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# JEE Advanced 2013 Paper -1 with Solutions

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## 60 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Advanced 2013 Paper -1 with Solutions

JEE Advanced 2013 Paper -1 with Solutions for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The JEE Advanced 2013 Paper -1 with Solutions questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced 2013 Paper -1 with Solutions MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced 2013 Paper -1 with Solutions below.
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JEE Advanced 2013 Paper -1 with Solutions - Question 1

### SECTION – 1: (Only one option correct Type) This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct. Q. 1 - 10 carry 2 marks each. Q. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

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JEE Advanced 2013 Paper -1 with Solutions - Question 2

### The work done on a particle of mass m by a force   (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 2

JEE Advanced 2013 Paper -1 with Solutions - Question 3

### Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

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JEE Advanced 2013 Paper -1 with Solutions - Question 4

A ray of light travelling in the direction   is incident on a plane mirror. After reflection, it travels
along the direction The angle of incidence is

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Let angle between the directions of incident ray and reflected ray be θ

JEE Advanced 2013 Paper -1 with Solutions - Question 5

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale
divisions. The diameter of the cylinder is

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JEE Advanced 2013 Paper -1 with Solutions - Question 6

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is

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Here ρ1 and ρ2 are the densities of gases in the vessel containing the mixture

JEE Advanced 2013 Paper -1 with Solutions - Question 7

In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in
terms of an integer n) corresponding to any point having half the peak intensity is

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JEE Advanced 2013 Paper -1 with Solutions - Question 8

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free
space. The radius of the curved surface of the lens is

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JEE Advanced 2013 Paper -1 with Solutions - Question 9

A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal.
At the highest point of its trajectory, it makes a completely inelastic collision with another identical
particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that
the composite system makes with the horizontal immediately after the collision is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 9

Velocity of particle performing projectile motion at highest point
= v1 = v0cos α
Velocity of particle thrown vertically upwards at the position of collision

JEE Advanced 2013 Paper -1 with Solutions - Question 10

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the
pulse is 30 mW and the speed of light is 3 x 108 m/s. The final momentum of the object is

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*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 11

SECTION – 2 : (One or more options correct Type)

This section contains 5  multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

Q. No. 11 -15 carry  4 marks each and 1 mark is deducted for incorrect answer

Q.

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch
S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge
the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time,

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 11

After switch S1 is closed, C1 is charged by 2CV0, when switch S2 is closed, C1 and C2 both have upper plate
charge CV0.
When S3 is closed, then upper plate of C2 becomes charged by -CV0 and lower plate by +CV0

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 12

A particle of mass M and positive charge Q, moving with a constant velocity  enters a region
of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x =
0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after
10 milliseconds with a velocity  The correct statement(s) is (are)

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JEE Advanced 2013 Paper -1 with Solutions - Question 13

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) = 0.01m sin [(62.8m-1)x] cos[(628s-1)t]. Assuming π = 3.14, the correct statement(s) is (are)

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JEE Advanced 2013 Paper -1 with Solutions - Question 14

A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k.
The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete
arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct
statement(s) is (are)

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 14

For equilibrium of the complete system, net force of buoyancy must be equal to
the total weight of the sphere which holds true in the given problem. So both
the spheres are completely submerged

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 15

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ1 and ρ2
respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere,
along the line joining the centre of the spheres is zero. The ratio ρ12 can be

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JEE Advanced 2013 Paper -1 with Solutions - Question 16

SECTION – 3 : (Integer value correct Type)

This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

Q. No. 16-20 carry 4 marks each and 1 mark is deducted for  every incorrect answer

Q.

A bob of mass m , suspended by a string of length l1 is given a minimum velocity required to complete a
full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m
suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible.
If the second bob, after collision acquires the minimum speed required to complete a full circle in the
vertical plane, the ratio l1/l2 is

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JEE Advanced 2013 Paper -1 with Solutions - Question 17

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is

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JEE Advanced 2013 Paper -1 with Solutions - Question 18

The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the
stopping potential versus frequency plot for Silver to that of Sodium is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 18

Slope of graph is h/e = constant
1

*Answer can only contain numeric values
JEE Advanced 2013 Paper -1 with Solutions - Question 19

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second.
Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage)
that will decay in the first 80 s after preparation of the sample is

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JEE Advanced 2013 Paper -1 with Solutions - Question 20

A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-1
about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m,
are gently placed symmetrically on the disc in such a manner that they are touching each other along the
axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest
relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s-1) of
the system is

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JEE Advanced 2013 Paper -1 with Solutions - Question 21

SECTION – 1

Q. No. 21- 40 carry 2 marks each

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Q.

In the reaction,

P+Q →R+S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q
varies with reaction time as shown in the figure. The overall order of the reaction is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 21

Overall order of reaction can be decided by the data given t75% = 2t50%
It is a first order reaction with respect to P.
From graph [Q] is linearly decreasing with time, i.e. order of reaction with respect to Q is zero and the rate
expression is r = k [P]1[Q]0.
Hence (D) is correct.

JEE Advanced 2013 Paper -1 with Solutions - Question 22

Consider the following complex ions, P, Q and R

The correct order of the complex ions, according to their spin–only magnetic moment values (in B.M.) is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 22

P = Fe+3 (no. of unpaired e- = 5)
Q = V+2 (no. of unpaired e- = 3)
R = Fe+2 (no. of unpaired e- = 4)
As all ligands are weak field, hence the no. of unpaired electrons remains same in the complex ion.

Hence (B) is correct.

JEE Advanced 2013 Paper -1 with Solutions - Question 23

The arrangement of X ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the

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According to the given figure, A+ is present in the octahedral void of X-. The limiting radius in octahedral void is related to the radius of sphere as

JEE Advanced 2013 Paper -1 with Solutions - Question 24

Concentrated nitric acid, upon long standing, turns yellow–brown due to the formation of

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NO2 remains dissolved in nitric acid colouring it yellow or even red at higher temperature

JEE Advanced 2013 Paper -1 with Solutions - Question 25

The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 25

pKa of PhOH (carbolic acid) is 9.98 and that of carbonic acid (H2CO3) is 6.63 thus phenol does not give
effervescence with  HCO3- ion.

JEE Advanced 2013 Paper -1 with Solutions - Question 26

Sulfide ores are common for the metals

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Sulfide ore of Ag → Argentite (Ag2S), Pb → Galena (PbS), Cu → Copper glance (Cu2S)
Hence (A) is correct.

JEE Advanced 2013 Paper -1 with Solutions - Question 27

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 250C. For this process, the
correct statement is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 27

Adsorption of methylene blue on activated charcoal is physical adsorption hence it is characterised by decrease in enthalpy. Hence (B) is correct

JEE Advanced 2013 Paper -1 with Solutions - Question 28

KI in acetone, undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 28

Relative reactivity for SN2 reaction in the given structures is

JEE Advanced 2013 Paper -1 with Solutions - Question 29

The standard enthalpies of formation of CO2(g), H2O(l) and glucose(s) at 250C are –400 kJ/mol,
–300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at
250C is

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JEE Advanced 2013 Paper -1 with Solutions - Question 30

Upon treatment with ammoniacal H2S, the metal ion that precipitates as a sulfide is

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Among Fe3+, Al3+, Mg2+, Zn2+ only Zn2+ is precipitated with ammonical H2S as ZnS.

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 31

SECTION – 2

Q.No 31 - 35 carry 4 marks each 1 mark is deducted for every incorrect answer.

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

Q.

The initial rate of hydrolysis of methyl acetate (1 M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1M), at 25oC. The Ka of HA is

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*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 32

The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 32

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 33

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

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(an octahedral complex) and   (a square planar complex) will show geometrical isomerism.

will show ionization isomerism

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 34

Among P, Q, R and S, the aromatic compound(s) is/are

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*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 35

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s)
is(are)

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JEE Advanced 2013 Paper -1 with Solutions - Question 36

SECTION-3 (Integer value correct Type)

Q. No 36 -40 carry 4 marks each  and 1 mark is deducted for every incorrect answer

This section contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. (both inclusive).

Q.

The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength
of He gas at – 73oC is “M” times that of the de Broglie wavelength of Ne at 727o C. M is

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JEE Advanced 2013 Paper -1 with Solutions - Question 37

EDTA4- is ethylenediaminetetraacetate ion. The total number of N – Co – O bond angles in [Co(EDTA)]1-
complex ion is

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JEE Advanced 2013 Paper -1 with Solutions - Question 38

The total number of carboxylic acid groups in the product P is

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JEE Advanced 2013 Paper -1 with Solutions - Question 39

A tetrapeptide has – COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine
(Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences
(primary structures) with – NH2 group attached to a chiral center is

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 39

Because –COOH group of tetrapeptide is intact on alanine, its NH2 must be participating in condensation.
Alanine is at one terminus, – – – A.
To fill the 3 blanks, possible options are:

(i) When NH2 group attached to non chiral carbon

(ii) When NH2 group attached to chiral carbon

where, Glycine (G)
Valine (V)
Phenyl alanine (P)
Alanine (A)
So the number of possible sequence are 4.

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JEE Advanced 2013 Paper -1 with Solutions - Question 40

The total number of lone-pairs of electrons in melamine is

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lone pairs

JEE Advanced 2013 Paper -1 with Solutions - Question 41

SECTION - 1

Q. No. 41-50 carry 2 marks each

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Q.

Perpendiculars are drawn from points on the line  to the plane x + y + z = 3. The feet of perpendiculars lie on the line

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 41

The foot of the perpendicular from point (– 2, – 1, 0) on the plane is the point A (0, 1, 2)

JEE Advanced 2013 Paper -1 with Solutions - Question 42

For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and

bx + ay + c = 0 is less than 2√2 , then

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JEE Advanced 2013 Paper -1 with Solutions - Question 43

The area enclosed by the curves y = sinx + cosx and y = |cosx - sinx| over the interval   is

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=

JEE Advanced 2013 Paper -1 with Solutions - Question 44

Four persons independently solve a certain problem correctly with probabilities    then the
probability that the problem is solved correctly by at least one of them is

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P(at least one of them solves correctly) = 1 – P(none of them solves correctly)

JEE Advanced 2013 Paper -1 with Solutions - Question 45

Let complex numbers  lie on circles

respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |α| =

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JEE Advanced 2013 Paper -1 with Solutions - Question 46

The number of points in (-∞, ∞), for which x2 - xsinx - cosx = 0, is

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JEE Advanced 2013 Paper -1 with Solutions - Question 47

Let  (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x) < 2f(x) and f(1/2) =1  Then the value of   lies in the interval

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JEE Advanced 2013 Paper -1 with Solutions - Question 48

Let  determine diagonals of a parallelogram PQRS and

be another vector. Then the volume of the parallelepiped determined by the vectors

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JEE Advanced 2013 Paper -1 with Solutions - Question 49

The value of

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JEE Advanced 2013 Paper -1 with Solutions - Question 50

A curve passes through the point   Let the slope of the curve at each point (x, y) be  Then the equation of the curve is

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*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 51

SECTION - 2

Q. No 51 -55 carry 4 marks each and 1 mark is deducted for every incorrect answer

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

Q.

A line l passing through the origin is perpendicular to the lines

Then, the coordinate(s) of the point(s) on l2 at a distance of from the point of intersection of l and l1 is
(are)

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 51

The common perpendicular is along

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 52

Let f(x) = xsin πx, x > 0. Then for all natural numbers n, f'(x) vanishes at

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*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 53

Let  Then Sn can take value(s)

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 53

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 54

For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 54

(A) (NTMN)T = NTMTN = NTMN if M is symmetric and is – NTMN if M is skew symmetric
(B) (MN - NM)T = NTMT - MTNT = NM - MN = –(MN – NM). So, (MN – NM) is skew symmetric
(C) (MN)T = NTMT = NM MN if M and N are symmetric. So, MN is not symmetric

*Multiple options can be correct
JEE Advanced 2013 Paper -1 with Solutions - Question 55

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an
open rectangular box by folding after removing squares of equal area from all four corners. If the total area
of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the
rectangular sheet are

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Let the sides of rectangle be 15k and 8k and side of square be x then (15k – 2x)(8k – 2x)x is volume

*Answer can only contain numeric values
JEE Advanced 2013 Paper -1 with Solutions - Question 56

SECTION - 3

Q. No 56-60 carry 4 marks each and 1 mark is deducted for every incorrect answer

This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).

Q.

Consider the set of eight vectors  Three non-coplanar vectors can be
chosen from V in 2p ways. Then p is ________

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 56

Let (1, 1, 1), (–1, 1, 1), (1, –1, 1), (–1, –1, 1) be vectors   rest of the vectors are   and let us find the number of ways of selecting co–planar vectors.
Observe that out of any 3 coplanar vectors two will be collinear (anti parallel)

Number of ways of selecting the anti parallel pair = 4
Number of ways of selecting the third vector = 6
Total = 24
Number of non co–planar selections =

*Answer can only contain numeric values
JEE Advanced 2013 Paper -1 with Solutions - Question 57

Of the three independent events E1, E2, and E3, the probability that only E1 occurs is α, only E2 occurs is β
and only E3 occurs is γ. Let the probability p that none of events E1, E2 or E3 occurs satisfy the equations
(α - 2β) p = αβ and (β - 3γ) p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

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JEE Advanced 2013 Paper -1 with Solutions - Question 58

The coefficients of three consecutive terms of (1 + x)n+5 are in the ratio 5 : 10 : 14. Then n = _______

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JEE Advanced 2013 Paper -1 with Solutions - Question 59

A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the
pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the
removed cards is k, then k ? 20 = ________

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JEE Advanced 2013 Paper -1 with Solutions - Question 60

A vertical line passing through the point (h, 0) intersects the ellipse  at the points P and Q. Let
the tangents to the ellipse at P and Q meet at the point R. If Δ(h) = area of the triangle PQR, Δ1 =

Detailed Solution for JEE Advanced 2013 Paper -1 with Solutions - Question 60

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