A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by ' $l$ '. Another wire of same material of length ' $2 \mathrm{~L}$ ' and radius ' $2 r$ ' is pulled by a force ' $2 f$ '. Then the increase in its length will be :

The position of a particle related to time is given by $x=\left(5 t^{2}-4 t+5\right) \mathrm{m}$. The magnitude of velocity of the particle at $t=2 s$ will be :

The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :

In the given circuit, the current (I) through the battery will be

The de Broglie wavelength of an electron having kinetic energy $\mathrm{E}$ is $\lambda$. If the kinetic energy of electron becomes $\frac{E}{4}$, then its de-Broglie wavelength will be :

In a linear Simple Harmonic Motion (SHM)

(A) Restoring force is directly proportional to the displacement.

(B) The acceleration and displacement are opposite in direction.

(C) The velocity is maximum at mean position.

(D) The acceleration is minimum at extreme points.

Choose the correct answer from the options given below:

Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :

A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600 \mathrm{~nm}$. The value of ' $a$ ' for which first minimum appears at $\theta=30^{\circ}$ on the screen will be :

The position vector of a particle related to time $t$ is given by

$\vec{r}=\left(10 t \hat{i}+15 t^{2} \hat{j}+7 \hat{k}\right) m$

The direction of net force experienced by the particle is :

A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be

(Given $g=$ acceleration due to gravity on the earth.)

A vector in $x-y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $\mathrm{y}$-component of vector is $2 \sqrt{3}$. The magnitude of $x$-component of the vector will be :

The speed of a wave produced in water is given by $v=\lambda^{a} g^{b} \rho^{c}$. Where $\lambda, g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ respectively, are :

For designing a voltmeter of range $50 \mathrm{~V}$ and an ammeter of range $10 \mathrm{~mA}$ using a galvanometer which has a coil of resistance $54 \Omega$ showing a full scale deflection for $1 \mathrm{~mA}$ as in figure.



(A) for voltmeter $R \approx 50 \mathrm{k} \Omega$

(B) for ammeter $\mathrm{r} \approx 0.2 \Omega$

(C) for ammeter $\mathrm{r}=6 \Omega$

(D) for voltmeter $R \approx 5 \mathrm{k} \Omega$

(E) for voltmeter $R \approx 500 \Omega$

Choose the correct answer from the options given below:

A thermodynamic system is taken through cyclic process. The total work done in the process is :

Given below are two statements:

Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.

Statement II : The resistivity of the material is independent of temperature.

In the light of the above statements, choose the correct answer from the options given below :

Match List I with List II of Electromagnetic waves with corresponding wavelength range :

List I	List II
(A) Microwave	(I) $400 \mathrm{~nm}$ to $1 \mathrm{~nm}$
(B) Ultraviolet	(II) $1 \mathrm{~nm}$ to $10^{-3} \mathrm{~nm}$
(C) X-Ray	(III) $1 \mathrm{~mm}$ to $700 \mathrm{~nm}$
(D) Infra-red	(IV) $0.1 \mathrm{~m}$ to $1 \mathrm{~mm}$

Choose the correct answer from the options given below:

A flask contains Hydrogen and Argon in the ratio $2: 1$ by mass. The temperature of the mixture is $30^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases ( $\mathrm{K}$ argon/K hydrogen) is :

(Given: Atomic Weight of $\mathrm{Ar}=39.9$ )

$12 \mathrm{~V}$ battery connected to a coil of resistance $6 \Omega$ through a switch, drives a constant current in the circuit. The switch is opened in $1 \mathrm{~ms}$. The emf induced across the coil is $20 \mathrm{~V}$. The inductance of the coil is :

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^6 \mathrm{~ms}^{-1}$ in an orbit of radius $0.52 \mathrm{~A}^{\circ}$. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

The fundamental frequency of vibration of a string stretched between two rigid support is $50 \mathrm{~Hz}$. The mass of the string is $18 \mathrm{~g}$ and its linear mass density is $20 \mathrm{~g} / \mathrm{m}$. The speed of the transverse waves so produced in the string is ___________ $\mathrm{ms}^{-1}$

In the given figure the total charge stored in the combination of capacitors is $100~ \mu \mathrm{C}$. The value of ' $x$ ' is _________.

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $\left(\right.$ i.e. $\left.\frac{\lambda_{1}}{\lambda_{2}}\right)$ is $\frac{7}{4 n}$, then the value of $n$ will be __________.

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be ___________ $$^\circ$$.

A block of mass $10 \mathrm{~kg}$ is moving along $\mathrm{x}$-axis under the action of force $F=5 x~ N$. The work done by the force in moving the block from $x=2 m$ to $4 m$ will be __________ J.

A network of four resistances is connected to $9 \mathrm{~V}$ battery, as shown in figure. The magnitude of voltage difference between the points $\mathrm{A}$ and $\mathrm{B}$ is __________ $V$.

A $20 \mathrm{~cm}$ long metallic rod is rotated with $210~ \mathrm{rpm}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $0.2 \mathrm{~T}$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____________ $\mathrm{mV}$.

Take $\pi=\frac{22}{7}$

There is an air bubble of radius $1.0 \mathrm{~mm}$ in a liquid of surface tension $0.075~ \mathrm{Nm}^{-1}$ and density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ at a depth of $10 \mathrm{~cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ $\mathrm{Pa}\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $\left(k_{\text {sph }}: k_{\text {cyl }}\right)$ is $2: \sqrt{x}$. The value of $x$ is ____________ .