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This contains 60 Multiple Choice Questions for JEE JEE Advanced 2015 Paper -2 with Solutions (mcq) to study with solutions a complete question bank.
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*Answer can only contain numeric values

QUESTION: 1

**Section 1**

**Q. No. 1 - 8 Carry 4 marks each**

**The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.**

**Q.**

An electron in an excited state of Li^{2+} ion has angular momentum 3h/2π. The de Broglie wavelength of the

electron in this state is pπa_{0} (where a_{0} is the Bohr radius). The value of p is

Solution:

*Answer can only contain numeric values

QUESTION: 2

A large spherical mass M is fixed at one position and two identical point masses m are kept on a line

passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of

length and this assembly is free to move along the line connecting them. All three masses interact only

through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3 from

M, the tension in the rod is zero for m = k(M/288). The value of k is

Solution:

*Answer can only contain numeric values

QUESTION: 3

The energy of a system as a function of time t is given as E(t) = A_{2}exp(-αt), where α = 0.2 s^{-1}. The

measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage

error in the value of E(t) at t = 5 s is

Solution:

*Answer can only contain numeric values

QUESTION: 4

The densities of two solid spheres A and B of the same radii R vary with radial distance r as ρ_{A}(r) =

, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are I_{A} and I_{B}, respectively. If

the value of n is

Solution:

QUESTION: 5

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, π/3, 2π/3 and π.

When they are superposed, the intensity of the resulting wave is nI_{0}. The value of n is

Solution:

First and fourth wave interfere destructively. So from the interference of 2^{nd} and 3^{rd} wave only,

*Answer can only contain numeric values

QUESTION: 6

For a radioactive material, its activity A and rate of change of its activity R are defined as and , where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life ) and

Q(mean life 2) have the same activity at t = 0. Their rates of change of activities at t = 2 are RP and RQ,

respectively. If , then the value of n is

Solution:

*Answer can only contain numeric values

QUESTION: 7

A monochromatic beam of light is incident at 60^{0} on one face of an equilateral prism of refractive index n and

emerges from the opposite face making an angle θ(n) with the normal (see the figure). For n = √3 the value of θ is 60^{0} and . The value of m is

Solution:

*Answer can only contain numeric values

QUESTION: 8

In the following circuit, the current through the resistor R (=2) is I Amperes. The value of I is

Solution:

*Multiple options can be correct

QUESTION: 9

**Section 2**

**Q. No. 9 -18 carry 4 marks each and 2 marks is deducted for every wrong answer.**

**Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct.**

**Q.**

A fission reaction is given by where x and y are two particles. Considering to be at rest, the kinetic energies of the products are denoted by K_{Xe}, K_{Sr}, K_{x}(2MeV) and K_{y}(2MeV),

respectively. Let the binding energies per nucleon of be 7.5 MeV, 8.5 MeV and 8.5 MeV respectively. Considering different conservation laws, the correct option(s) is(are)

Solution:

Q value of reaction = (140 + 94) × 8.5 – 236 × 7.5 = 219 Mev

So, total kinetic energy of Xe and Sr = 219 – 2 – 2 = 215 Mev

So, by conservation of momentum, energy, mass and charge, only option (A) is correct

*Multiple options can be correct

QUESTION: 10

Two spheres P and Q of equal radii have densities ρ_{1} and ρ_{2}, respectively. The spheres are connected by a massless string and placed in liquids L_{1} and L_{2} of densities σ_{1} and σ_{2} and viscosities η_{1} and

η_{2}, respectively. They float in equilibrium with the sphere P in L_{1} and sphere Q in L_{2} and the string being taut (see figure). If sphere P alone in L_{2} has terminal velocity and Q alone in L_{1} has terminal velocity ,

ρ then

Solution:

*Multiple options can be correct

QUESTION: 11

In terms of potential difference V, electric current I, permittivity ε_{0}, permeability μ_{0} and speed of light c,

the dimensionally correct equation(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 12

Consider a uniform spherical charge distribution of radius R1 centred at the origin O. In this distribution, a spherical cavity of radius R_{2}, centred at P with distance OP = a = R_{1} – R_{2} (see figure) is made. If the electric field inside the cavity at position then the correct statement(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 13

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 14

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own

gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 15

parallel plate capacitor having plates of area S and plate separation d, has capacitance C_{1} in air. When

two dielectrics of different relative permittivities (ε_{1} = 2 and ε_{2} = 4) are introduced between the two plates

as shown in the figure, the capacitance becomes C_{2}. The ratio C_{2}/C_{1 }is

Solution:

*Multiple options can be correct

QUESTION: 16

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the

figure). Initially the gas is at temperature T_{1}, pressure P_{1} and volume V_{1} and the spring is in its relaxed state.

The gas is then heated very slowly to temperature T_{2}, pressure P_{2} and volume V_{2}. During this process the

piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct

statement(s) is(are)

Solution:

Note: A and C will be true after assuming pressure to the right of piston has constant value P_{1}

*Multiple options can be correct

QUESTION: 17

**SECTION 3**

**Q. No. 17-20 carry 4 marks each and 2 marks is deducted for every wrong answer.**

**This section contains TWO paragraphs**

**Based on each paragraph, there will be TWO questions**

**Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct**

**PARAGRAPH 1**

**Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n _{1} surrounded by a medium of lower refractive index n_{2}. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_{1} and n_{2} as shown in the figure. All rays with the angle of incidence i less than a particular value i_{m} are confined in the medium of refractive index n_{1}. The numerical aperture (NA) of the structure is defined as sin i_{m}.**

Q.

**For two structures namely S _{1} with n_{1} = **

taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 18

**PARAGRAPH 1**

**Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n _{1} surrounded by a medium of lower refractive index n_{2}. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_{1} and n_{2} as shown in the figure. All rays with the angle of incidence i less than a particular value i_{m} are confined in the medium of refractive index n_{1}. The numerical aperture (NA) of the structure is defined as sin i_{m}.**

**Q.**

**If two structures of same cross-sectional area, but different numerical apertures NA _{1} and
NA_{2} (NA_{2} < NA_{1} ) are joined longitudinally, the numerical aperture of the combined structure is**

Solution:

For total internal reflection to take place in both structures, the numerical aperture should be the least one for the combined structure & hence, correct option is D.

*Multiple options can be correct

QUESTION: 19

**PARAGRAPH 2
In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are **

Q.

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are

w_{1} and w_{2} and thicknesses are d_{1} and d_{2}, respectively. Two points K and M are symmetrically located on

the opposite faces parallel to the x-y plane (see figure). V_{1} and V_{2} are the potential differences between K

and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic

field strength B, the correct statement(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 20

**PARAGRAPH 2
In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are **

Q.

Consider two different metallic strips (1 and 2) of same dimensions (lengths , width w and thickness d)

with carrier densities n_{1} and n_{2}, respectively. Strip 1 is placed in magnetic field B_{1} and strip 2 is placed in

magnetic field B_{2}, both along positive y-directions. Then V_{1} and V_{2} are the potential differences developed

between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips,

the correct option(s) is(are)

Solution:

*Answer can only contain numeric values

QUESTION: 21

**SECTION 1**

**Q. No. 21 -28 carry 4 marks each.**

**The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive**

**Q.**

**In dilute aqueous H _{2}SO_{4}, the complex diaquodioxalatoferrate(II) is oxidized by . For this reaction, the ratio of the rate of change of [H^{+}] to the rate of change of is**

Solution:

*Answer can only contain numeric values

QUESTION: 22

The number of hydroxyl group(s) in Q is

Solution:

*Answer can only contain numeric values

QUESTION: 23

Among the following, the number of reaction(s) that produce(s) benzaldehyde is

Solution:

*Answer can only contain numeric values

QUESTION: 24

In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe–C bond(s) is

Solution:

*Answer can only contain numeric values

QUESTION: 25

Among the complex ions,

number of complex

ion(s) that show(s) cis-trans isomerism is

Solution:

*Answer can only contain numeric values

QUESTION: 26

Three moles of B_{2}H_{6} are completely reacted with methanol. The number of moles of boron containing

product formed is

Solution:

1 mole of B_{2}H_{6} reacts with 6 mole of MeOH to give 2 moles of B(OMe)_{3}.

3 mole of B_{2}H_{6} will react with 18 mole of MeOH to give 6 moles of B(OMe)_{3}

*Answer can only contain numeric values

QUESTION: 27

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar

conductivity of a solution of a weak acid HY (0.10 M). If the difference in their pK_{a} values,

pK_{a} (HX) - pK_{a} (HY), is (consider degree of ionization of both acids to be << 1)

Solution:

*Answer can only contain numeric values

QUESTION: 28

closed vessel with rigid walls contains 1 mol of and 1 mol of air at 298 K. Considering complete

decay of , the ratio of the final pressure to the initial pressure of the system at 298 K is

Solution:

In conversion of particles are ejected.

The number of gaseous moles initially = 1 mol

The number of gaseous moles finally = 1 + 8 mol; (1 mol from air and 8 mol of _{2}He^{4})

So the ratio = 9/1 = 9

*Multiple options can be correct

QUESTION: 29

SECTION 2

Q. No. 29-36 carry 4 marks each and 2 marks is deducted for every wrong answer.

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four

option(s) is(are) correct

Q.

One mole of a monoatomic real gas satisfies the equation p(V – b) = RT where b is a constant. The

relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

Solution:

At large inter-ionic distances (because a → 0) the P.E. would remain constant.

However, when r → 0; repulsion would suddenly increase.

*Multiple options can be correct

QUESTION: 30

In the following reactions, the product S is

Solution:

*Multiple options can be correct

QUESTION: 31

The major product U in the following reactions is

Solution:

*Multiple options can be correct

QUESTION: 32

In the following reactions, the major product W is

Solution:

*Multiple options can be correct

QUESTION: 33

The correct statement(s) regarding, (i) HClO, (ii) HClO_{2}, (iii) HClO_{3} and (iv) HClO_{4}, is (are)

Solution:

*Multiple options can be correct

QUESTION: 34

The pair(s) of ions where BOTH the ions are precipitated upon passing H_{2}S gas in presence of dilute HCl,

is(are)

Solution:

Cu^{2+} , Pb^{2+} , Hg^{2+} , Bi^{3+} give ppt with H_{2}S in presence of dilute HCl.

*Multiple options can be correct

QUESTION: 35

Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain

termination, respectively, are

Solution:

*Multiple options can be correct

QUESTION: 36

When O_{2 }is adsorbed on a metallic surface, electron transfer occurs from the metal to O_{2}. The TRUE

statement(s) regarding this adsorption is(are)

Solution:

* Adsorption of O_{2} on metal surface is exothermic.

* During electron transfer from metal to O_{2} electron occupies π^{*}_{2p} orbital of O_{2}.

* Due to electron transfer to O_{2} the bond order of O_{2} decreases hence bond length increases

*Multiple options can be correct

QUESTION: 37

**SECTION 3**

**Q. No 37 - 40 carry 4 marks each and 2 marks is deducted for every wrong answer**

**This section contains TWO paragraphs
Based on each paragraph, there will be TWO questions
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct**

**PARAGRAPH 1**

**When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7 ^{o}C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (-57.0 kJ mol^{-1}), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (K_{a} = 2.0 × 10^{-5}) was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6^{o}C as measured. **

**(Consider heat capacity of all solutions as 4.2 J g ^{-1} K^{-1} and density of all solutions as 1.0 g mL^{-1})**

**Q.**

**Enthalpy of dissociation (in kJ mol-1) of acetic acid obtained from the Expt. 2 is**

Solution:

HCl + NaOH→NaCl + H_{2}O

n = 100 x1 = 100 m mole = 0.1 mole

Energy evolved due to neutralization of HCl and NaOH = 0.1 x 57 = 5.7 kJ = 5700 Joule

Energy used to increase temperature of solution = 200 x 4.2 x 5.7 = 4788 Joule

Energy used to increase temperature of calorimeter = 5700 – 4788 = 912 Joule

ms.Δt = 912

m.sx5.7 = 912

ms = 160 Joule/^{o}C [Calorimeter constant]

Energy evolved by neutralization of CH3COOH and NaOH

= 200x 4.2x5.6 +160x5.6 = 5600 Joule

So energy used in dissociation of 0.1 mole CH_{3}COOH = 5700 - 5600 = 100 Joule

Enthalpy of dissociation = 1 kJ/mole

*Multiple options can be correct

QUESTION: 38

**When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7 ^{o}C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (-57.0 kJ mol^{-1}), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (K_{a} = 2.0 × 10^{-5}) was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6^{o}C as measured. **

**(Consider heat capacity of all solutions as 4.2 J g ^{-1} K^{-1} and density of all solutions as 1.0 g mL^{-1})**

**Q.**

**The pH of the solution after Expt. 2 is**

Solution:

*Multiple options can be correct

QUESTION: 39

**PARAGRAPH 2
In the following reactions**

**Q.**

**Compound X is**

Solution:

*Multiple options can be correct

QUESTION: 40

**In the following reactions**

**Q.**

**The major compound Y is**

Solution:

*Answer can only contain numeric values

QUESTION: 41

**Section 1**

**Q. No. 41- 48 carry 4 marks each.**

**The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive**

**Q.**

**Suppose that are three non-coplanar vectors in R ^{3}. Let the components of a vector along be 4, 3 and 5, respectively. If the components of this vector and are x, y and z, respectively, then the value of 2x + y + z is**

Solution:

*Answer can only contain numeric values

QUESTION: 42

For any integer k, let . The value of the expression

Solution:

*Answer can only contain numeric values

QUESTION: 43

Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of

the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130

and 140, then the common difference of this A.P. is

Solution:

*Answer can only contain numeric values

QUESTION: 44

The coefficient of x^{9} in the expansion of (1 + x) (1 + x^{2}) (1 + x^{3}) ….. (1 + x^{100}) is

Solution:

*Answer can only contain numeric values

QUESTION: 45

Suppose that the foci of the ellipse are (f_{1}, 0) and (f_{2}, 0) where f_{1} > 0 and f_{2} < 0. Let P_{1} and P_{2}

be two parabolas with a common vertex at (0, 0) and with foci at (f_{1}, 0) and (2f_{2}, 0), respectively. Let T_{1} be

a tangent to P_{1} which passes through (2f_{2}, 0) and T_{2} be a tangent to P_{2} which passes through (f1, 0). The m1

is the slope of T_{1} and m_{2} is the slope of T_{2}, then the value of

Solution:

*Answer can only contain numeric values

QUESTION: 46

Let m and n be two positive integers greater than 1. If

Solution:

*Answer can only contain numeric values

QUESTION: 47

If

where tan^{-1}x takes only principal values, then the value of

Solution:

*Answer can only contain numeric values

QUESTION: 48

Let be a continuous odd function, which vanishes exactly at one point and f(1) =1/2. Suppose

that and then the value of f(1/2) is

Solution:

*Multiple options can be correct

QUESTION: 49

**Section 2**

**Q. No. 49 - 56 carry 4 marks eah and 2 mark is deducted forr every wrong answer.**

**Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct.**

Q.

Let for all , then the possible values of m and M are

Solution:

*Multiple options can be correct

QUESTION: 50

Let S be the set of all non-zero real numbers α such that the quadratic equation αx^{2} - x + α = 0 has two

distinct real roots x^{1} and x^{2} satisfying the inequality x^{1} - x^{2} < 1. Which of the following intervals is(are) a

subset(s) of S ?

Solution:

*Multiple options can be correct

QUESTION: 51

If , where the inverse trigonometric functions take only the principal

values, then the correct option(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 52

Let E_{1} and E_{2} be two ellipses whose centers are at the origin. The major axes of E_{1} and E_{2} lie along the

x-axis and the y-axis, respectively. Let S be the circle x^{2} + (y - 1)^{2} = 2. The straight line x + y = 3 touches the curves S, E_{1} and E_{2} at P, Q and R, respectively. Suppose that PQ = PR = . If e_{1} and e_{2} are the

eccentricities of E_{1} and E_{2}, respectively, then the correct expression(s) is(are)

Solution:

For the given line, point of contact for

and for

Point of contact of x + y = 3 and circle is (1, 2)

Also, general point on x + y = 3 can be taken as

*Multiple options can be correct

QUESTION: 53

Consider the hyperbola H : x^{2} - y^{2} = 1 and a circle S with center N(x_{2}, 0). Suppose that H and S touch each

other at a point P(x_{1}, y_{1}) with x_{1} > 1 and y_{1} > 0. The common tangent to H and S at P intersects the x-axis at

point M. If (l, m) is the centroid of the triangle ΔPMN, then the correct expression(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 54

The option(s) with the values of a and L that satisfy the following equation is(are)

Solution:

*Multiple options can be correct

QUESTION: 55

Let be continuous functions which are twice differentiable on the interval (-1, 2). Let the

values of f and g at the points -1, 0 and 2 be as given in the following table:

In each of the intervals (-1, 0) and (0, 2) the function (f - 3g)" never vanishes. Then the correct

statement(s) is(are)

Solution:

Let H (x) = f (x) – 3g (x)

H (- 1) = H (0) = H (2) = 3.

Applying Rolle’s Theorem in the interval [- 1, 0]

H'(x) = f'(x) – 3g'(x) = 0 for atleast one c (- 1, 0).

As H"(x) never vanishes in the interval

Exactly one c (- 1, 0) for which H'(x) = 0

Similarly, apply Rolle’s Theorem in the interval [0, 2].

H'(x) = 0 has exactly one solution in (0, 2)

*Multiple options can be correct

QUESTION: 56

Let f (x) = 7tan^{8}x + 7tan^{6}x - 3tan^{4}x - 3tan^{2}x for all Then the correct expression(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 57

**SECTION 3**

**Q. No. 57 - 60 carry 4 marks each and 2 mark is deducted for every wrong answer.**

**This section contains TWO paragraphs.
Based on each paragraph, there will be TWO questions
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct**

**PARAGRAPH 1**

**Let **** be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x ** **(1/2, 3). Let f (x) = xF(x) for all **

Q.

The correct statement(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 58

**PARAGRAPH **

**Let **** be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x ** **(1/2, 3). Let f (x) = xF(x) for all **

Q.

If then the correct expression(s) is(are)

Solution:

*Multiple options can be correct

QUESTION: 59

**PARAGRAPH 2**

**Let n _{1} and n_{2} be the number of red and black balls, respectively, in box I. Let n_{3} and n_{4} be the number of red and black balls, respectively, in box II.**

**Q.**

**One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is 1/3 then the correct option(s) with the possible values of n _{1}, n_{2}, n_{3} and n_{4} is(are)**

Solution:

*Multiple options can be correct

QUESTION: 60

**PARAGRAPH 2**

**Let n _{1} and n_{2} be the number of red and black balls, respectively, in box I. Let n_{3} and n_{4} be the number of red and black balls, respectively, in box II.**

**Q.**

A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from

box I, after this transfer, is 1/3, then the correct option(s) with the possible values of n_{1} and n_{2} is(are)

Solution:

P (Red after Transfer) = P(Red Transfer) . P(Red Transfer in II Case)

+ P (Black Transfer) . P(Red Transfer in II Case)

Of the given options, option C and D satisfy above condition.

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