In an LC circuit, angular frequency at resonance is $\omega$. The new angular frequency when inductance is made four times and capacitance is made eight times is

$$ \text { The electric flux through the surface } $$

A person observes two moving trains. First reaching the station and another leaves the station with equal speed of $30 \mathrm{~m} / \mathrm{s}$. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air $330 \mathrm{~m} / \mathrm{s}$ )

An open organ pipe and closed organ pipe of same length produce 2 beats per second, when they are set into vibrations together, in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled.

The number of beats produced per second will be (neglect end correction)

A beam of light of intensity $I_0$ falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through $60^{\circ}$ with respect to preceding one. The fraction of the incident light intensity that passes through the system is $\left(\cos 60^{\circ}=\frac{1}{2}\right)$

The angular momentum of a rotating body is ' $L$ '. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

An electric dipole of length 2 cm is placed with its axis making an angle of $60^{\circ}$ to a uniform electric field of $10^{+5} \mathrm{~N} / \mathrm{C}$. If it experiences a torque of $9 \sqrt{3} \mathrm{Nm}$, the magnitude of the charge on the dipole is $\left(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)$

Two inductors of 80 mH each are joined in parallel. The current passing through the combination is 2.1 A . The energy stored in this combination of inductors is

The liquid (mercury) meniscus in capillary tube will be convex if the angle of contact is

A 2.5 V battery is connected to a potentiometer wire. A cell of e.m.f. 1.08 V is balanced by the voltage drop across 2.16 m of wire. The length of the potentiometer wire is

A stone of mass ' m ' kg is tied to a string of length ' $L$ ' $m$ and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take $\pi^2=10$ and acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

A photosensitive surface has work function $\phi$. If photon of energy $3 \phi$ falls on this surface, the electron comes out with maximum velocity of $4 \times 10^6 \mathrm{~m} / \mathrm{s}$ When photon energy is increased to $7 \phi$ then maximum velocity of photoelectron will be

A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' $a$ ' and hole ' $Q$ ' is a circle of radius ' $r$ '. The water flowing out per second from both the holes is same, then side ' $a$ ' of hole ' $P$ ' is

A wire of length ' $L$ ' carries a current ' $I$ '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field $(\overrightarrow{\mathrm{B}})$ is

A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The moment of inertia of a thin uniform rod of mass ' $M$ ' and length ' $L$ ', about an axis perpendicular to length of the rod and at a distance ' $L / 4$ ' from one end is

The potential difference across the 4 capacitor in the following circuit is

The relation between efficiency $(\eta)$ of Carnot engine and coefficient of performance $\left(\eta_1\right)$ of refrigerator is

A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

500 gram of a diatomic gas is enclosed at a pressure of $10^5 \mathrm{Nm}^{-2}$. The density of the gas is $5 \mathrm{kgm}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

In metre-bridge experiment the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$. A shunt of $\mathrm{x} \Omega$ is added to $3 \Omega$ resistor to shift the balance point by 22.5 cm . The value of x is

All the springs in fig. (a), (b) and (c) are identical, each having force constant K each. Mass m is attached to each system. If $\mathrm{T}_a, \mathrm{~T}_b$ and $\mathrm{T}_{\mathrm{c}}$ are the time periods of oscillations of the three systems in fig. (a), (b) and (c) respectively, then

A physical quantity ' X ' is related to four measurable quantities ' $a$ ', ' $b$ ', ' $c$ ' and ' $d$ ' as $\mathrm{X}=\mathrm{a}^2 \mathrm{~b}^3 \mathrm{c}^{5 / 2} \mathrm{~d}^{-2}$. The percentage error in the measurement of 'a', 'b', 'c' and 'd' are $1 \%$, $2 \%, 2 \%$ and $4 \%$ respectively. The percentage error in measurement of quantity ' X ' is

A coil of effective area $3 \mathrm{~m}^2$ is placed at right angles to a magnetic field of induction $0.05 \mathrm{~Wb} / \mathrm{m}^2$ If the field is decreased to $20 \%$ of its original value in 10 second, the e.m.f. induced in the coil will be

Two vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other. When $3 \mathrm{a}+2 \mathrm{~b}=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is

Three immiscible transparent liquids with refractive indices $3 / 2,4 / 3$ and $6 / 5$ are arranged one above the other in a container. The depths of the liquids are $3 \mathrm{~cm}, 4 \mathrm{~cm}$ and 6 cm respectively. The apparent depth of the vessel is

A spherical liquid drop splits in to 729 identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of resulting drops, then $\frac{E}{U}=\frac{1}{x}$. The value of $x$ is

A circular coil carrying current has radius ' $R$ '. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$ th of its value at the centre of the coil is

A point particle of mass 200 gram is executing S.H.M. of amplitude 0.2 m . When the particle passes through the mean position, its kinetic energy is $16 \times 10^{-3} \mathrm{~J}$. The equation of motion of this particle is (Initial phase of oscillation $=0^{\circ}$ )

An inductor of $\left(\frac{100}{\pi}\right) \mathrm{mH}$, capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) \mathrm{F}$ and resistance of $10 \Omega$ are connected in series with an AC voltage source of $110 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The tangent of the phase angle ' $\phi$ ' between voltage and current is

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

A charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up, the total electric flux coming out of the surface

Resolving power of a telescope can be increased by increasing

The ratio of the total energy of the $2^{\text {nd }}$ orbit electron for the hydrogen atom ($^1\mathrm{H}$) to that of a helium ion ($\mathrm{He}^+$) is :

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' $R$ ' from the centre of a star of radius ' $r$ ' is $(R>r)(\sigma=$ Stefan's constant $)$

The magnetic field (B) inside a long solenoid having ' $n$ ' turns per unit length and carrying current ' i ' when iron core is kept in it, is ( $\mu_0=$ permeability of vacuum, $\chi=$ magnetic susceptibility)

A gas having $\gamma=\frac{5}{2}$ and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

In Young's double slit experiment, the intensity on screen at a point, where path difference is $\frac{\lambda}{4}$ is $\frac{K}{4}$. The intensity at a point when path difference is ' $\lambda$ ' will be $\left[\cos \frac{\pi}{2}=0, \cos 2 \pi=1\right]$

When LED is manufactured by using aluminium gallium arsenide (AlGaAs), it emits

A simple pendulum starts oscillating simple harmonically from its mean position ( $\mathrm{x}=0$ ) with amplitude ' $a$ ' and periodic time ' $T$ '. The magnitude of velocity of pendulum at $x=\frac{a}{2}$ is

A coil having ' $N$ ' turns and resistance ' $R$ ' $\Omega$ is connected to a galvanometer of resistance ' 6 R ' $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time ' t ' second. The induced current in the circuit is

Energy of the incident photons on the metal surface is initially 4 W and then 6 W where $W$ is the work function of that metal. The ratio of velocities of emitted photoelectrons is

A ball is dropped on the floor from a height of 20 m . It rebounds to a height of 5 m . Ball remains in contact with floor for 1 s . The average acceleration during contact is (acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )

Which of the following figure represents forward bias diode?

The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

An AND gate is followed by a NOT gate in series. With two inputs ' $A$ ' and ' $B$ ', the Boolean expression for the output ' Y ' will be

A uniform sphere has radius ' $R$ ' and mass ' $M$ '. The magnitude of gravitational field at distances ' $\mathrm{r}_1$ ' and ' $\mathrm{r}_2$ ' from the centre of the sphere are ' $E_1$ ' and ' $E_2$ ' respectively. The ratio $E_1: E_2$ is $\left(r_1>R\right.$ and $\left.r_2