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JEE Advanced 2014 Paper -1 with Solutions


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JEE Advanced 2014 Paper -1 with Solutions - 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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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.)

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 1

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
JEE Advanced 2014 Paper -1 with Solutions - 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).

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 2

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

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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.

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 3

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
JEE Advanced 2014 Paper -1 with Solutions - 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)

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 4

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
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 5

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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?

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 6

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 7

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 8

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 9

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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
floor is N2. If the ladder is about to slip, then

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 10

Condition of translational equilibrium

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

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 11

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

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 12

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

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 13

Ub = 200 J, Ui =100 J
Process iaf

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 14

 

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 15

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 16

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
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 17

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 18

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 19

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

Li = Lf

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

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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)


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 20

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 21

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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,

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 22

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
JEE Advanced 2014 Paper -1 with Solutions - Question 23

Hydrogen bonding plays a central role in the following phenomena:

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 23

(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
JEE Advanced 2014 Paper -1 with Solutions - Question 24

In a galvanic cell, the salt bridge

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 25

For the reaction:

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 25

The balanced equation is,

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 26

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 27

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 27

(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
JEE Advanced 2014 Paper -1 with Solutions - Question 28

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 28

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 29

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 29

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

(B) 

(c) 

(D)

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 30

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 30

Only amines undergo acetylation and not acid amides

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 31

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
JEE Advanced 2014 Paper -1 with Solutions - Question 32

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


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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 33

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 34

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 35

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JEE Advanced 2014 Paper -1 with Solutions - Question 36

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


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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 37

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JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 38

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JEE Advanced 2014 Paper -1 with Solutions - Question 39

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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 39

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

*Answer can only contain numeric values
JEE Advanced 2014 Paper -1 with Solutions - 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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 40

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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 

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 41

Hence, an odd function

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 42

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 42

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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)

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 43

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
JEE Advanced 2014 Paper -1 with Solutions - 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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 44

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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 

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 45

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - 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)

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 46

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 47

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 47

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 48

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 48

*Multiple options can be correct
JEE Advanced 2014 Paper -1 with Solutions - Question 49

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

Then

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 49

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
JEE Advanced 2014 Paper -1 with Solutions - Question 50

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

Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 50

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JEE Advanced 2014 Paper -1 with Solutions - 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 _________


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 51

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
JEE Advanced 2014 Paper -1 with Solutions - 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 _________


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 52

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JEE Advanced 2014 Paper -1 with Solutions - 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 __________


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JEE Advanced 2014 Paper -1 with Solutions - 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 


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JEE Advanced 2014 Paper -1 with Solutions - 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 ___________________


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JEE Advanced 2014 Paper -1 with Solutions - Question 56

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


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 56

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JEE Advanced 2014 Paper -1 with Solutions - Question 57

The value of 


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 57

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JEE Advanced 2014 Paper -1 with Solutions - Question 58

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


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JEE Advanced 2014 Paper -1 with Solutions - Question 59

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

equation 


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JEE Advanced 2014 Paper -1 with Solutions - 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 ___________________


Detailed Solution for JEE Advanced 2014 Paper -1 with Solutions - Question 60

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