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A cubical metal block of edge $12\text{cm}$ floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is immersed in it. Height of the water column to be poured is [specific gravity of mercury$=13.6$]

A parallel beam of light is incident from air at an angle as shown on the side $\text{PQ}$ of a right-angled triangular prism of refractive index $n=\sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $\alpha$ has minimum value of ${45}^{\circ }$. The angle $\theta$ of the prism is:


(correct answer + 2, wrong answer - 0.50)

A circuit is shown below.





Currently the switch is in position A and steady current is flowing through circuit. Capacitor is uncharged. At $t=0$, switch is instantly moved to position B.

Find the current in the $LC$ circuit.$\left(\mathrm{Given}\mathrm{that}\omega =\frac{1}{\sqrt{LC}}\right)$

The amplitude of a wave represented by displacement equation $y=\frac{1}{\sqrt{a}}sin\omega t\pm \frac{1}{\sqrt{b}}cos\omega t$ will be

Two resistors with temperature coefficients of resistance ${\alpha }_1$ and ${\alpha }_2$ have resistances $R_1$ and $R_2$ at $0^{\circ }C$. What is the temperature coefficient of the compound resistor consisting of the two resistors connected in parallel?

Water is pumped from a depth of 10 m and delivered through a pipe of cross-section ${10}^{-2}{m}^2$. If it is needed to deliver a volume of ${10}^{-1}{m}^3$ per second, the power required will be:

A single slit of width $b$ is illuminated by a coherent monochromatic light of wavelength $\lambda$. If the second and the fourth minima in the diffraction pattern at a distance $1\text{m}$ from the slit are at $3\text{cm}$ and $6\text{cm}$ respectively from the central maximum, what is the width of the central maximum?

One plate of a capacitor is fixed and the other is connected to a spring as shown in the figure. Area of both the plates is $A$. In steady state (equilibrium), separation between the plates is $0.8d$ (spring was unstretched and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

A uniform rope of length $L$ and mass $M$ is hanging from a rigid support. The tension in the rope at a distance $x$ from the rigid support is

Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

A soap bubble of diameter $8\text{mm}$ is formed in air. If the surface tension of liquid is $30\text{dyne/cm}$, then excess pressure inside the soap bubble is

The dimensions of the quantity $\frac{1}{{ϵ}_0}\frac{e^2}{hc}$ is
e = charge of electron
h = planck’s constant
c = velocity of light
${ϵ}_0$ = permittivity of free space

A cylinder of radius $R$ and length $L$ is placed in a uniform electric field of magnitude $E$ parallel to the axis of the cylinder. The outward flux over the surface of the cylinder is

One plate of a capacitor is fixed and the other is connected to a spring as shown in the figure. Area of both the plates is $A$. In steady state (equilibrium), separation between the plates is $0.8d$ (spring was unstretched and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

An air core solenoid has 1000 turns and is one metre long. Its cross – sectional area is $10c{m}^2$. Its self – inductance is

The amount of solar energy received on the earth's surface per unit time is defined as solar constant. The dimension of solar constant is:

A ray of light is incident normally on one of the faces of a prism of apex angle ${30}^{\circ }$ and refractive index $\sqrt{2}$. The angle of deviation of the ray is

Which combination of magnetic field lines and poles shows two magnets repelling each other?

If a disc with hole is heated why does diameter of hole increase and what happens if the hole is not circular

In the given circuit, the charge on $2\mu \text{F}$ capacitor $($connected to $-ve$ terminal of $25\text{V}$ battery $)$ will be

(Initially, all capacitors are uncharged)

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the range $(40-20000\text{Hz})$
[Assume, speed of sound in air = $340{\text{ms}}^{-1}$]

Given that density of $NaCl$ is nearly $2\times {10}^{3}kg{m}^{-3}$ and molecular weight is $58.5\times {10}^{-3}kgmo{l}^{-1}$. Then calculate the value of $a^3$ for unit cell of sodium chloride.

Here a is edge length of the fcc unit cell.



Take $N_A=6\times {10}^{23}$

Two resistors of $10\Omega$ and $20\Omega$, and an ideal inductor of $10\text{H}$ are connected to a $2V$ battery as shown. The key $K$ is closed at time $t=0$. At the initial $(t=0)$ and final $(t\to \infty )$, the currents through the battery are

A body of mass $\left(4m\right)$ is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(m\right)$ move perpendicular to each other with equal speeds $\left(v\right)$. The total kinetic energy generated due to explosion is