JEE (Main) 2013 - PAPER


90 Questions MCQ Test JEE Main Mock Test Series 2020 & Previous Year Papers | JEE (Main) 2013 - PAPER


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This mock test of JEE (Main) 2013 - PAPER for JEE helps you for every JEE entrance exam. This contains 90 Multiple Choice Questions for JEE JEE (Main) 2013 - PAPER (mcq) to study with solutions a complete question bank. The solved questions answers in this JEE (Main) 2013 - PAPER quiz give you a good mix of easy questions and tough questions. JEE students definitely take this JEE (Main) 2013 - PAPER exercise for a better result in the exam. You can find other JEE (Main) 2013 - PAPER extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

PART A

Q. No. 1 -30 carry 4 marks each and 1 mark is deducted for every wrong answer.

Q. 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:

Solution:

Reaction proceeds through carbocation formation as 30 carbocation is highly stable, hence reaction proceeds
through SN1 with 30 alcohol.

QUESTION: 2

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

Solution:

 here the backward reaction releases same amount of energy and known as Electron gain enthalpy.

QUESTION: 3

Stability of the species  increases in the order of:

Solution:

  is more stable than    has more numbers of antibonding electrons

QUESTION: 4

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

Solution:

QUESTION: 5

Which of the following is the wrong statement?

Solution:

(All the options are correct statements)

(2) Correct, as ozone is violet-black solid.
(3) Correct, as ozone is diamagnetic.
(4) Correct, as ONCl = 32 electrons and

ONO = 24 electron hence are not isoelectronic.

QUESTION: 6

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  value?

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

As2S3 is an anionic sol (negative sol) hence coagulation will depend upon coagulating power of cation, which is directly proportional to the valency of cation (Hardy-Schulze rule).

QUESTION: 9

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?

Solution:

*Multiple options can be correct
QUESTION: 10

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

Solution:

C→ Dimagametic

QUESTION: 11

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

Solution:

The exothermic hydration enthalpies of the given trivalent cations are:
Sc+3 = 3960 kJ/mole
Fe+3 = 4429 kJ/mole
Co+3 = 4653 kJ/mole
Cr+3 = 4563 kJ/mole
Hence Sc+3 is least hydrated; so least stable (not most stable)
Fe+2 contains 4 unpaired electrons where as Mn+2 contains 5 unpaired electrons hence (4) is incorrect.

QUESTION: 12

Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+ and M3+ in
its oxide. Fraction of the metal which exists as M3+ would be:

Solution:

Metal oxide = M0.98O
If ‘x’ ions of M are in +3 state, then
3x + (0.98 – x) × 2 = 2
x = 0.04
So the percentage of metal in +3 state would be 

QUESTION: 13

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:

Solution:

QUESTION: 14

Given

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

Solution:

As per data mentioned
 is strongest oxidising agent as it has maximum SRP value.

QUESTION: 15

Arrange the following compounds in order of decreasing acidity:

Solution:

Correct order of acidic strength is III > I > II > IV

QUESTION: 16

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)

Solution:

QUESTION: 17

Synthesis of each molecule of glucose in photosynthesis involves:

Solution:

QUESTION: 18

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

Solution:

[Co(NH3)3Cl3] exists in two forms (facial and meridonial)

Both of these forms are achiral. Hence, [Co(NH3)3Cl3] does not show optical isomerism

QUESTION: 19

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 37.00C. 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)

Solution:

Process is isothermal reversible expansion, hence ΔU = 0.
q = −W
As q = +208 J
Hence W = −208 J

 

QUESTION: 20

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

Solution:

QUESTION: 21

The order of stability of the following carbocations:

 is

Solution:

Order of stability is III > I > II.

QUESTION: 22

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

Solution:

Increasing order of first ionization enthalpy is
Ba < Ca < Se < S < Ar

QUESTION: 23

For gaseous state, if most probable speed is denoated by C*, average speed by  and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Solution:

QUESTION: 24

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

Solution:

It was methyl isocyanate (CH3NCO)

QUESTION: 25

Consider the following reaction: 

The values of x, y and z in the reaction are, respectively:

Solution:

QUESTION: 26

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

Solution:

Silicon (Si) – covalent solid
Sulphur (S8) – molecular solid
Phosphorous (P4) – Molecular solid
Iodine (I2) – Molecular solid

QUESTION: 27

Compound (A), C8H9Br, gives a white precipitate when warmed with alcoholic AgNO3. Oxidation of (A)
gives a acid (B), C8H6O4. (B) easily forms anhydride on heating. Identify the compound (A).

Solution:

QUESTION: 28

Energy of an electron is given by  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)

Solution:

QUESTION: 29

An organic compound A upon reacting with NH3 gives B. On heating B gives C. C in presence of KOH
reacts with Br2 to give CH3CH2NH2. A is

Solution:

QUESTION: 30

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

Solution:

Bond order of  and He2 is zero, thus their existence is not possible.

QUESTION: 31

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point

Solution:

QUESTION: 32

ABCD is a trapezium such that AB and CD are parallel and BCCD. If ADB = q, BC = p and CD = q,
then AB is equal to

Solution:

QUESTION: 33

Given : A circle, 2x2 + 2y2 = 5 and a parabola, y2 =  x.

Statement − I : An equation of a common tangent to these curves is y  = 

Statement − II : If the line,  is their common tangent, then m satisfies m4 - 3m2+2=0

Solution:

QUESTION: 34

A ray of light along  gets reflected upon reaching x-axis, the equation of the reflected rays is

Solution:

Slope of the incident ray is 

So, the slope of the reflected ray must be 

The point of incidence is √30 So, the equation of reflected ray is 

QUESTION: 35

All the students of a class performed poorly in Mathematics. 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 ?

Solution:

QUESTION: 36

If x, y, z are in A.P. and tan−1x, tan−1y and tan−1z are also in A.P., then

Solution:

QUESTION: 37

if  

Solution:

QUESTION: 38

The equation of the circle passing through the foci of the ellipse and having centre at (0, 3) is

Solution:

QUESTION: 39

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

Solution:

 

QUESTION: 40

The intercepts on x-axis made by tangents to the curve, are parallel to the line
y = 2x, are equal to

Solution:

QUESTION: 41

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

Solution:

QUESTION: 42

Consider :
Statement − I : is a fallacy.

Statement − II :  is a tautology.

Solution:

QUESTION: 43

The area (in square units) bounded by the curves y = , 2y − x + 3 = 0 , x-axis, and lying in the first
quadrant is

Solution:

QUESTION: 44

The expression  can be written as

Solution:

QUESTION: 45

The real number k for which the equation, 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]

Solution:

If 2x3 + 3x + k = 0 has 2 distinct real roots in [0, 1], then f' (x) will change sign
but f'(x) = 6x2 + 3 > 0
So no value of k exists.

QUESTION: 46

 is equal to

Solution:

QUESTION: 47

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If
Tn+1 − Tn = 10, then the value of n is

Solution:

QUESTION: 48

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 . If the firm employs 25 more workers, then
the new level of production of items is

Solution:

QUESTION: 49

Statement − I : The value of the integral  

Statement − II : 

Solution:

QUESTION: 50

If    is the adjoint of a 3 × 3 matrix A and |A| = 4, then α is equal to

Solution:

QUESTION: 51

The number of values of k, for which the system of equations
(k + 1)x + 8y = 4k
kx + (k + 3)y = 3k − 1
has no solution, is

Solution:

which means, k has only one value where the equation has no solution

QUESTION: 52

If   is equal to

Solution:

QUESTION: 53

If the lines  are coplanar, then k can have

Solution:

QUESTION: 54

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B
having 3 or more elements is

Solution:

QUESTION: 55

If the vectors  are the sides of a triangle ABC, then the length of the
median through A is

Solution:

QUESTION: 56

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

Solution:

P (correct answer) = 1/3

QUESTION: 57

If z is a complex number of unit modulus and argument θ, then arg  equals

Solution:

QUESTION: 58

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c R, have a common root, then a : b : c is

Solution:

QUESTION: 59

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

Solution:

QUESTION: 60

The term independent of x in expansion of 

Solution:

QUESTION: 61

Q. No. 61 - 90 carry 4 marks each and 1 mark is deducted for every wrong answer

Q. In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, S2 kept open. (q is charge on the capacitor and t = RC is capacitive time constant). Which of the following statement is correct?

Solution:

Charge on the capacitor at any time ‘t’ is

QUESTION: 62

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of
capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated
frequency which could be detected by it.

Solution:

 

QUESTION: 63

The supply voltage to a room is 120 V. The resistance of the lead wires is 6 W. 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?

Solution:

QUESTION: 64

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 massless spring, such that it is half submerged in a liquid of density σ at
equilibrium position. The extension x0 of the spring when it is in equilibrium is:

Solution:

QUESTION: 65

Two charges, each equal to q, are kept at x = −a and x = a on the x-axis. A particle of mass m and charge

q0= q/2 is placed at the origin. If charge q0 is given a small displacement  along the y-axis, the net force acting on the particle is proportional to:

Solution:

QUESTION: 66

A beam of unpolarised light of intensity I0 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° relative to that of A. The intensity of
the emergent light is:

Solution:
QUESTION: 67

The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is
gradually changed. The plate current I of the photocell varies as follows:

Solution:
QUESTION: 68

Two coherent point sources S1 and S2 are separated by a small distance ‘d’ as
shown. The fringes obtained on the screen will be:

Solution: C)
So, on a circle, path difference will be same locus of points having same path difference will be a circle, so fringes will make concentric circles.
QUESTION: 69

A metallic rod of length ‘’ is tied to a string of length 2l and made to rotate with angular speed ω 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:

Solution:

QUESTION: 70

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another
with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to

Solution:

QUESTION: 71

Assume that a drop of liquid evaporates by decrease 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 r and L is its latent heat of vaporization.

Solution:

QUESTION: 72

The graph between angle of deviation (d) and angle of incidence (i) for a triangular prism is represented by:

Solution:
QUESTION: 73

Let [ε0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time
and A = electric current, then:

Solution:

QUESTION: 74

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

Solution:

Heat is extracted from the source in path DA and AB is

QUESTION: 75

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 × 103 kg/m3 and
2.2 × 1011N/m2 respectively?

Solution:

QUESTION: 76

This question has statement I and statement II. Of the four choices given after the statements, choose the
one that best describes the two statements.
Statement- I: Higher the range, greater is the resistance of ammeter.
Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

Solution:

For Ammeter, S 

So for I to increase, S should decrease, so additional S can be connected across it.

QUESTION: 77

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?

Solution:

QUESTION: 78

A projectile is given an initial velocity of   is along the ground and   is along the
vertical. If g = 10 m/s2, the equation of its trajectory is

Solution:

x = t
 y = 2t − 5t2
Equation of trajectory is y = 2x − 5x2

QUESTION: 79

Two capacitors C1 and  C2 are charged to 120 V and 200 V respectively. It is found that by connecting
them together the potential on each one can be made zero. Then :

Solution:

120C1= 200C2

6C1= 10C2

3C1= 5C2

QUESTION: 80

A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface.
The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop
when it ceases to slip?

Solution:

From conservation of angular momentum about any fix point on the surface

QUESTION: 81

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The
piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the
gas is V0 and its pressure is P0. 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 frequency:

Solution:

QUESTION: 82

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 a distance L from the end A is:

Solution:

QUESTION: 83

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of
the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of
2.0 A flows through the smaller loop, then the flux linked with bigger loop is

Solution:

QUESTION: 84

If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature
θ0 the graph between the temperature T of the metal and time t will be closest to :

Solution:

The temperature goes on decreasing with time (non-linearly) The rate of decrease will be more initially which is depicted in the second graph.

QUESTION: 85

The I – V characteristic of an LED is

Solution:

For LED, in forward bias, intensity increases with voltage

QUESTION: 86

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.
Statement – I : A point particle of mass m moving with speed v collides with stationary point particle of
mass M. If the maximum energy loss possible is given as 

Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the
collision.

Solution:

Loss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation.

 

QUESTION: 87

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it
will decrease to α times its original magnitude, where α equals.

Solution:

QUESTION: 88

Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of
lens is 2 × 108 m/s, the focal length of the lens is :

Solution:

 

QUESTION: 89

The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of
electric field strength is :

Solution:

QUESTION: 90

Two short bar magnets of length 1 cm each have magnetic moments 1.20 Am2 and 1.00 Am2 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
(Horizontal component of earth’s magnetic induction is 3.6 × 10–5 Wb/m2)

Solution:

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