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This mock test of JEE Advanced Mock Test - 4 for JEE helps you for every JEE entrance exam.
This contains 54 Multiple Choice Questions for JEE JEE Advanced Mock Test - 4 (mcq) to study with solutions a complete question bank.
The solved questions answers in this JEE Advanced Mock Test - 4 quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this JEE Advanced Mock Test - 4 exercise for a better result in the exam. You can find other JEE Advanced Mock Test - 4 extra questions,
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QUESTION: 1

This section contains 4 multiple choice questions numbered 1 to 4. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height h from the bottom, the particle will leave the sphere

Solution:

QUESTION: 2

A source is moving on a circle of radius 3 m with constant angular velocity ω = 5 rad/s. If the observer is at a distance 5 m from the centre of circle, the time interval between maximum and minimum frequency received by the observer is

Solution:

QUESTION: 3

In the cyclic process 1-2-3-4 shown in figure for a monoatomic gas, thevolume of the gas in process 1.

Solution:

In a P-V diagram clockwise cyclic process means positive work is done. Here, with non zero anti clockwise area negative work is being done.

W = P∆V

∆V is negative, since, P is positive.

So, the volume decreases.

QUESTION: 4

A capacitor is charged to a potential of V_{0}. It is connected with an inductor through a switch S. The switch is closed at time t = 0. Which of the following statement is correct.

Solution:

*Multiple options can be correct

QUESTION: 5

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct

A disc of radius R rolls on a horizontal surface with linear velocity V and angular velocity ω. There is a point P on circumference of disc at angle θ with upward vertical diameter measured anticlockwise (see figure), which has a vertical velocity. Here θ is equal to

Solution:

*Multiple options can be correct

QUESTION: 6

A source of sound moves along a circle of radius 2 m with constant angular velocity 40 rad/s. Frequency of the source is 300 Hz. A detector is kept at some distance from the circle in the same plane of the circle (as shown in figure). Which of the following is not the possible value of frequency registered by the detector? (Speed of sound = 320 m/s)

Solution:

*Multiple options can be correct

QUESTION: 7

An electron in H-atom jumps from second excited state to first excited state and then from first excited to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively. Then

Solution:

QUESTION: 8

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct

**Paragraph for Question Nos. 10 and 11**

Four satellites A, B, C and D are orbiting around a spherical planet of uniform density. The orbits of all the satellites are coplanar. Orbits of satellites A and B are circular where radius of orbit A is greater than diameter of orbit B. Orbit C is touching orbits A and B. While orbit D is touching orbit A but its nearest distance from the planet is least among all four orbits. All the satellites have same mass and these satellite can be considered as particles. There is no gravitational force between the satellite and also there is no chance of collision between the satellites. Consider gravitational potential energy to be zero under infinite separation.

In which orbit can the gravitational potential energy have least possible value?

Solution:

QUESTION: 9

Four satellites A, B, C and D are orbiting around a spherical planet of uniform density. The orbits of all the satellites are coplanar. Orbits of satellites A and B are circular where radius of orbit A is greater than diameter of orbit B. Orbit C is touching orbits A and B. While orbit D is touching orbit A but its nearest distance from the planet is least among all four orbits. All the satellites have same mass and these satellite can be considered as particles. There is no gravitational force between the satellite and also there is no chance of collision between the satellites. Consider gravitational potential energy to be zero under infinite separation.

In which orbit does the angular momentum have largest magnitude?

Solution:

QUESTION: 10

**Paragraph for Question Nos. 12 and 14**

A thin non-conducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.

The magnitude of induced emf will be

Solution:

QUESTION: 11

A thin non-conducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.

The magnitude of an electric field on the surface of the ring is

Solution:

QUESTION: 12

A thin non-conducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.

Find instantaneous power developed by electric force acting on the ring at t = 1 sec.

Solution:

QUESTION: 13

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following:

Figure shows a set-up to perform Young’s double slit experiment. A monochromatic source of light is placed at S. S_{1} and S_{2} act as coherent sources and interference pattern is obtained on the screen. Match Column-I with Column-II in regard to interference in Young’s double slit

experiment:

Solution:

QUESTION: 14

Referring to the given circuit, match Column-I with Column-II.

Solution:

*Answer can only contain numeric values

QUESTION: 15

This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

The lengths of sides of a cuboid are a, 2a and 3a. If the relative percentage error in the

measurement of a is 1%, then find the relative percentage error in the measurement of volume of cube (in percentage)….

Solution:

*Answer can only contain numeric values

QUESTION: 16

For the arrangement shown in figure, the masses of the blocks are m_{A} = 2 kg, m_{B} = 1 kg, m_{C} = 1 kg. Find the frictional force between the blocks A and B (in Newton) (coefficient of friction between any two surfaces is 0.5)

Solution:

*Answer can only contain numeric values

QUESTION: 17

Suppose potential energy between particle A and B at separation r is given by U = k ln r, where k is constant. For such hypothetical system, find the ratio of energy difference between energy

levels (n = 1 and n = 2) and (n = 2 and n = 4) (The energy of a particle in n^{th} level is –13.6/n^{2})

Solution:

*Answer can only contain numeric values

QUESTION: 18

A uniform disc of radius R having charge Q distributed uniformly all over its surface is placed on a smooth horizontal surface. A magnetic field, B = kxt^{2}, where k is a constant, x is the distance (in metre) from the centre of the disc and t is the time (in second), is switched on perpendicular to the plane of the disc. Find the torque (in N-m) acting on the disc after 15 sec. (Take 4kQ = 1 S.I.unit and R = 1m) is

Solution:

*Answer can only contain numeric values

QUESTION: 19

The hydrogen atom in its ground state are excited by means of monochromatic radiation of

wavelength 1023 Å. Find the number of lines which can be seen in the resulting spectrum…

Solution:

QUESTION: 20

Potash alum contains the metals like potassium and aluminium. What are the metal ions present in chrome alum?

Solution:

QUESTION: 21

For a gaseous reaction, the rate of reaction is expressed in terms of dp/dt instead of dc/dt or dn/dt where C is concentration and n is the number of moles. Hence, the relation between expression is:

Solution:

QUESTION: 22

An excited electron of H-atoms emits of photon of wavelength λ and returns in the ground state, the principal quantum number of excited state is given by:

Solution:

QUESTION: 23

One mole of a monatomic 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:

Here attraction is zero , so potential energy can’t be less than 0

*Multiple options can be correct

QUESTION: 24

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct

Identify the correct relationship:

Solution:

Ni^{2+} complex becomes 3d^{8} with all e^{-} paired.

*Multiple options can be correct

QUESTION: 25

Identify the chiral molecule/molecules:

Solution:

Chiral molecules do not have plane of symmetry

*Multiple options can be correct

QUESTION: 26

The correct statement/statements is/are:

Solution:

QUESTION: 27

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct

**Paragraph for Question Nos. 10 and 11**

The cloud consist of charged particles of water dispersed in air. Some of them are +vely charged and other are -vely charged. When +vely charged clouds come closer they have lightening and thundering whereas - ve and +ve charged colloids come closer they cause heavy rain due to the aggregation of minute particles. It is possible to cause artificial rain by throwing electrified sand or AgI from aeroplane and thus coagulation the mist hanging in air.

When excess of 3 AgNO is treated withKI solution, AgI forms.

Solution:

+vely charged colloid and –vely charged solution

QUESTION: 28

The cloud consist of charged particles of water dispersed in air. Some of them are +vely charged and other are -vely charged. When +vely charged clouds come closer they have lightening and thundering whereas - ve and +ve charged colloids come closer they cause heavy rain due to the aggregation of minute particles. It is possible to cause artificial rain by throwing electrified sand or AgI from aeroplane and thus coagulation the mist hanging in air.

Electrical chimney are made on the principal of

Solution:

Neutralisation of charge of colloidal particle.

QUESTION: 29

**Paragraph for Question Nos. 12 and 14**

Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions-

Compound ' B' should be:

Solution:

QUESTION: 30

Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions-

Compound ' A' should be:

Solution:

QUESTION: 31

Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions-

Compound 'C '

Solution:

QUESTION: 32

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as

illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s

and t; then the correct darkening of bubbles will look like the following:

Match the following metal given in column-I with the appropriate metal exaction process listed

with column- II

Solution:

QUESTION: 33

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as

illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s

and t; then the correct darkening of bubbles will look like the following:

Match the following metal given in column-I with the appropriate metal exaction process listed

with column- II

Solution:

*Answer can only contain numeric values

QUESTION: 34

This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

A saturated solution of spraingly soluble salt MCl_{2} has a vapour pressure of 31.78 mm of Hg at 30^{0}C while pure water exerts a pressure of 31.82 mm of Hg at the same temperature. The

solubility product is . The value of x is

Solution:

*Answer can only contain numeric values

QUESTION: 35

The number of unpaired e^{-} in first excited state of O_{2} is

Solution:

in excited state it is

*Answer can only contain numeric values

QUESTION: 36

The number of geometrical isomers of the octahedral complex of the type [Mabcdef] is n x 3. . The value of n is

Solution:

Total 15 gemetrical isomers

*Answer can only contain numeric values

QUESTION: 37

How many double bond equivalents does amoxicillin (shown below) possesses?

Solution:

QUESTION: 38

Let where [.] denotes the greatest integer function. The value of S is

Solution:

Usemaxima minima concept

QUESTION: 39

Minimum value of function f (x) = x^{3} (x^{3} +1)(x^{3} + 2)(x^{3} + 3) : x ∈ R, is

Solution:

QUESTION: 40

The hands of a clock has lengths 3 & 4 units. The distance between their tips when the distanceis increasing most rapidly is

Solution:

QUESTION: 41

is rotated about O (origin) by 90° such that it crosses the positive y axis during the rotation. If A goes to B then

Solution:

*Multiple options can be correct

QUESTION: 42

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct

In ΔABC, if A = 45^{0}, B = 75^{0} then

Solution:

*Multiple options can be correct

QUESTION: 43

Equation of plane through A(1, 0, 0), B(0,1, 0) and making an angle π/4with the plane x + y = 3 canbe

Solution:

*Multiple options can be correct

QUESTION: 44

If the area bounded by the curve y = x - x^{2} and the line y = mx equals 9/2. Then the value of q m is

Solution:

use graph

QUESTION: 45

This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct

A box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.

Probability that head appears is

Solution:

Use binomial triad for probability

QUESTION: 46

A box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.

Probability that the coin is fair given that head has appeared is

Solution:

QUESTION: 47

ABC is a triangle. Complex numbers z_{1} , z_{2} , z_{3} are represented by A, B, C respectively. Which are in anticlock wise order. let |z_{1}|=|z_{2}|=|z_{3}| and arg

Solution:

Use rotation of complex numbers

QUESTION: 48

Orthocentre H of ΔABC denotes the complex no.

Solution:

Use rotation of complex numbers.

QUESTION: 49

If T(z) is any point such that HBTC is a parallelogram then | z - z_{1} |=

Solution:

Use rotation of complex numbers.

QUESTION: 50

illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s

and t; then the correct darkening of bubbles will look like the following:

Solution:

QUESTION: 51

illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s

and t; then the correct darkening of bubbles will look like the following:

Solution:

*Answer can only contain numeric values

QUESTION: 52

This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

In equilateral triangle ABC of side p, a square is inscribed in its incircle. If area of the square is p^{2}/k then value of k is

Solution:

*Answer can only contain numeric values

QUESTION: 53

f is a function such that f (x) + 2 f (1- x) = x^{2} +1 . Value of f (3) is

Solution:

Replace x by (1-x) solve to get the result

*Answer can only contain numeric values

QUESTION: 54

Degree of differential equation of family of ellipses of same size having minor axis along a given line is

Solution:

See minimum number of unknowns

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