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# JEE(Advanced) 2014 - Paper -1

## 60 Questions MCQ Test JEE Main Mock Test Series 2020 & Previous Year Papers | JEE(Advanced) 2014 - Paper -1

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This mock test of JEE(Advanced) 2014 - Paper -1 for JEE helps you for every JEE entrance exam. This contains 60 Multiple Choice Questions for JEE JEE(Advanced) 2014 - Paper -1 (mcq) to study with solutions a complete question bank. The solved questions answers in this JEE(Advanced) 2014 - Paper -1 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this JEE(Advanced) 2014 - Paper -1 exercise for a better result in the exam. You can find other JEE(Advanced) 2014 - Paper -1 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

### Q. 1 - 10 carry 3 marks each. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. Q. A student is performing an experiment using a resonance column and a tuning fork of frequency 244s-1 . He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 0.005)m , the gas in the tube is (Useful information:    The molar masses M in grams are given in the options. Take the values of  for each gas as given there.)

Solution:

Calculations for   for gases mentioned in options A, B, C and D, work out to be 0.459 m, 0.363 m 0.340 m & 0.348 m respectively. As   . Hence correct option is D.

*Multiple options can be correct
QUESTION: 2

### At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I0 cos (ωt), with I0 = 1A and ω = 500 rad/s starts flowing in it with the initial direction shown in the figure. At   the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 μF, R = 10 ? and the battery is ideal with emf of 50 V, identify the correct statement(s).

Solution:

As current leads voltage by π/2 in the given circuit initially, then ac voltage can be represent as

*Multiple options can be correct
QUESTION: 3

### A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.

Solution:

As E = V/d
E1/E2 = 1 (both parts have common potential difference)
Assume C0 be the capacitance without dielectric for whole capacitor.

*Multiple options can be correct
QUESTION: 4

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string
is 100 ms-1. The other end of the string is vibrating in the y direction so that stationary waves are set up in
the string. The possible waveform(s) of these stationary waves is (are)

Solution:

Taking y(t) = A f(x) g(t) & Applying the conditions:
1; here x = 3m is antinode & x = 0 is node
2; possible frequencies are odd multiple of fundamental frequency.

*Multiple options can be correct
QUESTION: 5

A transparent thin film of uniform thickness and refractive index n1 = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distance f2 from the film. Then

Solution:

*Multiple options can be correct
QUESTION: 6

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the
temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same
material, each of length L and diameter 2d. The way these wires are connected is given in the options.
How much time in minutes will it take to raise the temperature of the same amount of water by 40K?

Solution:

*Multiple options can be correct
QUESTION: 7

Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if

Solution:

*Multiple options can be correct
QUESTION: 8

Let  E1 (r), E2 (r) and E3 (r) be the respective electric fields at a distance r from a point charge Q, an
infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge
density σ. If E1(r0 ) = E2 (r0 ) = E3 (r0 ) at a given distance r0, then

Solution:

*Multiple options can be correct
QUESTION: 9

A light source, which emits two wavelengths λ1 = 400 nm and λ2 = 600 nm, is used in a Young’s double
slit experiment. If recorded fringe widths for λ1 and λ2 are β1 and β2 and the number of fringes for them
within a distance y on one side of the central maximum are m1 and m2, respectively, then

Solution:

*Multiple options can be correct
QUESTION: 10

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle
θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ1 and that
between the floor and the ladder is μ2. The normal reaction of the wall on the ladder is N1 and that of the

Solution:

Condition of translational equilibrium

Applying torque equation about corner (left) point on the floor

*Answer can only contain numeric values
QUESTION: 11

Q. No. 11 - 20  carry 3 Marks  each

Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Q.

During Searle’s experiment, zero of the Vernier scale lies between 3.20 x 10-2 m and 3.25 x 10-2 m of the
main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions.
When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 x
10-2 m and 3.25 x10-2 m of the main scale but now the 45th division of Vernier scale coincides with one of
the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 x 10-7
m2. The least count of the Vernier scale is 1.0 x 10-5 m. The maximum percentage error in the Young’s
modulus of the wire is

Solution:

change in lengths = 25(LC)
and the maximum permissible error in elongation is one LC

*Answer can only contain numeric values
QUESTION: 12

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 300 and 600 with
respect to the horizontal respectively as shown in the figure. The speed of A is 100√3 ms-1. At time t = 0
s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity
perpendicular to the line of motion of A. If at t = t0, A just escapes being hit by B, t0 in seconds is

Solution:

The relative velocity of B with respect to A is perpendicular to line of motion of A.

*Answer can only contain numeric values
QUESTION: 13

A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f
along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system
along the paths af, ib and bf are Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to
the system along the path iaf, ib and bf are iaf ib Q , Q and Qbf respectively. If the internal energy of the
system in the state b is Ub = 200 J and Qiaf = 500 J, the ratio Qbf / Qib is

Solution:

Ub = 200 J, Ui =100 J
Process iaf

*Answer can only contain numeric values
QUESTION: 14

Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u
between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of
magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast,
if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. id X0/X =3  the value of  R1/ R2  is

Solution:

*Answer can only contain numeric values
QUESTION: 15

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses
dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity
(power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to
S1/n. The value of n is

Solution:

*Answer can only contain numeric values
QUESTION: 16

A rocket is moving in a gravity free space with a constant acceleration of 2 ms–2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 ms–1 relative to the rocket. At the same time, another ball is thrown in +x direction with a speed of 0.2 ms–1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Solution:

Maximum displacement of the left ball from the left wall of the chamber is 2.25 cm, so the right ball has to travel almost the whole length of the chamber (4m) to hit the left ball. So the time taken by the right ball is
1.9 sec (approximately 2 sec)

*Answer can only contain numeric values
QUESTION: 17

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990  resistance, it can be converted into a voltmeter of range 0 – 30 V. If connected to a 2n/249  resistance, it becomes an ammeter of range 0 – 1.5 A. The value of n is

Solution:

*Answer can only contain numeric values
QUESTION: 18

A uniform circular disc of mass 1.5 kg and radius 0.5 m isinitially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral
triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s–1 is

Solution:

*Answer can only contain numeric values
QUESTION: 19

A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 ms–1 with respect to the ground. The rotational speed of the platform in rad s–1 after the balls leave the platform is

Solution:

Since net torque about centre of rotation is zero, so we can apply conservation of angular momentum of the

Li = Lf

0 = Iω + 2mv (r/2); comparing magnitude

*Answer can only contain numeric values
QUESTION: 20

Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n×10) Joules. The
value of n is (take acceleration due to gravity = 10 ms–2)

Solution:

*Multiple options can be correct
QUESTION: 21

Q. No. 21- 30 carry 3 mark  each.

Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.

Q. The correct combination of names for isomeric alcohols with molecular formula C4H10O is/are

Solution:

*Multiple options can be correct
QUESTION: 22

An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1 and absolute
temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final
internal pressure, volume and absolute temperature of the gas are P2, V2 and T2, respectively. For this
expansion,

Solution:

Since container is thermally insulated. So, q = 0, and it is a case of free expansion therefore W = 0 and

ΔE = 0
So, T1 = T2
Also, P1V1 = P2V2

*Multiple options can be correct
QUESTION: 23

Hydrogen bonding plays a central role in the following phenomena:

Solution:

(A) Ice has cage-like structure in which each water molecule is surrounded by four other water molecules tetrahedrally through hydrogen boding, due to this density of ice is less than water and it floats in
water.

The cation (I) more stabilized through hydrogen boding than cation (II) . So, R–NH2 is better base than (R)3N in aqueous solution.

(C) HCOOH is stronger acid than CH3COOH due to inductive effect and not due to hydrogen bonding.

(D) Acetic acid dimerizes in benzene through intermolecular hydrogen bonding.

*Multiple options can be correct
QUESTION: 24

In a galvanic cell, the salt bridge

Solution:
*Multiple options can be correct
QUESTION: 25

For the reaction:

The correct statement(s) in the balanced equation is/are:

Solution:

The balanced equation is,

*Multiple options can be correct
QUESTION: 26

The reactivity of compound Z with different halogens under appropriate conditions is given below:

The observed pattern of electrophilic substitution can be explained by

Solution:

*Multiple options can be correct
QUESTION: 27

The correct statement(s) for orthoboric acid is/are

Solution:

(A) H3BO3 is a weak monobasic Lewis acid.

(B) Equilibrium (i) is shifted in forward direction by the addition of syn-diols like ethylene glycol which forms a stable complex with

(C) It has a planar sheet like structure due to hydrogen bonding.
(D) H3BO3 is a weak electrolyte in water.

*Multiple options can be correct
QUESTION: 28

Upon heating with Cu2S, the reagent(s) that give copper metal is/are

Solution:

*Multiple options can be correct
QUESTION: 29

The pair(s) of reagents that yield paramagnetic species is/are

Solution:

(A) sodium (Na) when dissolved in excess liquid ammonia, forms a blue coloured paramagnetic solution.

(B)

(c)

(D)

*Multiple options can be correct
QUESTION: 30

In the reaction shown below, the major product(s) formed is/are

Solution:

Only amines undergo acetylation and not acid amides

*Answer can only contain numeric values
QUESTION: 31

Q. No. 31 - 40 Carry 3 marks each

Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Q.

Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK coloured
sulphides is

Solution:

Black coloured sulphides (PbS,CuS,HgS,Ag2S,NiS,CoS)
* Bi2S3 in its crystalline form is dark brown but Bi2S3 precipitate obtained is black in colour.

*Answer can only contain numeric values
QUESTION: 32

The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)

Solution:

*Answer can only contain numeric values
QUESTION: 33

Consider the following list of reagents:
Acidified K2Cr2O7 , alkaline KMnO4 ,CuSO4,H2O2 ,Cl2 ,O3,FeCl3,HNO3 and Na2S2O3 .
The total number of reagents that can oxidise aqueous iodide to iodine is

Solution:

*Answer can only contain numeric values
QUESTION: 34

A list of species having the formula XZ4 is given below.

Defining shape on the basis of the location of X and Z atoms, the total number of species having a square
planar shape is

Solution:

*Answer can only contain numeric values
QUESTION: 35

Consider all possible isomeric ketones, including stereoisomers of MW = 100. All these isomers are
independently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of
ketones that give a racemic product(s) is/are

Solution:

*Answer can only contain numeric values
QUESTION: 36

In an atom, the total number of electrons having quantum numbers n = 4, |ml| = 1 and ms = –1/2 is

Solution:

*Answer can only contain numeric values
QUESTION: 37

If the value of Avogadro number is 6.023 x 1023 mol–1 and the value of Boltzmann constant is
1.380x10-23 JK-1 , then the number of significant digits in the calculated value of the universal gas constant
is

Solution:

*Answer can only contain numeric values
QUESTION: 38

MX2 dissociates in M2+ and X- ions in an aqueous solution, with a degree of dissociation (α) of 0.5. The
ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of
freezing point in the absence of ionic dissociation is

Solution:

*Answer can only contain numeric values
QUESTION: 39

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the
peptide shown below is

Solution:

This peptide on complete hydrolysis produced 4 distinct amino acids which are given below:

*Answer can only contain numeric values
QUESTION: 40

A compound H2X with molar weight of 80g is dissolved in a solvent having density of 0.4 gml–1. Assuming
no change in volume upon dissolution, the molality of a 3.2 molar solution is

Solution:

*Multiple options can be correct
QUESTION: 41

Q. No. 41 to 50 carry 3 marks each.

Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.

Q.

Let    be given by

Solution:

Hence, an odd function

*Multiple options can be correct
QUESTION: 42

Let a R and let f : R → R be given by f (x) = x5 - 5x + a, then

Solution:

*Multiple options can be correct
QUESTION: 43

For every pair of continuous functions , g : [0, 1] → R such that max{ f (x) : x [0, 1]} = max{g(x) : x
[0, 1]}, the correct statement(s) is(are)

Solution:

Let f (x) and g (x) achieve their maximum value at x1 and x2 respectively
h (x) = f (x) - g (x)
h (x1) = f (x1) - g (x1) 0
h (x2) = f (x2) - g (x2) 0
h (c) = 0 where c [0, 1] f (c) = g (c).

*Multiple options can be correct
QUESTION: 44

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)2 + y2 = 16 and x2 + y2 = 1.
Then

Solution:

*Multiple options can be correct
QUESTION: 45

Let   be three vectors each of magnitude √2 and the angle between each pair of them is π/3. If  is a non-zero vector perpendicular to   is a non-zero vector perpendicular to  and

Solution:

*Multiple options can be correct
QUESTION: 46

From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that QPR is a right angle, then the possible value(s) of λ is(are)

Solution:

*Multiple options can be correct
QUESTION: 47

Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if

Solution:

*Multiple options can be correct
QUESTION: 48

Let M and N be two 3 x 3 matrices such that MN = NM. Further, if M N2 and M2 = N4, then

Solution:

*Multiple options can be correct
QUESTION: 49

Let be a continuous function and let g : R → R be defined as

Then

Solution:

Hence g(x) is not differentiable at x = a
Similarly LHD at x = b is greater than 1
g(x) is not differentiable at x = b

*Multiple options can be correct
QUESTION: 50

Let   be given by f(x) = (log(sec x + tan x))3. Then

Solution:

*Answer can only contain numeric values
QUESTION: 51

Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Q.

Let n1 < n2 < n3 < n4 < n5 be positive integers such that n1 + n2 + n3 + n4 + n5 = 20. Then the number of such distinct arrangements (n1, n2, n3, n4, n5) is _________

Solution:

When n5 takes value from 10 to 6 the carry forward moves from 0 to 4 which can be arranged in

*Answer can only contain numeric values
QUESTION: 52

Let n 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment.
Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of
red and blue line segments are equal, then the value of n is _________

Solution:

*Answer can only contain numeric values
QUESTION: 53

Let f : R → R and g : R → R be respectively given by  by

Then number of points at which h(x) is not differentiable is __________

Solution:

*Answer can only contain numeric values
QUESTION: 54

Let a, b, c be positive integers such that b/a is an integer. If a, b, c are in geometric progression and the
arithmetic mean of a, b, c is b + 2, then the value of

Solution:

*Answer can only contain numeric values
QUESTION: 55

Let  be three non-coplanar unit vectors such that the angle between every pair of them is π/3 . if   where p, q and r are scalars, then the value of  is ___________________

Solution:

*Answer can only contain numeric values
QUESTION: 56

The slope of the tangent to the curve  at the point (1, 3) is ______

Solution:

*Answer can only contain numeric values
QUESTION: 57

The value of

Solution:

*Answer can only contain numeric values
QUESTION: 58

The largest value of the non-negative integer a for which

Solution:

*Answer can only contain numeric values
QUESTION: 59

Let  be defined by f (x) = cos-1(cos x). The number of points x [0, 4π] satisfying the

equation

Solution:

*Answer can only contain numeric values
QUESTION: 60

For a point P in the plane, let d1(P) and d2(P) be the distances of the point P from the lines x - y = 0 and x +
y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane
and satisfying  is ___________________

Solution: