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# Test Yourself | Mini Mock 4 for JEE 2021

Attempt now to get your rank among 110 students!

Question 1

Find the moment of inertia of the disk with inner radius 5 cm and outer radius 10 cm about an axis perpendicular to the plane and passing through a point 3cm from the center. Mass of the disk is 10 kg.

Question 2

The moment of inertia of a thin uniform rod about an axis passing through its centre and normal to its length is I0. Then the moment of inertia of the same rod about an axis passing through one end and normal to its length is

Question 3

The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of loop is

Question 4

Particles of masses m, 2m, 3m, ..., nm are placed on the same line at distances L, 2L, 3L,..., nL from 0. The distance of centre of mass from 0 is

Question 5

A square of side ‘a/2’ is cut out from the square of side ‘a’ as show below. Find the centre of mass of the square lamina.

Question 6

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is , the initial angular acceleration of the rod will be :

Question 7

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is

Question 8

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities and . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

Question 9

A wheel has angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2 s it has rotated through an angle (in radian) of :

Question 10

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30 ° with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is :

Question 11

If the K.E. of electron is 2.5 x 10-24 J, then calculate its de-Broglie wavelength?

Question 12

Calculate the velocity of a neutron with a wavelength of 65 pm

Question 13

Find velocity of electron whose wavelength is 7×10-10m. h= 6.626×10-34Js.

Question 14

The fraction of void available in a primitive unit cell is:

Question 15

An element with molar mass 2.7*10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7*103 kg m-3, the nature of the cubic unit cell is:

Question 16

Copper has a face-centred cubic structure with a unit-cell edge length of 3.61Å. What is the size of the largest atom which could fit into the interstices of the copper lattice without distorting it?

(Hint : Calculate the radius of the smallest circle in the figure)

Question 17

Aromatic aldehydes undergoes condensation on heating with an ethanolic solution of KCN. This reaction is called as

Question 18

Identify the final product formed in the following sequence of reactions?

Question 19

End product of following sequence of reaction is

Question 20

Which of the following will not show mutarotation?

Question 21

The equation of the bisector of the acute angle between the lines 3x − 4y + 7 = 0 and 12x + 5y − 2 = 0 is

Question 22

If 2 circles and intersect in 2 distinct points Then:

Question 23

Find the equation of the parabola, which is symmetric about the y-axis and passes through the point P(2, -3).

Question 24

If the reciprocal and modulus of a complex number are  and √13 respectively, then its conjugate will be

Question 25

What is the sum of all three-digit numbers that can be formed using all the digits 3,4 and 5, when repetition of digits is not allowed?

Question 26

Direction: The question has FOUR options. ONLY ONE of these four options is the correct answer.
The principle value of sin–1 is

Question 27

If the quadratic equations and , have a common root, then the value of is

Question 28

Value of is

Question 29

If zr = cos 1, 2, …….up to infinity, then z1 z2 z3..... is equal to

Question 30

The eccentric angle of the point (2,) lying on  is
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