up four,

{E_2}

is the event that die

B

shows up two and

{E_3}

is the event that the sum of numbers on both dice is odd, then which of the following statements is

NOT

true?

A

{E_1}

and

{E_2}

are independent.

B

{E_2}

and

{E_3}

are independent.

C

{E_1}

and

{E_3}

are independent.

D

{E_1},

{E_2}

and

{E_3}

are independent.

Q 69MathematicsSection A • MCQvector algebra

+4 / -1

Let

\overrightarrow a ,\overrightarrow b

and

\overrightarrow c

be three unit vectors such that

\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow b + \overrightarrow c } \right).

If

{\overrightarrow b }

is not parallel to

{\overrightarrow c },

then the angle between

{\overrightarrow a }

and

{\overrightarrow b }

is:

A

{{2\pi } \over 3}

B

{{5\pi } \over 6}

C

{{3\pi } \over 4}

D

{{\pi } \over 2}

Q 70MathematicsSection A • MCQheight and distance

+4 / -1

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^o. Then the time taken (in minutes) by him, from B to reach the pillar, is :

A

6

B

10

C

20

D

5

Q 71MathematicsSection A • MCQcircle

+4 / -1

If one of the diameters of the circle, given by the equation,

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

is a chord of a circle

S

, whose centre is at

(-3, 2)

, then the radius of

S

is :

A

5

B

10

C

5\sqrt 2

D

5\sqrt 3

Q 72MathematicsSection A • MCQcircle

+4 / -1

The centres of those circles which touch the circle,

{x^2} + {y^2} - 8x - 8y - 4 = 0

, externally and also touch the

x

-axis, lie on :

A

a circle

B

an ellipse which is not a circle

C

a hyperbola

D

a parabola

Q 73MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

For

x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,

and

\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,

then :

A

g

is not differentiable at

x=0

B

g'\left( 0 \right) = \cos \left( {\log 2} \right)

C

g'\left( 0 \right) = - \cos \left( {\log 2} \right)

D

g

is differentiable at

x=0

and

g'\left( 0 \right) = - \sin \left( {\log 2} \right)

Q 74MathematicsSection A • MCQbinomial theorem

+4 / -1

If the number of terms in the expansion of

{\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,

is 28, then the sum of the coefficients of all the terms in this expansion, is :

A

243

B

729

C

64

D

2187

Q 75MathematicsSection A • MCQfunctions

+4 / -1

If

f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0

, and

\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}

; then

\mathrm{S}:

A

is an empty set.

B

contains exactly one element.

C

contains exactly two elements.

D

contains more than two elements.

Q 76MathematicsSection A • MCQmathematical reasoning

+4 / -1

The Boolean expression

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

is equivalent to :

A

{ \sim p \wedge q}

B

{p \wedge q}

C

p \vee q

D

p \vee \sim q

Q 77MathematicsSection A • MCQapplication of derivatives

+4 / -1

A wire of length

2

units is cut into two parts which are bent respectively to form a square of side

=x

units and a circle of radius

=r

units. If the sum of the areas of the square and the circle so formed is minimum, then:

A

x=2r

B

2x=r

C

2x = \left( {\pi + 4} \right)r

D

\left( {4 - \pi } \right)x = \pi \,\, r

Q 78MathematicsSection A • MCQmatrices and determinants

+4 / -1

The system of linear equations

$\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr }$

has a non-trivial solution for :

A

infinitely many values of

\lambda .

B

exactly one value of

\lambda .

C

exactly two values of

\lambda .

D

exactly three values of

\lambda .

Q 79MathematicsSection A • MCQ3d geometry

+4 / -1

If the line,

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

lies in the planes,

lx+my-z=9,

then

{l^2} + {m^2}

is equal to :

A

5

B

2

C

26

D

18

Q 80MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7x - y - 5 = 0

. If its diagonals intersect at

(-1, -2)

, then which one of the following is a vertex of this rhombus?

A

\left( {{{ 1} \over 3}, - {8 \over 3}} \right)

B

\left( - {{{ 10} \over 3}, - {7 \over 3}} \right)

C

\left( { - 3, - 9} \right)

D

\left( { - 3, - 8} \right)

Q 81MathematicsSection A • MCQapplication of derivatives

+4 / -1

Consider :
f

\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).

A normal to $y =$ f $\left( x \right)$ at $x = {\pi \over 6}$ also passes through the point:

A

\left( {{\pi \over 6},0} \right)

B

\left( {{\pi \over 4},0} \right)

C

(0,0)

D

\left( {0,{{2\pi } \over 3}} \right)

Q 82MathematicsSection A • MCQmatrices and determinants

+4 / -1

If

A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]

and

A

adj

A=A

{A^T},

then

5a+b

is equal to :

A

4

B

13

C

-1

D

5

Q 83MathematicsSection A • MCQhyperbola

+4 / -1

The eccentricity of the hyperbola whose length of the latus rectum is equal to

8

and the length of its conjugate axis is equal to half of the distance between its foci, is :

A

{2 \over {\sqrt 3 }}

B

{\sqrt 3 }

C

{{4 \over 3}}

D

{4 \over {\sqrt 3 }}

Q 84MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let

p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}}

then

log

p

is equal to :

A

{1 \over 2}

B

{1 \over 4}

C

2

D

1

Q 85MathematicsSection A • MCQtrigonometric functions and equations

+4 / -1

If

0 \le x < 2\pi

, then the number of real values of

x

, which satisfy the equation

\,\cos x + \cos 2x + \cos 3x + \cos 4x = 0

is:

A

7

B

9

C

3

D

5

Q 86MathematicsSection A • MCQsequences and series

+4 / -1

If the

{2^{nd}},{5^{th}}\,and\,{9^{th}}

terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

A

1

B

{7 \over 4}

C

{8 \over 5}

D

{4 \over 3}

Q 87MathematicsSection A • MCQ3d geometry

+4 / -1

The distance of the point

(1,-5,9)

from the plane

x-y+z=5

measured along the line

x=y=z

is :

A

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

B

{20 \over 3}

C

3\sqrt {10}

D

10\sqrt {3}

Q 88MathematicsSection A • MCQsequences and series

+4 / -1

If the sum of the first ten terms of the series

{\left( {1{3 \over 5}} \right)^2} + {\left( {2{2 \over 5}} \right)^2} + {\left( {3{1 \over 5}} \right)^2} + {4^2} + {\left( {4{4 \over 5}} \right)^2} + .......is\,{{16} \over 5}m,

then m is equal to :

A

100

B

99

C

102

D

101

Q 89MathematicsSection A • MCQcomplex numbers

+4 / -1

A value of

\theta \,

for which

{{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}

is purely imaginary, is :

A

{\sin ^{ - 1}}\left( {{{\sqrt 3 } \over 4}} \right)

B

{\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)\,

C

{\pi \over 3}

D

{\pi \over 6}

Q 90MathematicsSection A • MCQstatistics

+4 / -1

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

A

3

a

² - 26

a

+ 55 = 0

B

3

a

² - 32

a

+ 84 = 0

C

3

a

² - 34

a

+ 91 = 0

D

3

a

² - 23

a

+ 44 = 0

JEE Main 2016 Question Paper with Solutions