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 thin circular ring of mass {tex}M {/tex} and radius {tex} r {/tex} is rotating about its axis with a constant angular velocity {tex} \omega , {/tex} Two objects, each of mass {tex} m , {/tex} are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity

{tex} \frac { \omega M } { ( M + m ) } {/tex}

{tex} \frac { \omega ( M - 2 m ) } { ( M + 2 m ) } {/tex}

{tex} \frac { \omega M } { ( M + 2 m ) } {/tex}

{tex} \frac { \omega ( M + 2 m ) } { M } {/tex}

Q 2.

Correct4

Incorrect-1

Two point masses of {tex} 0.3 \mathrm { kg } {/tex} and {tex} 0.7 \mathrm { kg } {/tex} are fixed at the ends of a rod of length {tex} 1.4 \mathrm { m } {/tex} and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

{tex} 0.42 \mathrm {m} {/tex} from mass of {tex} 0.3 \mathrm { kg } {/tex}

{tex} 0.70 \mathrm { m} {/tex} from mass of {tex} 0.7 \mathrm { kg } {/tex}

{tex} 0.98 \mathrm {m} {/tex} from mass of {tex} 0.3 \mathrm { kg } {/tex}

{tex} 0.98 \mathrm {m} {/tex} from mass of {tex} 0.7 \mathrm { kg } {/tex}

Q 3.

Correct4

Incorrect-1

A smooth sphere {tex} A {/tex} is moving on a frictionless horizontal plane with angular speed {tex} \omega {/tex} and centre of mass velocity {tex} v {/tex}. It collides elastically and head on with an identical sphere {tex} { B } {/tex} at rest. Neglect friction everywhere. After the collision, their angular speeds are {tex} \omega _ { A } {/tex} and {tex} \omega _ { B } , {/tex} respectively. Then

{tex} \omega _ { A } < \omega _ { B } {/tex}

{tex} \omega _ { A } = \omega _ { B } {/tex}

{tex} \omega _ { A } = \omega {/tex}

{tex} \omega _ { \mathrm { B } } = \omega {/tex}

Q 4.

Correct4

Incorrect-1

A disc of mass {tex} M {/tex} and radius {tex} R {/tex} is rolling with angular speed {tex} \omega {/tex} on a horizontal plane as shown in Figure. The magnitude of angular momentum of the disc about the origin {tex} O {/tex} is

{tex} ( 1 / 2 ) M R ^ { 2 } \omega {/tex}

{tex} M R ^ { 2 } \omega {/tex}

{tex} ( 3 / 2 ) M R ^ { 2 } \omega {/tex}

{tex} 2 M R ^ { 2 } \omega {/tex}

Q 5.

Correct4

Incorrect-1

A cubical block of side {tex}a{/tex} is moving with velocity {tex} V {/tex} on a horizontal smooth plane as shown in Figure. It hits a ridge at point {tex} O . {/tex} The angular speed of the block after it hits {tex} O {/tex} is

{tex} 3 V / ( 4 a ) {/tex}

{tex} 3 V / ( 2 a ) {/tex}

{tex} \sqrt { 3 V } / ( \sqrt { 2 a } ) {/tex}

zero

Q 6.

Correct4

Incorrect-1

A long horizontal rod has a bead which can slide along its length and initially placed at a distance {tex} L {/tex} from one end {tex} A {/tex} of the rod. The rod is set in angular motion about {tex} A {/tex} with constant angular acceleration {tex} \alpha . {/tex} If the coefficient of friction between the rod and the bead is {tex} \mu , {/tex} and gravity is neglected, then the time after which the bead starts slipping is

{tex} \sqrt { \mu / \alpha } {/tex}

{tex} \mu / \sqrt { \alpha } {/tex}

{tex} \frac { 1 } { \sqrt { \mu \alpha } } {/tex}

infinitesimal

Q 7.

Correct4

Incorrect-1

A cubical block of side {tex} L {/tex} rests on a rough horizontal surface with coefficient of friction {tex} \mu {/tex}. A horizontal force {tex} F {/tex} is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

infinitesimal

{tex} \mathrm { mg } / 4 {/tex}

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

{tex} \mathrm { mg } ( 1 - \mu ) {/tex}

Q 8.

Correct4

Incorrect-1

A thin wire of length {tex} L {/tex} and uniform linear mass density {tex} \rho {/tex} is bent into a circular loop with centre at {tex} O {/tex} as shown. The moment of inertia of the loop about the axis {tex} X X' {/tex} is

{tex} \frac { \rho L ^ { 3 } } { 8 \pi ^ { 2 } } {/tex}

{tex} \frac { \rho L ^ { 3 } } { 16 \pi ^ { 2 } } {/tex}

{tex} \frac { 5 \rho L ^ { 3 } } { 16 \pi ^ { 2 } } {/tex}

{tex} \frac { 3 \rho L ^ { 3 } } { 8 \pi ^ { 2 } } {/tex}

Q 9.

Correct4

Incorrect-1

An equilateral triangle {tex} A B C {/tex} formed from a uniform wire has two small identical beads initially located at {tex} A {/tex}. The triangle is set rotating about the vertical axis {tex} A O . {/tex} Then the beads are released from rest simultaneously and allowed to slide down, one along {tex} A B {/tex} and the other along {tex} A C {/tex} as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

angular velocity and total energy (kinetic and potential)

Total angular momentum and total energy

angular velocity and moment of inertia about the axis of rotation

total angular momentum and moment of inertia about the axis of rotation

Q 10.

Correct4

Incorrect-1

One quarter sector is cut from a uniform circular disc of radius {tex} R . {/tex} This sector has mass {tex} M . {/tex} It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

{tex} \frac { 1 } { 2 } M R ^ { 2 } {/tex}

{tex} \frac { 1 } { 4 } M R ^ { 2 } {/tex}

{tex} \frac { 1 } { 8 } M R ^ { 2 } {/tex}

{tex} \sqrt { 2 } M R ^ { 2 } {/tex}

Q 11.

Correct4

Incorrect-1

A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are

up the incline while ascending and down the incline descending

up the incline while ascending as well as descending

down the incline while ascending and up the incline while descending

down the incline while ascending as well as descending

Q 12.

Correct4

Incorrect-1

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity {tex} \omega _ { 0 } {/tex}. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform {tex} \omega ( t ) {/tex} will vary with time {tex} t {/tex} as

Q 13.

Correct4

Incorrect-1

A block of mass {tex} m {/tex} is at rest under the action of force {tex} F {/tex} against a wall as shown in figure. Which of the following statement is incorrect?

{tex} f = \mathrm { mg } {/tex}[f friction force]

{tex} F = N{/tex}[{tex}N{/tex} normal force]

{tex} F {/tex} will not produce torque

{tex} N {/tex} will not produce torque

Q 14.

Correct4

Incorrect-1

From a circular disc of radius {tex} R {/tex} and mass {tex} 9 M , {/tex} a small disc of radius {tex} R / 3 {/tex} is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through {tex} O {/tex} is

{tex} 4 M R ^ { 2 } {/tex}

{tex} \frac { 40 } { 9 } M R ^ { 2 } {/tex}

{tex} 10 M R ^ { 2 } {/tex}

{tex} \frac { 37 } { 9 } M R ^ { 2 } {/tex}

Q 15.

Correct4

Incorrect-1

A particle is confined to rotate in a circular path decreasing linear speed, then which of the following is correct?

{tex} \vec { L } {/tex} (angular momentum) is conserved about the centre

only direction of angular momentum {tex} \vec { L } {/tex} is conserved

It spirals towards the centre

its acceleration is towards the centre.

Q 16.

Correct4

Incorrect-1

A solid sphere of mass {tex} M {/tex} and radius {tex} R {/tex} having moment of inertia {tex}I{/tex} about its diameter is recast into a solid disc of radius {tex} r {/tex} and thickness {tex} t {/tex}. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains {tex}I{/tex}. Then {tex} R {/tex} and {tex} r {/tex} are related as

{tex} r = \sqrt { \frac { 2 } { 15 } } R {/tex}

{tex} r = \frac { 2 } { \sqrt { 15 } } R {/tex}

{tex} r = \frac { 2 } { 15 } R {/tex}

{tex} r = \frac { \sqrt { 2 } } { 15 } R {/tex}

Q 17.

Correct4

Incorrect-1

A small object of uniform density rolls up a curved surface with an initial velocity {tex} v {/tex}. It reaches up to a maximum height of {tex} \frac { 3 v ^ { 2 } } { 4 g } {/tex} with respect to the initial position. The object is

ring

solid sphere

hollow sphere

{tex} \mathrm { disc } {/tex}

Q 18.

Correct4

Incorrect-1

A bob of mass {tex} M {/tex} is suspended by a massless string of length {tex} L . {/tex} The horizontal velocity {tex} v {/tex} at position {tex} A {/tex} is just sufficient to make it reach the point {tex} B . {/tex} The angle {tex} \theta {/tex} at which the speed of the bob is half of that at {tex}A {/tex}, satisfies

{tex} \theta = \frac { \pi } { 4 } {/tex}

{tex} \frac { \pi } { 4 } < \theta < \frac { \pi } { 2 } {/tex}

{tex} \frac { \pi } { 2 } < \theta < \frac { 3 \pi } { 4 } {/tex}

{tex} \frac { 3 \pi } { 4 } < \theta < \pi {/tex}

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