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This mock test of JEE Main Mock Test 4 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The long wavelength limit of Lyman series is

Solution:

QUESTION: 2

Two particles having mass M and m are moving in a circular having radius R and r. If their time periods are same then the radio of angular velocity will be

Solution:

QUESTION: 3

If A is the mass no. of an element, then volume of the nucleus of an atom of this element is proportional to

Solution:

QUESTION: 4

Which one of the following is not made of soft iron

Solution:

QUESTION: 5

When X-rays pass through a strong uniform magnetic field, then they

Solution:

QUESTION: 6

The r.m.s. value of an a.c. of 50 Hz is 10A. The time taken by a.c. in reaching from zero to maximum value and the peak value of current will be

Solution:

QUESTION: 7

An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ is

Solution:

QUESTION: 8

A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it, but will break if the mass exceeds 25 kg. What is the maximum acceleration, with which the monkey can climb up along the rope? (Take g = 10 m−s⁻^{2})

Solution:
M(g+a)=250N
So a=2.5 ms-Â²

QUESTION: 9

Electric field at the centroid of a triangle carrying q charge at each corner is

Solution:

QUESTION: 10

A ball of wt. 0.1 kg coming with speed 30 m/s strikes with a bat and returns in opposite direction with speed 40 m/s, then impulse is

Solution:

QUESTION: 11

A galvanometer having a resistance of 8 Ω is shunted by a wire of resistance 2 Ω. If the total current is 1 A, then current passing through the shunt will be

Solution:

QUESTION: 12

The logic circuit shown below has the input wave forms '*A*' and '*B*' as shown. Pick out the correct output wave form.

Solution:

QUESTION: 13

A motor boat of mass 300 kg is standing in water. If the area of the bottom surface is 120 m^{2}, then the boat will exert a pressure of (Take g=10 m-s⁻^{2})

Solution:

QUESTION: 14

The function of the moderator in a nuclear reactor is

Solution:

QUESTION: 15

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): In general magnetic force between two charges is much smaller compared to the electric force .

Reason(R): In general velocity of charges << velocity of light in free space.

Solution:

QUESTION: 16

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): Speed of light in water is less than the speed in air.

Reason(R): Refractive index of water is greater than one .

Solution:

QUESTION: 17

For motion in a plane with constant acceleration, a → , initial velocity v 0 → and final velocity ν → after time t, we have

Solution:

QUESTION: 18

The least coefficient of friction for an inclined plane inclined at angle α with horizontal in order that a solid cylinder will roll down it without slipping is

Solution:

QUESTION: 19

A measure of the degree of disorder of a system is known as

Solution:

QUESTION: 20

The energy density and pressure have

Solution:

'Co-efficient of friction' is a physical quantity that has no unit and no dimensions.

Though energy density and pressuire have the same dimensions, they do not share the same units, hence they are different physical quantities.

QUESTION: 21

In young's double slit experiment, the intensity of central maximum is I. It one slit is closed, the intensity at the same place will become

Solution:

QUESTION: 22

In young's double slit experiment, three light, blue, yellow and red are used successively. For which colour, will the fringe width be maximum?

Solution:

QUESTION: 23

A wavefront is an imaginary surface where

Solution:

QUESTION: 24

A transverse progressive wave is given by the equation y = 2 cos [π (0.5x - 200t)], where x and y are in cm and t in sec. Which of the following statement is true for this wave

Solution:

QUESTION: 25

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube ?

Solution:

QUESTION: 26

A condenser is connected across another charged condenser. The energy in the two condenser will be

Solution:

QUESTION: 27

A tachometer is a device to measure

Solution:

QUESTION: 28

In an experiment to measure the internal resistance of a cell, by a potentiometer, it is found that the balance point is at a length of 2 m, when the cell is shunted by a 5 Ω resistance and is at a length of 3m when the cell is shunted by a 10 Ω resistance. The internal resistance of the cell is

Solution:

QUESTION: 29

The figure to the right shows an edge-on view of three extremely large, parallel insulating sheets positively charged with uniform and identical surface charge densities. In which of the regions shown is the electric field a maximum?

Solution:

QUESTION: 30

Cathode rays enter into a uniform magnetic field perpendicular to the direction of the field. In the magnetic field their path will be

Solution:

QUESTION: 31

Methanol is manufactured by

Solution:

QUESTION: 32

1-Phenylethanol can be prepared by reaction of benzaldehyde with

Solution:

QUESTION: 33

Pick out the unsaturated fatty acid from the following

Solution:

QUESTION: 34

For the first order reaction with rate constant k, which expression gives the half-life period? (Initial conc. = a)

Solution:

QUESTION: 35

The element with highest electron affinity among the halogens is

Solution:

As we move from Cl to I, the electron affinity becomes less due to a corresponding increase in their atomic radii. The electron affinity of F is, however, unexpectedly less than that of Cl, because due to its small size, there are electron-electron repulsions in the relatively compact 2p-subshell.

QUESTION: 36

At certain temperature, 50% of HI is dissociated into H_{2} and I_{2}, the equilibrium constant is

Solution:

Let the entire reaction take place in a vessel of Volume V

Given the equation

2HI= I2 + H2

Here let initial moles of HI=N. Moles vanished=y

So at time=0 N= 0 0

At time =t

N-2y= y y

Given 50% of HI dissociates. So conc. of HI left=50%

So we can say

N-2y=50%of N

N-2y=N/2

2y=N-N/2

y=N/4

[I2] =N/4V=[H2]

[HI] =N/2V

So Kc=[I2].[H2]/[HI]^2

Kc=(N^2/16)/(N^2/4) =(N^2x4)/(N^2x16) =4/16 =0.25

QUESTION: 37

Variation of heat of reaction with temperature is known as

Solution:

QUESTION: 38

The shape of cuprammonium ion is

Solution:

QUESTION: 39

Dye test can be used to distinguish between

Solution:

QUESTION: 40

Two platinum electrodes were immersed in a solution of CuSO₄ and electric current was passed through the solution. After sometimes it was found that colour of CuSO₄ disappeared with evolution of gas at the electrode. The colourless solution contains

Solution:

QUESTION: 41

The hydroxide ion concentration of a wine is 8 ´ 10^{–11} M. What is the pH of the wine?

Solution:

QUESTION: 42

The pH of 10 M HCl aqueous solution is

Solution:

QUESTION: 43

The compound whose 0.1 M solutions is basic is

Solution:

QUESTION: 44

The compound whose water solution has the highest pH is

Solution:

QUESTION: 45

The dissociation constant is highest for

Solution:
The dissociation constant is highest for Phenol (C6H5OH). This result can be obtained from the fact that dissociation constant is higher for reactions in which more products are obtained, or the products are more stable.

QUESTION: 46

The order of decreasing ease of reaction with ammonia is

Solution:

QUESTION: 47

Which is not the primary carbocation?

Solution:

QUESTION: 48

Ethane is obtained from ethylene by which of the following methods?

Solution:

QUESTION: 49

Zn converts its melting state to its solid state, it has HCP structure, then find out the nearest number of atoms

Solution:

QUESTION: 50

An element (atomic mass = 100 g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is

Solution:

QUESTION: 51

A solute is soluble in two immiscible liquids which are present in the mixture. The concentration of the solute in the upper layer will be

Solution:

QUESTION: 52

An example of natural biopolymer is

Solution:

QUESTION: 53

Identify the mixture that shows positive deviations from Raoult's law

Solution:

QUESTION: 54

Which of the following is formed when alkyne reacts with water in the presence of sulphuric acid and mercurous acid?

Solution:

QUESTION: 55

The radius of which of the following orbit is same as that of the Bohr's first orbit of hydrogen atom?

Solution:

QUESTION: 56

Which of the following electronic transition in a hydrogen atom will require the largest amount of energy?

Solution:

QUESTION: 57

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283kJ-mol⁻1 respectively. The enthalpy of formation of carbon monoxide is

Solution:

QUESTION: 58

For a second order reaction, the time required for half change is _

Solution:

For a second order reaction.

where a = b

QUESTION: 59

If the length of CO bond in carbon monoxide is 1.128Å, then what is the value of CO bond length in Fe(CO)_{5}?

Solution:

Due to synergic bond formation between metal and CO, the bond order of CO decreases

QUESTION: 60

If nitrogen and sulphur both are present in an organic compound, then during the Lassaigne's test, both will change into

Solution:

QUESTION: 61

220 cannot be the sum of the first n cubes for a suitable n, because 220 is :

Solution:

Sum of n cubes is equal to the square (n+1) square by4

n sq .(n+1) square\4=220

n square.(n+1) square=4Ã—220

here n square can be 4

(n+1) square cannot be equal to 220

Hence b option is correct.

QUESTION: 62

If *'n'* is a positive integer, then *n*^{3} + 2*n* is divisible by

Solution:

QUESTION: 63

The area of the region bounded by the curve y = x - x^{2}between x = 0 and x = 1 is

Solution:

QUESTION: 64

The circle x^{2} + y^{2} + 4x + 6y + 3 = 0 and 2(x^{2}+y^{2}) + 6x + 4y + c = 0 will cut orthogonally if c equals

Solution:

QUESTION: 65

If the circles x^{2} + y^{2} = 9 and x + y + 2ax + 2y + 1 = 0 touch each other, then a is

Solution:

QUESTION: 66

If z₁ and z₂ are two complex numbers, then |z₁ - z₂| =

Solution:

QUESTION: 67

The triangle formed by the points 1, (1 + i)/√2 and i as vertices in the Argand diagram is

Solution:

QUESTION: 68

The solution of y'- y = 1, y(0) = 1 is given by y (x)

Solution:

QUESTION: 69

At x=3, (d/dx)[|x-1|+|x-5|]=

Solution:

QUESTION: 70

The value of n ∈I for which the function f(x) = sinnx/sin(x/n) has 4π as its period is

Solution:

QUESTION: 71

Which of the following is not a statement ?

Solution:

QUESTION: 72

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): If k is odd, then ^{k}C_{r} is maximum for r equal to

Reason(R): The number of combinations of n distinct objects taken r at a time is given by

Solution:

QUESTION: 73

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): The solution of the differential equation

Reason(R): As the integrating factor of given differential equation is (1/y) .

Solution:

QUESTION: 74

If A is a square matrix such that A_{2 }= A, then det equals :

Solution:

QUESTION: 75

How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?

Solution:
The no. is divisible by 5 iff it's unit digit is 0 or 5 but we have only 5 so for unit digit 1 way.

the no. is in b/w 3000&4000 so the no. start with 3 as 1 way

now we have 4 more digit which will be put in 4 and 3 ways to avoid repitition.

total no.is 1Ã—4Ã—3Ã—1=12

the no. is in b/w 3000&4000 so the no. start with 3 as 1 way

now we have 4 more digit which will be put in 4 and 3 ways to avoid repitition.

total no.is 1Ã—4Ã—3Ã—1=12

QUESTION: 76

The line y=mx+c touches the parabola x^{2}=4ay if

Solution:

QUESTION: 77

In a Poisson distribution mean is 16, then S.D. is

Solution:

QUESTION: 78

In a bivariate data ∑x = 30, ∑y = 400, ∑x^{2} = 196, ∑xy = 850 and n = 10. The regression co-efficient of y on x is

Solution:

QUESTION: 79

The perpendicular distance of a line 12x+5y=7 from the origin is

Solution:

QUESTION: 80

The points whose position vectors are 2i+3j+4k, 3i+4j+2k, 4i+2j+3k, then they are

Solution:

QUESTION: 81

If cosA=(3/4) then 32 sin(A/2) cos(5A/2)=

Solution:

QUESTION: 82

The radius of the circle in which the sphere x^{2} + y^{2} + z^{2} + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is

Solution:

QUESTION: 83

The angle at which the two curves x^{3}-3xy^{2}=4 and 3x^{2}y-y^{3}=4 intersect is

Solution:

QUESTION: 84

If the modulus of a is 5 in the direction of north-east and the modulus of b is 5 in the direction of north-west, then |a-b|=

Solution:

QUESTION: 85

Solution:

QUESTION: 86

The value of

Solution:

QUESTION: 87

In the following questions, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the statements carefully and mark the correct answer -

Assertion (A): Sum of n AM's between a and b is

Reason (R): If S_{n} be the sum of n terms of an AP whose first term is a and last term is l, then S_{n} = n2n2(a + l).

Solution:

QUESTION: 88

If A and B are square matrices of equal degree, then which one is correct among the following ?

Solution:

QUESTION: 89

If the function f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0, attains its max. and min. at p and q respectively such that p² = q then a equal

Solution:

QUESTION: 90

The product of n positive numbers is unity, then their sum is :

Solution:

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