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

If a machine is lubricated with oil

the mechanical advantage of the machine increases.

the mechanical efficiency of the machine increases.

both its mechanical advantage and efficiency increase.

its efficiency increases, but its mechanical advantage decreases.

Q 2.

Correct4

Incorrect-1

Two masses of 1 {tex} \mathrm { gm } {/tex} and 4 {tex} \mathrm { gm } {/tex} are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

{tex}4:1{/tex}

{tex} \sqrt { 2 }: 1 {/tex}

{tex}1:2{/tex}

{tex}1:16{/tex}

Q 3.

Correct4

Incorrect-1

A particle of mass {tex} \mathrm { m } {/tex} is moving in a circular path of constant radius {tex} r {/tex} such that its centripetal acceleration {tex} a _ { c } {/tex} is varying with time {tex} t {/tex} as {tex} a _ { c } = k ^ { 2 } r t ^ { 2 } {/tex} where {tex} k {/tex} is a constant. The power delivered to the particles by the force acting on it is:

{tex} 2 \pi m k ^ { 2 } r ^ { 2 } t {/tex}

{tex} m k ^ { 2 } r ^ { 2 } t {/tex}

{tex} \frac { \left( m k ^ { 4 } r ^ { 2 } t ^ { 5 } \right) } { 3 } {/tex}

zero

Q 4.

Correct4

Incorrect-1

A spring of force-constant {tex} k {/tex} is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of

{tex} ( 2 / 3 ) k {/tex}

{tex} ( 3 / 2 ) k {/tex}

{tex} 3 k {/tex}

{tex} 6 k {/tex}

Q 5.

Correct4

Incorrect-1

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed {tex} v , {/tex} the electrical power output will be proportional to

{tex} v {/tex}

{tex} v ^ { 2 } {/tex}

{tex} v ^ { 3 } {/tex}

{tex} v ^ { 4 } {/tex}

Q 6.

Correct4

Incorrect-1

A particle, which is constrained to move along the {tex} x {/tex} -axis, is subjected to a force in the same direction which varies with the distance {tex} x {/tex} of the particle from the origin as {tex} F ( x ) = - k x + a x ^ { 3 } . {/tex} Here {tex} k {/tex} and {tex} a {/tex} are positive constants. For {tex} x \geq 0 , {/tex} the functional form of the potential energy {tex} U ( x ) {/tex} of the particle is

Q 7.

Correct4

Incorrect-1

An ideal spring with spring-constant {tex} k {/tex} is hung from the ceiling and a block of mass {tex} M {/tex} is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

{tex} \frac { 4 M g } { k } {/tex}

{tex} \frac { 2 M g } { k } {/tex}

{tex} \frac { M g } { k } {/tex}

{tex} \frac { M g } { 2 k } {/tex}

Q 8.

Correct4

Incorrect-1

If {tex} W _ { 1 } , W _ { 2 } {/tex} and {tex} W _ { 3 } {/tex} represent the work done in moving a particle from {tex} A {/tex} to {tex} B {/tex} along three different paths {tex} 1,2 {/tex} and {tex}3{/tex} respectively (as shown) in the gravitational field of a point mass {tex} m , {/tex} find the correct relation between {tex} W _ { 1 } , W _ { 2 } {/tex} and {tex} W _ { 3 } {/tex}

{tex} W _ { 1 } > W _ { 2 } > W _ { 3 } {/tex}

{tex} W _ { 1 } = W _ { 2 } = W _ { 3 } {/tex}

{tex} W _ { 1 } < W _ { 2 } < W _ { 3 } {/tex}

{tex} W _ { 2 } > W _ { 1 } > W _ { 3 } {/tex}

Q 9.

Correct4

Incorrect-1

A particle is acted by a force {tex} F = k x , {/tex} where {tex} k {/tex} is a +ve constant. Its potential energy at {tex} x = 0 {/tex} is zero. Which curve correctly represents the variation of potential energy of the block with respect to {tex} x {/tex}

Q 10.

Correct4

Incorrect-1

A block {tex} ( B ) {/tex} is attached to two unstretched springs {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} with spring constants {tex} k {/tex} and {tex} 4 k , {/tex} respectively (see fig. I). The other ends are attached to identical supports {tex} M _ { 1 } {/tex} and {tex} M _ { 2 } {/tex} not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The (figure II) and released. The block returns and moves a maximum distance {tex} y {/tex} towards wall {tex} 2 . {/tex} Displacements {tex} x {/tex} and {tex} y {/tex} are measured with respect to the equilibrium position of the block {tex} B {/tex}. The ratio {tex} y / x {/tex} is -

{tex} 4 {/tex}

{tex} 2 {/tex}

{tex} 1 / 2 {/tex}

{tex} 1 / 4 {/tex}

Q 11.

Correct4

Incorrect-1

Two small particles of equal masses start moving in opposite directions from a point {tex} A {/tex} in a horizontal circular orbit. Their tangential velocities are {tex} v {/tex} and {tex} 2 v {/tex}, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at {tex} A , {/tex} these two particles will again reach the point {tex} A ? {/tex}

4

3

2

1

Q 12.

Correct4

Incorrect-1

A piece of wire is bent in the shape of a parabola {tex} y = k x ^ { 2 } {/tex} (y-axis vertical) with a bead of mass {tex} m {/tex} on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the {tex} x {/tex} -axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the {tex} y {/tex} -axis is

{tex} \frac { a } { g k } {/tex}

{tex} \frac { a } { 2 g k } {/tex}

{tex} \frac { 2 a } { g k } {/tex}

{tex} \frac { a } { 4 g k } {/tex}

Q 13.

Correct4

Incorrect-1

A block of mass {tex} 2 \mathrm { kg } {/tex} is free to move along the x-axis. It is at rest and from {tex} \mathrm { t } = 0 {/tex} onwards it is subjected to a time-dependent force {tex} F ( t ) {/tex} in the {tex} x {/tex} direction. The force {tex} F ( t ) {/tex} varies with {tex} t {/tex} as shown in the figure. The kinetic energy of the block after {tex}4.5{/tex} seconds is

{tex} 4.50 \mathrm { J } {/tex}

{tex} 7.50 \mathrm { J } {/tex}

{tex} 5.06 \mathrm J {/tex}

{tex} 14.06 \mathrm { J } {/tex}

Q 14.

Correct4

Incorrect-1

The work done on a particle of mass {tex} m {/tex} by a force,

{tex} K \left[ \frac { x } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } } \hat { i } + \frac { y } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } } \hat { j } \right] {/tex}

(K being a constant of appropriate dimensions), when the particle is taken from the point (a,0) to the point (0, a) along a circular path of radius a about the origin in the x–y plane is

{tex} \frac { 2 K \pi } { a } {/tex}

{tex} \frac { K \pi } { a } {/tex}

{tex} \frac { K \pi } { 2 a } {/tex}

0

Q 15.

Correct4

Incorrect-1

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy {tex} K {/tex} with time {tex} t {/tex} most appropriately? The figure are only illustrative and not to the scale.

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