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JEE (Advanced) 2018 Paper - 2


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54 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE (Advanced) 2018 Paper - 2

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*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 1

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. It's kinetic energy K changes with time as dK/dt = γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 1

(i) force is constant.
(ii) speed is proportional to t
(iii) Force is constant, so it is conservative

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 2

Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u0. Which of the following statements is (are) true?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 2

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 3

An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density λ. It pierces a thin nonconducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ε0. Which of the following statements is (are) true?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 3

Charge inside the spherical shell = λ. 2Rcos 30º = λR √3
So, electric flux = 

 

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 4

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 4

 

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 5

In a radioactive decay chain, Th nucleus decays to  Pb nucleus. Let Nα and Nβ be the number of α and β- particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 5

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 6

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 6

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 7

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4 kg is at rest on this surface. An impulse of 1.0 Ns is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity v(t) = , where v0 is a constant and   The displacement of the block, in meters, at is _________. Take e-1 = 0.37.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 7

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JEE (Advanced) 2018 Paper - 2 - Question 8

A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in metres, is ___________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 8

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JEE (Advanced) 2018 Paper - 2 - Question 9

A particle, of mass 10-3 kg and charge 1.0 C, is initially at rest. At time t = 0, the particle comes under the influence of an electric field , where E0 = 1.0 NC-1 and ω = 103 rad s-1 . Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s-1, attained by the particle at subsequent times is ____________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 9

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JEE (Advanced) 2018 Paper - 2 - Question 10

A moving coil galvanometer has 50 turns and each turn has an area 2 x 10-4 m2. The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is 10-4 N m rad-1. When a current flows through the galvanometer, a full-scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 Ω. This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 - 1.0 A. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is __________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 10

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JEE (Advanced) 2018 Paper - 2 - Question 11

A steel wire of diameter 0.5 mm and Young’s modulus 2 x 1011 Nm-2 carries a load of mass M. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is __________. Take g = 10 ms-2 and is π = 3.2.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 11

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JEE (Advanced) 2018 Paper - 2 - Question 12

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant R = 8.0 J mol-1K-1, the decrease in its internal energy, in Joule, is__________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 12

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JEE (Advanced) 2018 Paper - 2 - Question 13

In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F = n x 10-4 N due to the impact of the electrons. The value of n is __________. Mass of the electron me = 9 x 10-31 kg and 1.0 eV = 1.6 x 10-19 J.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 13

No. of photoelectrons emitted per second

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 14

Consider a hydrogen-like ionized atom with atomic number Z with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n = 1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 eV. The value of Z is __________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 14

JEE (Advanced) 2018 Paper - 2 - Question 15

The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.


       

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 15

JEE (Advanced) 2018 Paper - 2 - Question 16

A planet of mass M, has two natural satellites with masses m1 and m2. The radii of their circular orbits are
R1 and R2 respectively. Ignore the gravitational force between the satellites. Define v1, L1, K1 and T1 to be,
respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite
1; and v2, L2, K2 and T2 to be the corresponding quantities of satellite 2. Given m1/m2 = 2 and R1/R2 = 1/4,
match the ratios in List-I to the numbers in List-II.

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 16

JEE (Advanced) 2018 Paper - 2 - Question 17

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PVdiagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

 

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 17

Process 1 is adiabatic process, hence Q = 0

Process 2 is isobaric, hence W = P.ΔV = 6 P0V0

Process 3 is isochoric, hence W = 0

Process 4 is isothermal.

JEE (Advanced) 2018 Paper - 2 - Question 18

In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimensions and . In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned:  the linear momentum, the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 18

‘P’ is straight line with zero acceleration.
‘Q’ is elliptical path.
‘R’ is circular path
‘S’ is parabolic path

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 19

The correct option(s) regarding the complex (en = H2NCH2CH2NH2) is (are)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 19

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 20

The correct option(s) to distinguish nitrate salts of Mn2+ and Cu2+ taken separately is (are)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 20

Cu2+ shows the characteristic green colour in the flame test.
Ksp of CuS < Ksp of MnS

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 21

Aniline reacts with mixed acid (conc. HNO3 and conc. H2SO4) at 288 K to give P (51%), Q (47%) and R(2%). The major product(s) of the following reaction sequence is (are)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 21

 

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 22

The Fischer presentation of D-glucose is given below

     D-glucose
The correct structures(s) of β - L-glucopyranose is(are)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 22

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 23

For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are Po and Pt, respectively. Initially, only A is present with concentration [A]0, and the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 23

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 24

For a reaction, A ⇌ P, the plots of [A] and [P] with time at temperatures T1 and T2 are given below.

If T2 > T1, the correct statement(s) is (are) (Assume ΔHθ and ΔSθ are independent of temperature and ratio
of lnK at T1 to lnK at T2 is greater than T2/T1. Here H, S, G and K are enthalpy, entropy, Gibbs energy and
equilibrium constant, respectively.)

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 24

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 25

The total number of compounds having at least one bridging oxo group among the molecules given below
is ____.

N2O3, N2O5, P4O6, P4O7, H4P2O5, H5P3O10, H2S2O3, H2S2O5


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 25

 

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 26

Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the
passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo
self-reduction. The weight (in kg) of Pb produced per kg of O2 consumed is ____.
(Atomic weights in g mol-1: O = 16, S = 32, Pb = 207)


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 26

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JEE (Advanced) 2018 Paper - 2 - Question 27

To measure the quantity of MnCl2 dissolved in an aqueous solution, it was completely converted to KMnO4
using the reaction, MnCl2 + K2S2O8 + H2O -->KMnO4 + H2SO4 + HCl (equation not balanced). Few drops
of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was
added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl2 (in mg)
present in the initial solution is ____.
(Atomic weights in g mol−1: Mn = 55, Cl = 35.5)


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 27

Number of meq of MnCl2 = number of meq of KMnO4
= number of meq of H2C2O4
= 5

Weight of MnCl2 taken =  = 126 mg

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 28

For the given compound X, the total number of optically active stereoisomers is ____


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 28

 

 

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 29

In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.
(Atomic weights in g mol–1: H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%) corresponding to the
product in each step is given in the parenthesis)


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 29

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 30

The surface of copper gets tarnished by the formation of copper oxide. N2 gas was passed to prevent the
oxide formation during heating of copper at 1250 K. However, the N2 gas contains 1 mole % of water
vapour as impurity. The water vapour oxidises copper as per the reaction given below:

is the minimum partial pressure of H2 (in bar) needed to prevent the oxidation at 1250 K. The value of
ln  is ____.
(Given: total pressure = 1 bar, R (universal gas constant) = 8 J K-1 mol-1, ln(10) = 2.3. Cu(s) and Cu2O(s)
are mutually immiscible.
At 1250 K: 2Cu(s) + ½ O2(g) --> Cu2O(s); ΔGθ = − 78,000 J mol−1
H2(g) + ½ O2(g) --> H2O(g); ΔGθ = − 1,78,000 J mol−1; G is the Gibbs energy)


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 30

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JEE (Advanced) 2018 Paper - 2 - Question 31

Consider the following reversible reaction,

A(g)+ B(g) ⇌ AB(g)

The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J mol−1 ). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔGƟ (in J mol−1 ) for the reaction at 300 K is ____.

(Given; ln(2) = 0.7, RT = 2500 J mol−1 at 300 K and G is the Gibbs energy)


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 31

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JEE (Advanced) 2018 Paper - 2 - Question 32

Consider an electrochemical cell: A(s) | An+ (aq, 2 M) || B2n+ (aq, 1 M) | B(s). The value of ΔHƟ for the cell reaction is twice that of ΔGƟ at 300 K. If the emf of the cell is zero, the ΔSƟ (in J K−1 mol−1 ) of the cell reaction per mole of B formed at 300 K is ____. (Given: ln(2) = 0.7, R (universal gas constant) = 8.3 J K−1 mol−1 . H, S and G are enthalpy, entropy and Gibbs energy, respectively.) 


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 32

JEE (Advanced) 2018 Paper - 2 - Question 33

Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

The correct option is

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 33

JEE (Advanced) 2018 Paper - 2 - Question 34

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.

(Given, order of migratory aptitude: aryl > alkyl > hydrogen)

 The correct option is

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 34

 

JEE (Advanced) 2018 Paper - 2 - Question 35

LIST-I contains reactions and LIST-II contains major products.

Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option.

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 35

JEE (Advanced) 2018 Paper - 2 - Question 36

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [H+ ] are given in LIST-II.

(Note: Degree of dissociation (α) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [H+ ] represents the concentration of H+ ions)

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 36

JEE (Advanced) 2018 Paper - 2 - Question 37

For any positive integer n, define  as

(Here the inverse trigonometric function tan-1 x assumes values in )

Then, which of the following statement(s) is (are) TRUE?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 37

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 38

Let T be the line passing through the points P(-2, 7) and Q(2, -5). Let F1 be the set of all pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1, S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2. Let E2 be the set of the mid-points of the line segments in the set F2. Then, which of the following statement(s) is (are) TRUE ?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 38

Locus of M is circle center (0, 1) and radius   , excluding points P and Q

=> x2 + y2 – 2y = 39 excluding points P and Q

(–2, 7) is excluded from locus and  does not lie in E1

Locus of point in E2 is circle with diameter (0, 1) and (1, 1), excluding midpoints of chords passing through P or Q

=> x 2 – x + (y – 1)2 = 0

 does not lie in E2 and doesn’t lie in E2 since latter is midpoint of chord through P

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 39

Let S be the set of all column matrices such that b1, b2, bε R and the system of equations (in real variables)

has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each 

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 39

as planes are non parallel is must represent family of planes for solution to exist 

Must be 2x + b + 3z + b3 = 0 which gives μ = 1, b1 + b2 + 3b3 = 0 which is not true always

 

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 40

Consider two straight lines, each of which is tangent to both the circle x2 + y2 = 1/2 and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose center is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is , then which of the following statement(s) is (are) TRUE?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 40

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 41

Let s, t, r be non-zero complex numbers and L be the set of solutions z = x + iy (x, y ε R, i =  ) of the equation , where .Then, which of the following statement(s) is (are) TRUE ?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 41

Eliminating 

(A) L has one element exactly 

(B) s = t = i and r = i => L has no element

(C) Adding both equations 

Which either represents no points or a straight line In either case, number of points of intersection of given circle and L cannot be more than 2

(D) If α and β both satisfy the given equation then any number of form satisfies the given equation where

*Multiple options can be correct
JEE (Advanced) 2018 Paper - 2 - Question 42

Let be a twice differentiable function such that 

If  , then which of the following statement(s) is (are) TRUE ?

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 42

Using L Hospitals rule

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 43

The value of the integral 

 


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 43

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 44

Let P be a matrix of order 3 x 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the maximum possible value of the determinant of P is _____ .


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 44

If 0 is used maximum can only be 4 If 0 not used then by using only {–1, 1} can only form matrix with maximum determinant value 4

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 45

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of    is ________________ .


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 45

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JEE (Advanced) 2018 Paper - 2 - Question 46

Let f : R --> R be a differentiable function with f (0) = 0. If y = f (x) satisfies the differential equation  then the value of  is ____________ .


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 46

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JEE (Advanced) 2018 Paper - 2 - Question 47

Let f : R--> R be a differentiable function with f (0) = 1 and satisfying the equation for all x, y ε R. Then, the value of loge(f (4)) is _____ .


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 47

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JEE (Advanced) 2018 Paper - 2 - Question 48

Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is _______________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 48

Let Q = (0, 0, z1) then P is image of Q in x + y = 3

P = (3, 3, z1)

=> (3)2 + z12 = 25  z1 =4

Length of PR = 2 z1 = 8

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 49

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis,
respectively, where O(0, 0, 0) is the origin. Let  be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If  and  , then the value of  is __________.


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 49

*Answer can only contain numeric values
JEE (Advanced) 2018 Paper - 2 - Question 50

Let where denote binomial coefficients. Then the value of  X is ____________. 


Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 50

JEE (Advanced) 2018 Paper - 2 - Question 51

Let E1 = and E2 =  is a real number Here, the inverse trigonometric function sin 1 x assumes values in  Let  be the function defined by  and be the function defined by 

The correct option is :

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 51

JEE (Advanced) 2018 Paper - 2 - Question 52

In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls
G1, G2, G3, G4, G5.
(i) Let α1 be the total number of ways in which the committee can be formed such that the committee has
5 members, having exactly 3 boys and 2 girls.
(ii) Let α2 be the total number of ways in which the committee can be formed such that the committee has
at least 2 members, and having an equal number of boys and girls.
(iii) Let α3 be the total number of ways in which the committee can be formed such that the committee has
5 members, at least 2 of them being girls.
(iv) Let α4 be the total number of ways in which the committee can be formed such that the committee has
4 members, having atleast 2 girls and such that both M1 and G1 are NOT in the committee together.

The correct option is :

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 52

JEE (Advanced) 2018 Paper - 2 - Question 53

Let H : , where a > b > 0, be a hyperbola in the xy-plane whose conjugate axis LM subtends an angle of 60° at one of its vertices N. Let the area of the triangle LMN be .

The correct option is :

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 53

JEE (Advanced) 2018 Paper - 2 - Question 54

Let and  be functions defined by

 (i) 

(ii)  where the inverse trigonometric function tan1x assumes values in 

(iii)  where, for t ε R, [t] denotes the greatest integer less than or equal to t,

(iv) 

The correct option is :

Detailed Solution for JEE (Advanced) 2018 Paper - 2 - Question 54

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