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KEAM Paper 1 Mock Test - 3 - JEE MCQ


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30 Questions MCQ Test KEAM Mock Test Series 2024 - KEAM Paper 1 Mock Test - 3

KEAM Paper 1 Mock Test - 3 for JEE 2024 is part of KEAM Mock Test Series 2024 preparation. The KEAM Paper 1 Mock Test - 3 questions and answers have been prepared according to the JEE exam syllabus.The KEAM Paper 1 Mock Test - 3 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for KEAM Paper 1 Mock Test - 3 below.
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KEAM Paper 1 Mock Test - 3 - Question 1

A box is floating in the river of speed 5m/s. The position of the block is shown in the figure at t = 0. A stone is thrown from point O at time t = 0 with a velocity  Find the value of v1, v such that the stone hits the box.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 1

Position vector of box and stone are 

When stone hits the block,

KEAM Paper 1 Mock Test - 3 - Question 2

Two cannon ball  A and B fall in water (density of balls is 0.6 x 103 Kg/m3 from the height 10m and 25m  respectively. Find the ratio of the depth of ball A and B sink. Assume g=10m/s2
.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 2

For ball A, The velocity of the ball before entering the water surface is 

When ball enters into the water, due to Upthrust of water the velocity of ball decrease (retarded). 

If h be the depth up to which ball sink, then v2 - u2 = 2as

For ball  B, The velocity of the ball before entering the water surface is 

When ball enters into the water, due to Upthrust of water the velocity of ball decrease (retarded).
So retardation,

If h be the depth up to which ball sink, then v2 - u2 = 2as

Ratio of the depth of ball 

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KEAM Paper 1 Mock Test - 3 - Question 3

A light of intensity I0 is incident on a Polaroid which placed at 30º . Find the ratio of the intensity of light after and before polarization, if the light is polarized when Polaroid is at 60º.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 3

Intensity of light after polarization is  Since the light is polarized at angle 60º so the intensity of polarized light is 

KEAM Paper 1 Mock Test - 3 - Question 4

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet, while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g-°C) (1 cal = 4.2 x 107 ergs) is close to

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 4

Given data:
Mass of the bullet, m = 5 g
Velocity of the bullet v = 210 m/s
Specific heat of bullet material, s = 0.030 cal/(g-°C) = 30 cal/(kg-°C)
Considering the given data,

KEAM Paper 1 Mock Test - 3 - Question 5

Carnot's heat engine works with an ideal monoatomic gas, and an adiabatic expansion ratio 5:3. Find the efficiency of Carnot's engine.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 5

Efficiency of the Carnot's engine 

KEAM Paper 1 Mock Test - 3 - Question 6

A wall has two layers A and B ach made of different materials. Both layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36C. The temperature difference across the layer A is:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 6

Consider two walls 'A' and 'B' of thickness 't' each, and thermal conductivity of ' 2K ' and 'K' respectively.
The temperatures at the left of A=Ta, The temperatures at the right of B=Tb, The temperature at the junction 
= T. 

Heat flow is a constant in steady state:

Equating heat flow for both walls we get:  

Which simplifies to:  

Also given that the temperature difference between the walls is 36º C

Combining the two equation in T,Ta,Tb and eliminating Tb

.

KEAM Paper 1 Mock Test - 3 - Question 7

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of system is at a point

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 7

KEAM Paper 1 Mock Test - 3 - Question 8

 two single turn circular loop of wire have radius  20 cm and 2 cm. The loops lies in the same plane and are concentric. Find the mutual inductance of the pair is: 

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 8

Let the current i in the large loop of radius R = 20cm produces a magnetic field of magnitude at its centre. Since the radius r = 2cm of the smaller loop is  r<<R, so we may treat the flux through the small loop as being approximately

So, the mutual inductance of the loop is

KEAM Paper 1 Mock Test - 3 - Question 9

A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 9

Putting values,
Frequency  0.2 x 1010/sec
or Frequency ≌ 1010/sec

KEAM Paper 1 Mock Test - 3 - Question 10

Two identical charged particles each having a mass 10 g and charge 2.0 x 10-7 C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms-2]

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 10

According to given information:

Putting the values, we get
L = 12 cm

KEAM Paper 1 Mock Test - 3 - Question 11

A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m/2 collides with A with a velocity which is half  the instantaneous velocity of A. The collision is completely inelastic. Then the combined body:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 11

KEAM Paper 1 Mock Test - 3 - Question 12

An electrical power line, having a total resistance of 2 Ω, delivers 10 kW at 220 V. The efficiency of the transmission line is approximately

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 12

Efficiency of the transmission line,

Current through the transmission line

Loss in the transmission line, Ploss =I2Rtrans  = 45.452 x 2 = 4,131.405
So, efficiency of the transmission line  
 which is approximately equal to 96%.

KEAM Paper 1 Mock Test - 3 - Question 13

Asymmetric lamina of mass M = 10 kg, consists of a square shape with a semi-circular section over each of the edge of the square as in the figure. The side of the square is 2a=10 m. The moment of inertia of the lamina about an axis through its center of mass and perpendicular to the plane is 25Ma2. Find the radius of gyration about the tangent PQ in the plane of the lamina.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 13

According to the perpendicular axis theorem, 

So,

According to parallel axis theorem, 

KEAM Paper 1 Mock Test - 3 - Question 14

A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt?
[Specific heat of copper: 0.39 J g-1°C-1 and latent heat of fusion of water: 335 J g-1]

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 14

KEAM Paper 1 Mock Test - 3 - Question 15

In the given circuit, charge Qon the 2μF capacitor changes as C is varied from 1μF to 3μF. Q as a function of C  is given properly by:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 15

Let the charge on the capacitor C be Q. Charge on the combination of 1 and 2μF is also Q

As we can see, since C  is between 1 and 3, Q will increase until  C= 3

KEAM Paper 1 Mock Test - 3 - Question 16

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represents the correct relation between A and α when ball goes from Q to R?

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 16

The ball is released from point P as seen in the figure.
We get,

KEAM Paper 1 Mock Test - 3 - Question 17

Which is the correct truth table for the circuit diagram as shown below? Assume that the  'C'  is always  0.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 17

Since C is 0 so the output of both first NAND gates will be 1 and these 1 are the input of other NAND gates.

The truth table of NAND gate:-

KEAM Paper 1 Mock Test - 3 - Question 18

A nucleus of mass M emits γ-ray photon of frequency 'v'. The loss of internal energy by the nucleus is:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 18

KEAM Paper 1 Mock Test - 3 - Question 19

When 5V potential difference is applied across a wire length 0.1 m, the drift speed of electron is 2.5 x 10-4 ms-1 . If the electron density in the wire is 8 x 1028 m-3 , the resistivity of the material is close to

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 19

where, symbols have their usual meaning.

KEAM Paper 1 Mock Test - 3 - Question 20

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 20

on solving (1) & (2), we get
x = 0.865
y = 0.792
Therefore, ΔV = 0.073 V
R = 15Ω (Given)

KEAM Paper 1 Mock Test - 3 - Question 21

In thermodynamics, heat and work are:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 21

Heat and work are treated as path functions in thermodynamics.
ΔQ = ΔU + ΔW
Since work done by gas depends on the type of process, i.e. path, and ΔU depends just on the initial and final states, ΔQ, i.e. heat, also has to depend on path.

KEAM Paper 1 Mock Test - 3 - Question 22

Two gases A and B have equal pressure P, temperature T, and volume V. The two gases are mixed together and the resulting mixture has the same temperature T and volume V as before. The ratio of pressure exerted by the mixture to either of the two gases is:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 22

Let P1 and P2 be the partial pressures of gases A and B, respectively. Under equal conditions of temperature and volume, P1 = P2
Let P be the total pressure exerted by the mixture of two gases A and B. Using Dalton's law of partial pressures, P = P1 + P2
⇒ P = 2P1 ⇒ P/P1 = 2/1 ⇒ P : P1 = 2 : 1

KEAM Paper 1 Mock Test - 3 - Question 23

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 23

KEAM Paper 1 Mock Test - 3 - Question 24

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be:
(Given: gas constant R = 8.3 JK-1 mol-1)

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 24

No. of moles = 44.8/22.4 = 2
The gas is monatomic, so CV = 3/2 R.
ΔQ = nCvΔT
= 2 × 3/2 R × 20
= 60R
= 60 × 8.3
= 498 J

KEAM Paper 1 Mock Test - 3 - Question 25

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 25


ΔQcycle = 40 - 60 = ΔW
⇒ ΔW = -20J = WBC + WCA
⇒ WCA = -20J - WBC
= -20 - (-50)
= 30 J

KEAM Paper 1 Mock Test - 3 - Question 26

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be:

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 26

KEAM Paper 1 Mock Test - 3 - Question 27

A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is:
[Take g = 10 ms-2]

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 27


μ = 0.4
Velocity of the conveyor belt = 2 m/s
Initially, when the bag is dropped on the conveyor belt, it starts slipping.
So, kinetic friction acts on it, due to which it finally stops after some time.
Motion with respect to belt:

KEAM Paper 1 Mock Test - 3 - Question 28

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms-1. [Use g = 10 ms-2]

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 28

Let us assume that both the balls meet at time t.

= 4 sec
Time taken by ball B to meet A = 2 sec
Using, S = ut + 1/2 at2
-80 = -u × 2 + 1/2(-10)(2)2
u = 30 ms-1

KEAM Paper 1 Mock Test - 3 - Question 29

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms-1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is [use g = 9.8 ms-2]

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 29

KEAM Paper 1 Mock Test - 3 - Question 30

A person can throw a ball up to a maximum range of 100 m. How high above the ground can he throw the same ball?

Detailed Solution for KEAM Paper 1 Mock Test - 3 - Question 30

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