Physics

Electrostatics
Current Electricity
Magnetic Effects of Current and Magnetism
Electromagnetic Induction and Alternating Currents
Dual Nature of Matter and Radiation
Physical World and Measurement
Kinematics
Vectors
Laws of Motion
Work, Energy and Power
Motion of System of Particles and Rigid Body
Gravitation
Properties of Bulk Matter
Thermodynamics
Behaviour of Perfect Gas and Kinetic Theory
Oscillations and Waves
Electromagnetic Waves
Optics
Atoms and Nuclei
Electronic Devices & Semiconductor
Communication System
Physics

Chemistry

Hydrocarbons
Chemistry
Some Basic Concepts of Chemistry
Structure of Atom
Classification of Elements and Periodicity in Properties
Chemical Bonding and Molecular Structure
States of Matter: Gases and Liquids
Equilibrium
Redox Reactions
Hydrogen
s-Block Element (Alkali and Alkaline earth metals)
Some p-Block Elements
Organic Chemistry- Some Basic Principles and Techniques
Environmental Chemistry
Solid State
Solutions
Thermodynamics
Electrochemistry
Chemical Kinetics
Surface Chemistry
General Principles and Processes of Isolation of Elements
p-Block Elements
d and f Block Elements
Coordination Compounds
Haloalkanes and Haloarenes
Alcohols, Phenols and Ethers
Aldehydes, Ketones and Carboxylic Acids
Organic Compounds Containing Nitrogen
Amines
Biomolecules
Polymers
Chemistry in Everyday Life

Mathematics

Sets, Relations and Functions
Mathematical Reasoning
Statistics and Probability
Properties of Triangle
Vectors and Three-Dimensional Geometry
Linear Programming
Matrices and Determinants
Mathematics
Trigonometric Ratios & Identities
Algebra
Permutations and Combinations
Coordinate Geometry
Circle and System of Circles
Calculus
Logarithm, Indices, Surds and Partial Fraction
Progressions
Correlation and Regression

Q 1.

Correct4

Incorrect-1

A ship of mass {tex} 3 \times 10 ^ { 7 } \mathrm { kg } {/tex} initially at rest, is pulled by a force of {tex} 5 \times 10 ^ { 4 } \mathrm { N } {/tex} through a distance of {tex} 3 \mathrm { m } {/tex}. Assuming that the resistance due to water is negligible, the speed of the ship is

{tex} 1.5 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 60 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 0.1 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 5 \mathrm { m } / \mathrm { sec } {/tex}

Q 2.

Correct4

Incorrect-1

A block of mass {tex} 2 \mathrm { kg } {/tex} rests on a rough inclined plane making an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal. The coefficient of static friction between the block and the plane is {tex} 0.7 . {/tex} The frictional force on the block is

{tex} 9.8 \mathrm { N } {/tex}

{tex} 0.7 \times 9.8 \times \sqrt { 3 } \mathrm { N } {/tex}

{tex} 9.8 \times \sqrt { 3 } \mathrm { N } {/tex}

{tex} 0.7 \times 9.8 \mathrm { N } {/tex}

Q 3.

Correct4

Incorrect-1

A block of mass {tex}0.1{/tex} is held against a wall applying a horizontal force of {tex} 5 \mathrm { N } {/tex} on the block. If the coefficient of friction between the block and the wall is {tex} 0.5 , {/tex} the magnitude of the frictional force acting on the block is:

{tex} 2.5 \mathrm { N } {/tex}

{tex} 0.98 \mathrm { N } {/tex}

{tex} 4.9 \mathrm { N } {/tex}

{tex} 0.49 \mathrm { N } {/tex}

Q 4.

Correct4

Incorrect-1

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

Q 5.

Correct4

Incorrect-1

An insect crawls up a hemispherical surface very slowly (see fig.). The coefficient of friction between the insect and the surface is {tex} 1 / 3 . {/tex} If the line joining the center of the hemispherical surface to the insect makes an angle {tex} \alpha {/tex} with the vertical, the maximum possible value of {tex} \alpha {/tex} is given by

{tex} \cot \alpha = 3 {/tex}

{tex} \tan \alpha = 3 {/tex}

{tex} \sec \alpha = 3 {/tex}

{tex} \cosec \alpha = 3 {/tex}

Q 6.

Correct4

Incorrect-1

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle {tex} \theta {/tex} should be

{tex} \mathrm { 0 } ^ { \circ } {/tex}

{tex} 30 ^ { \circ } {/tex}

{tex} 45 ^ { \circ } {/tex}

{tex} 60 ^ { \circ } {/tex}

Q 7.

Correct4

Incorrect-1

A string of negligible mass going over a damped pulley of mass {tex} m {/tex} supports a block of mass {tex} M {/tex} as shown in the figure. The force on the pulley by the clamp is given by

{tex} \sqrt { 2 } \mathrm { Mg } {/tex}

{tex} \sqrt { 2 } \mathrm { mg } {/tex}

{tex} \sqrt { ( M + m ) ^ { 2 } + m ^ { 2 } } g {/tex}

{tex} \sqrt { ( M + m ) ^ { 2 } + M ^ { 2 } } g {/tex}

Q 8.

Correct4

Incorrect-1

What is the maximum value of the force {tex} F {/tex} such that the block shown in the arrangement, does not move?

{tex} 20 \mathrm { N } {/tex}

{tex} 10 \mathrm { N } {/tex}

{tex} 12 \mathrm { N } {/tex}

{tex} 15 \mathrm { N } {/tex}

Q 9.

Correct4

Incorrect-1

A block {tex} P {/tex} of mass {tex} m {/tex} is placed on a horizontal frictionless plane. A second block of same mass {tex} m {/tex} is placed on it and is connected to a spring of spring constant {tex} k , {/tex} the two blocks are pulled by distance {tex} A . {/tex} Block {tex} Q {/tex} oscillates without slipping. What is the maximum value of frictional force between the two blocks.

{tex} k A / 2 {/tex}

{tex} k A {/tex}

{tex} \mu _ { S } \mathrm { mg } {/tex}

zero

Q 10.

Correct4

Incorrect-1

The string between blocks of mass {tex} m {/tex} and {tex} 2 { m } {/tex} is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass {tex} 2 m {/tex} and {tex} m {/tex} (immediately after cutting)

{tex} g , g {/tex}

{tex} g , \frac { g } { 2 } {/tex}

{tex} \frac { g } { 2 } , g {/tex}

{tex} \frac { g } { 2 } , \frac { g } { 2 } {/tex}

Q 11.

Correct4

Incorrect-1

Two particles of mass {tex} m {/tex} each are tied at the ends of a light string of length {tex} 2 a {/tex}. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance {tex}^\prime a ^ { \prime } {/tex} from the centre {tex} P {/tex} (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force {tex} F . {/tex} As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes {tex} 2 x , {/tex} is

{tex} \frac { F } { 2 m } \frac { a } { \sqrt { a ^ { 2 } - x ^ { 2 } } } {/tex}

{tex} \frac { F } { 2 m } \frac { x } { \sqrt { a ^ { 2 } - x ^ { 2 } } } {/tex}

{tex} \frac { F } { 2 m } \frac { x } { a } {/tex}

{tex} \frac { F } { 2 m } \frac { \sqrt { a ^ { 2 } - x ^ { 2 } } } { x } {/tex}

Q 12.

Correct4

Incorrect-1

A particle moves in the {tex} X - Y {/tex} plane under the influence of a force such that its linear momentum is {tex} \vec { p } ( t ) = A [ \hat { i } \cos ( k t ) - \hat { j } \sin ( k t ) ] , {/tex} where {tex} A {/tex} and {tex} k {/tex} are constants. The angle between the force and the momentum is

{tex} \mathrm { 0 } ^ { \circ } {/tex}

{tex} 30 ^ { \circ } {/tex}

{tex} 45 ^ { \circ } {/tex}

{tex} 90 ^ { \circ } {/tex}

Q 13.

Correct4

Incorrect-1

A block of base {tex} 10 \mathrm { cm } \times 10 \mathrm { cm } {/tex} and height {tex} 15 \mathrm { cm } {/tex} is kept on an inclined plane. The coefficient of friction between them is {tex} \sqrt { 3 } {/tex}. The inclination {tex} \theta {/tex} of this inclined plane from the horizontal plane is gradually increased from {tex} 0 ^ { \circ } . {/tex} Then

at {tex} \theta = 30 ^ { \circ } , {/tex} the block will start sliding down the plane

the block will remain at rest on the plane up to certain {tex} \theta {/tex} and then it will topple

at {tex} \theta = 60 ^ { \circ } , {/tex} the block will start sliding down the plane and continue to do so at higher angles

at {tex} \theta = 60 ^ { \circ } , {/tex} the block will start sliding down the plane and on further increasing {tex} \theta , {/tex} it will topple at certain {tex} \theta . {/tex}

Q 14.

Correct4

Incorrect-1

A block of mass {tex} m {/tex} is on an inclined plane of angle {tex} \theta . {/tex} The coefficient of friction between the block and the plane is {tex} \mu {/tex} and tan {tex} \theta > \mu {/tex}. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As {tex} P {/tex} is varied from {tex} P _ { 1 } = m g ( \sin \theta - \mu \cos \theta ) {/tex} to {tex} P _ { 2 } = \operatorname { mg } ( \sin \theta + \mu \cos \theta ) , {/tex} the frictional force {tex} f {/tex} versus {tex} P {/tex} graph will look like

Q 15.

Correct4

Incorrect-1

A ball of mass {tex} ( \mathrm { m } ) 0.5 \mathrm { kg } {/tex} is attached to the end of a string having length {tex} ( \mathrm { L } ) {tex} 0.5 \mathrm { m } {/tex}. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is {tex} 324 \mathrm { N } {/tex}. The maximum possible value of anguar velocity of ball (in radian/s) is

9

18

27

36

Q 16.

Correct4

Incorrect-1

The image of an object, formed by a plano-convex lens at a distance of {tex} 8 \mathrm { m } {/tex} behind the lens, is real is one-third the size of the object. The wavelength of light inside the lens is {tex} \frac { 2 } { 3 } {/tex} times the wavelength in free space. The radius of the curved surface of the lens is

{tex} 1 \mathrm { m } {/tex}

{tex} 2 \mathrm { m } {/tex}

{tex} 3 \mathrm { m } {/tex}

{tex} 6 \mathrm { m } {/tex}

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