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JEE (Advanced) 2016 Paper - 1 with Solutions


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JEE (Advanced) 2016 Paper - 1 with Solutions - Question 1

Inst.

Q. 1 to 5 carry 3 marks each

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

Q.

In a historical experiment to determine Planck’s constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential (V0) are given below:

Given that c = 3 x108 ms-1 and e = 1.6 x 10-19C, Planck’s constant (in units of J s) found from such an
experiment is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 1



 

Alternate Solution
From first two date points.

⇒ 6.4 * 10-34.

We get same value from second and third data points.

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 2

A uniform wooden stick of mass 1.6 kg and length   rests in an inclined manner on a smooth, vertical wall of height h (<) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 300 with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio h/ and the frictional force f at the bottom of the stick are (g = 10 ms-2)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 2

On the basis of given data, it is not possible for the rod to stay at rest.
Note: If we take the normal reaction at the wall equal to the normal reaction at the floor, the answer
will be D.

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 3

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 300C and the entire stored 120 litres of water is initially cooled to 100C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is

(Specific heat of water is 4.2 kJ kg-1 K-1 and the density of water is 1000 kg m-3)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 3

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 4

A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n = √2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 450. The angle θ of the prism is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 4


For TIR  on face PR,

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 5

An infinite line charge of uniform electric charge density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity ε and electrical conductivity σ. The electrical conduction in the material follows Ohm’s law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 5

For infinite line,

Current through an elemental shell;

This current is radially outwards so; 


 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 6

Q. 6 to 13 carry 4 marks each

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

Q.  Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 6





 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 7

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP, vQ and vR be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m s-1. Which of the following statement(s) is(are) true regarding the sound
heard by the person?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 7





Now, v (between P and Q) 




Now, sin θ = 1  at Q (maximum)
∴ rate of change in beat frequency is maximum at Q



*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 8

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 8

When filament breaks up, the temperature of filament will be higher so according to wein’s law

, the filament emits more light at higher band of frequencies. As voltage is constant, so consumed electrical power is P=V2/R 
As R increases with increase in temperature so the filament consumes less electrical power towards the end of the life of the bulb.

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 9

A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away
in front of the curved surface of the lens, an image of double the size of the object is produced. Due to
reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away
from the lens. Which of the following statement(s) is(are) true?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 9

For refraction through lens,

The faint image is erect and virtual.

 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 10

A length-scale () depends on the permittivity (ε) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for  is(are) dimensionally correct? 

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 10

kBT ≈ FL,ε≈Q2/FL2 and n ≈L-3; where F is force, Q is charge and L is length So (B) and (D) are correct

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 11

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s-1. Which of the following statement(s) is(are) true?

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 12

The position vector  of a particle of mass m is given by the following equation , where α = 10/3 m s-3, β= 5 m s-2 and m = 0.1 kg. At t = 1 s, which of the following statement(s) is(are) true about the particle?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 12







 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 13

A transparent slab of thickness d has a refractive index n (z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (> n1), as shown in the figure. A ray of light is incident with angle θi from medium 1 and emerges in medium 2 with refraction angle  θf with a lateral displacement l.

Which of the following statement (s) is (are) true?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 13

From Snell's Law

The deviation of ray in the slab will depend on n (z)
Hence, l will depend on n (z) but not on n2

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 14

Q. 14 to 18 carry 3 marks each

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

Q.

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log2 (P/P0), where P0 is a constant. When the metal surface is at a temperature of 487°C, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 °C?

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 14






*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 15

The isotope  having a mass 12.014 u undergoes β-decay to .  has an excited state of the nucleus at 4.041 MeV above its ground state. If decays to , the maximum kinetic energy of the β- particle in units of MeV is (1 u = 931.5 MeV/c2, where c is the speed of light in vacuum).


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 15


Hence, β particle will have a maximum KE of 9 MeV

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 16

Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1cm and 0.5cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity η = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm–3 and viscosity η = 2 poiseulles. The ratio of the terminal velocities of P and Q is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 16

Terminal velocity   where ρ is the density of the solid sphere and σ is the density of the liquid

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 17

A hydrogen atom in its ground state is irradiated by light of wavelength 970 Å. Taking hc/e = 1.237×10–6 eV m and the ground state energy of hydrogen atom as –13.6 eV, the number of lines present in the emission spectrum is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 17

Note : Unit of hc/e in original paper is incorrect Energy available  (4th  energy level of hydrogen atom). Hence, the number of lines present in the emission spectrum = 4C2 = 6

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 18

Two inductors L1 (inductance 1 mH, internal resistance 3) and L2 (inductance 2 mH, internal resistance 4), and a resistor R (resistance 12) are all connected in parallel across a 5V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax / Imin) drawn from the battery is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 18

At t = 0, current will flow only in 12Ω resistance

At t → ∝ both L1 and L2 behave as conducting wires 
 

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 19

Q. 19 to 23 carry 3 marks each

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

Q.

P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4πr2dr. The qualitative sketch of the dependence of P on r is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 19

The probability distribution curve for 1s electron of hydrogen atom.

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 20

One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surrounding (ΔSsurr)in JK–1 is (1L atm = 101.3 J)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 20

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 21

The increasing order of atomic radii of the following Group 13 elements is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 21

Increasing order of atomic radius of group 13 elements Ga < Al < In < Tl.
Due to poor shielding of d-electrons in Ga, its radius decreases below Al.

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 22

Among [Ni(CO)4], [NiCl4]2–, [Co(NH3)4Cl2]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compounds is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 22

Number of paramagnetic compounds are 3.
Following compounds are paramagnetic.

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 23

On complete hydrogenation, natural rubber produces

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 23



*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 24

Q. 24 to 31 carry 4 marks each

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

Q.

According to the Arrhenius equation

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 25

A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is(are)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 25


Positron, emission 

Both process cause an increase in n/p ratio towards 1 thus stabilising the nucleus.
 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 26

The crystalline form of borax has

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 26

The structure of anion of borax is 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 27

The compound(s) with TWO lone pairs of electrons on the central atom is(are)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 27

CIF3 abd XeF4 contain two lone pair of electrons on the central atom.

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 28

The reagent(s) that can selectively precipitate S2– from a mixture of S2– and  in aqueous solution is(are)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 28

The reagent that can selectively precipitate S2– and in aqueous solution is CuCl2.

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 29

Positive Tollen’s test is observed for

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 29

Beside aldehyde α-hydroxy ketones can also show Tollen’s test due to rearrangement in aldehyde via ene
diol intermediate. (however this needs a terminal α-carbon)

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 30

The product(s) of the following reaction sequence is (are)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 30

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 31

The correct statement(s) about the following reaction sequence is(are)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 31

Q (not R) is steam volatile due to intramolecular hydrogen bonding.
Q gives violet colouration due to phenolic functional group.
S gives yellow precipitate due to aldehydic group with 2, 4 –DNP.
S does not have free phenolic group to respond to FeCl3 test.

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 32

Inst.

Q, No- 32 to 36 carry 3 marks each

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

Q.

The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm–3. The ratio of the molecular weights of the solute
and solvent,  


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 32


*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 33

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 33

Diffusion coefficient (D) is proportional to both mean free path and mean speed

If T1 is increased 4 times and P1 is increased 2 times.

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 34

In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 34

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 35

The number of geometric isomers possible for the complex 

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 35

Number of geometrical isomers = 5.

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 36

In the following monobromination reaction, the number of possible chiral products is

(enantiomerically pure)


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 36

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 37

Inst.

Q No. 37 - 41 carry 3 marks each

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

Q.

Let   Suppose α1 and β1 are the roots of the equation x2 – 2x secθ + 1 = 0 and α2 and β2 are the roots of the equation x2 + 2x tanθ – 1 = 0. If α1 > β1 and α2 > β2, then α1 + β2 equals

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 37


JEE (Advanced) 2016 Paper - 1 with Solutions - Question 38

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 38

If a boy is selected then number of ways = 4C1.6C3
If a boy is not selcected then number of ways = 6C4
Captain can be selected in 4C1 ways 
Required number of  ways = 

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 39

Let   The sum of all distinct solutions of the equation  in the set S is equal to

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 39



 

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 40

A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective given that it is produced in plant T1) = 10 P(computer turns out to be defective given that it is produced in plant T2), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2 is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 40

E1 : Computer is produced by plant T1
E2 : Computer is produced by plant T2
A : Computer is defective

JEE (Advanced) 2016 Paper - 1 with Solutions - Question 41

The least value of  for which   for all x > 0, is

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 41

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 42

Q. No. 42 - 49 carry 4 marks each

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

Q.

Consider a pyramid OPQRS located in the first octant (x 0, y 0, z 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The bases OPQR of the pyramid is a square with OP = 3. The point S is directly above the mid-point T of diagonal OQ such that TS = 3. Then

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 42

Points O, P, Q, R, S are   respectively.

Angle between OQ and OS is 

Equation of plane containing the points O, Q and S is x ? y = 0
Perpendicular distance from P(3, 0, 0) to the plane

perpenicular distance from O (0,0,0) to the line RS:

 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 43

Let   be a differentiable function such that  Then

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 43





(D) for   f(x) is unbounded function  for 

 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 44

Let where   Suppose Q = [qij] is a matrix such that PQ = kI, where   and I is the identity matrix of order 3. If 

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 44

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 45

In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X, Y, Z, respectively, and  and area of incircle of the triangle XYZ is 8π/3 , then

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 45






 

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 46

A solution curve of the differential equation   passes through the point (1, 3). Then the solution curve

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 46


 



Hence  no solution

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 47

Let   be differentiable functions such that f(x) = x3 + 3x + 2, , then

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 47

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 48

The circle C1 : x2 + y2 = 3, with centre at O, intersects the parabola x2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2√3 and centres Q2 and Q3, respectively. If Q2 and Q3 lie on the y-axis, then

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 48

Equation of tangent at P(√2,1) is √2 x+y-3=0

If centre of C2 at (0, α) and radius equal to 2√3

*Multiple options can be correct
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 49

Let RS be the diameter of the circle x2 + y2 = 1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s)

Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 49

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 50

Q. No. 50 - 55 carry 3 marks each.

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

Q.

The total number of distinct x  R for which is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 50




*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 51

Let m be the smallest positive integer such that the coefficient of x2 in the expansion of (1 + x)2 + (1 + x)3 + for some positive integer n. Then the value of n is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 51



Least positive integer m for which n is an  integer is m = 16 for which n = 5

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 52

The total number of distinct x [0, 1] for which 


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 52

*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 53

Let α,β  be such that  Then 6(α + β) equals


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 53


*Answer can only contain numeric values
JEE (Advanced) 2016 Paper - 1 with Solutions - Question 54

Let   and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P2 = – I is


Detailed Solution for JEE (Advanced) 2016 Paper - 1 with Solutions - Question 54

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