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A $5.0\mu \text{F}$ capacitor having a charge of $20\mu \text{C}$ is discharged through a wire of resistance of $5.0\Omega$. Find the heat dissipated in the wire between $25\mu \text{s}$ to $50\mu \text{s}$ after the connections are made. (Take, $1/e^2=0.135)$

Four point objects of mass $m$ are located at the corners of a square of side $\text{S}$ as shown in the figure below. Determine the moment of inertia of this system about $\text{cd}$ as shown in the figure.

An electric dipole of length $2\text{cm}$ is placed with its axis making an angle of ${30}^{\circ }$ to a uniform electric field having intensity ${10}^5\text{N/C}$. If it experiences a torque of $10\sqrt{3}\text{N-m}$, then the potential energy of the dipole is

A time varying force $F=10\sqrt{2}t$ starts acting on the $3\text{kg}$ block kept on a rough horizontal surface $(\mu =0.2)$ at $t=0$. Find the time when the horizontal motion begins.

(Take $g=10{\text{m/s}}^2$)

A vertical disc of mass $5\text{kg}$ and radius $50\text{cm}$ rests against a step of height $25\text{cm}$ as shown in the figure. What is the minimum horizontal force applied perpendicular to the axis which will make the disk to climb the step? $(g=10{\text{m/s}}^2)$

In an LC oscillator circuit, $L=10\text{mH},C=40\mu \text{F}$. At $t=0$, the capacitor is fully charged with $q_0=4\mu \text{C}$. Find the current in the circuit, when the capacitor and inductor share energies equally.

If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=5$ and $|\overrightarrow{a}\times \overrightarrow{b}|=8,$ then $|\overrightarrow{a}\cdot \overrightarrow{b}|$ is equal to

If the distance between centers of earth and moon is D and the mass of earth is 81 times the mass of moon, then at what distance from centre of earth the gravitational force will be zero

A block of mass $m$ is located on a horizontal plane. The block acquires a horizontal velocity $v_0$ due to friction. Find the mean power developed by the friction force during the motion of the body. The frictional cofficient is $\mu =0.3,m=2\text{kg}$ and $v_0=5\text{m/s}$ (Take $g=10{\text{m/s}}^2$)

Identify the operation performed by the circuit given below.

1. NOT

2. OR

3. AND

4. NAND

The temperature $\left(T\right)$ and dependence of resistivity $\left(\rho \right)$ of a semiconductor is represented by,

A variable air gap type capacitor consists of two parallel plates : a fixed plate and a moving Plate at a distance x. If a potential voltage is applied across the two plates, then force of attraction between the plates is related to x as

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

A potential difference of 20 kV is plied across and X - ray tube. The minimum wavelength of X-rays generated is ___Å. (IIT JEE 1996)

A block slides along a track from one level to another level, by moving through an intermediate valley. Find the maximum value of $h$ (height) that the block can reach, if the initial speed of the block is $v_0$. (Assume track is frictionless)

Consider two solid spheres $\text{P}$ and $\text{Q}$ each of density $8{\text{g/cm}}^3$ and diameter $1\text{cm}$ and $0.5\text{cm}$, respectively. Sphere $\text{P}$ is dropped into a liquid of density $0.8{\text{g/cm}}^3$ and viscosity $\eta =3\text{Poiseuille}$. Sphere $\text{Q}$ is dropped into a liquid of density $1.6{\text{g/cm}}^3$ and viscosity $\eta =2\text{Poiseuille}$. The ratio of the terminal velocities of $\text{P}$ and $\text{Q}$ is

Which of the following graphs correctly shows the variation of magnetic field intensity (B) with perpendicular distance (r) for a thin long straight wire carrying a current?



निम्नलिखित में से कौनसा आरेख एक पतले लम्बे सीधे धारावाही तार के लिए लम्बवत् दूरी (r) के साथ चुम्बकीय क्षेत्र तीव्रता (B) के परिवर्तन को सही रूप से दर्शाता है?

A particle is projected vertically upwards with speed $20\text{m/s}$ from top of a tower of height $20\text{m}$ as shown in figure. Given $B$ is top most point of trajectory and $C$ is at same height as $A$ :
$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ \left(A\right)& \text{ratio of maximum height from ground (BD)}& \left(P\right)& \frac{1}{\sqrt{2}}\\ & \text{to the initial height from ground (AD)is}& & \\ \left(B\right)& \text{ratio of distance travelled in 1}{}^{st}\text{second to}& \left(Q\right)& \frac{1}{\sqrt{3}}\\ & \text{the distance travelled in 2}{}^{nd}\text{second is}& & \\ \left(C\right)& \text{ratio of initial speed at A to the final}& \left(R\right)& 1\\ & \text{just before reaching to ground (D) is}& & \\ \left(D\right)& \text{ratio of time taken from A to C and time}& \left(S\right)& 2\\ & \text{taken from A to B is}& & \\ & & \left(T\right)& 4\\ & & \left(U\right)& 3\end{array}$
Which of the following option has the correct combination considering column-I and column-II

A sphere of radius $4\text{cm}$ is removed from a sphere of radius $8\text{cm}$ as shown in figure. If $\text{O}$ is the $COM$ of the complete sphere, the position of $COM$ of the remaining sphere will shift towards left from $\text{O}$ by

A block of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the first block through another string. Find the tensions in the two strings. Take g = $10m/s^2$.

A body is freely falling under the action of gravity. It covers half the total distance in the last second of its fall. If it falls for $n$ second, then the value of $n$ is

Two particles move parallel to $x-$ axis about the origin with the same amplitude and frequency. At a certain instant, they are found at distance $\frac{A}{3}$ from the origin on opposite sides, but their velocities are found to be in the same direction. Find the phase difference between the two particles.

The velocity $\upsilon$ (in cm/s) of a particle is given in terms of time (t) by the equation: $\upsilon =at+\frac{b}{t+c}.$ Dimensions of a, b and c are

A block of mass m is suspended through a spring of spring constant k and is in equilibrium. A sharp blow gives the block an initial downward velocity v. How far below the equilibrium position, the block comes to an instantaneous rest?

A squre loop of side l, mass m and resistance R falls vertically into a uniform magnetic field directed perpendicular to the plane of the coil. One of the sides of the coil is always outside the magnetic field. The height h through which the loop falls so that it attains terminal velocity on entering the region of magnetic field is given by

There is an insulator of length $L$ and of negligible mass with two small balls of mass $m$ and electric charge $q$ attached to its ends. The rod can rotate in the horizontal plane around a vertical axis crossing it at a distance $\frac{L}{4}$ from one of its ends. A uniform electric field $E$ exists in the region as shown in the figure. Find the time period for the small oscillations of the rod.