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A capacitor has a capacity $C$ and reactance $X$. If the capacitance and frequency both are doubled, the reactance will become

At high temperature of $727{}^{\circ }C$ a dynamic equilibrium exists between $CO,C{O}_2$ and solid carbon.
$C\left(s\right)+C{O}_2\left(g\right)\rightleftharpoons 2CO\left(g\right)$; $K_c=0.1M$
Then value of $K_p$ at given temperature is:

A diffraction is obtained by using a beam of red light. What will happen if the red light is replaced by the blue light

[KCET 2000; BHU 2001]

A particle is projected with a speed u at an angle $\theta$ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circle ? This radius is called the radius of curvature of the curve at the point.

White light is passed through a prism of angle $5^{\circ }$. If the refractive indices for red and violet colours are 1.641 and 1.659 respectively, the angle of dispersion between them is

A man can row a boat $4km/hr$ in still water. He is crossing a river where the current is $2km/hr$. If the width of the river is $8km$, the time taken by him to cross with zero drift is

A 4-bit ripple counter and a 4-bit synchronous counter are made by flip -flops having a propagation delay of 10 ns each. If the worst case delay in the ripple counter and the synchronous counter be R and S respectively then

The essential difference between an AC generator and a DC generator is that:

For photoelectric effect in a metal, the graph of the stopping potential $V_0\text{(in V)}$ versus frequency $\nu \text{(in Hz)}$ of the incident radiation is shown. The work function of the metal ( $\text{(in eV)}$ is-

In a coil of resistance $10\Omega$, the induced current developed by changing magnetic flux through it, as shown in figure is a function of time. The magnitude of change in flux through the coil in $\text{weber}$ is:

The sun (S') and the planet (P') of an epicyclic gear train shown in the figure have identical number of teeth





If the sun (S') and the outer ring (R) gears are rotated in the same direction with angular speed ${\omega }_S$ and ${\omega }_R$ respectively, then the angular speed of the arm AB is

In the figure shown, all the blocks are of equal mass of $10\text{kg}$ and $F=300\text{N}$. Find the tension in the string $T_{AB}$. Assume all surface to be smooth and $g=10{\text{m/s}}^2$.

An electron gun emits 2.0 $\times {10}^{16}$ electrons per second. What electric current does this correspond to ?

Two blocks of mass m₁ and m₂ interconnected with a spring of stiffness 'k' are kept on a smooth horizontal surface. Which of the following ratios are correct, if the spring was extended and released?

(Where X = displacement, v = speed, P = momentum, a = acceleration, all relative to the surface, KE = kinetic energy, F = force.)

If $y=\sin x$, then $\frac{d^{2}y}{d{x}^2}$ will be

A pendulum with a time period of 1 s is losing energy due to damping. At a certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, find its damping constant.

The pressure exerted by 12g of an ideal gas at t∘C in a vessel of V L volume is 1 atm. When the temperature is increased by 10∘C in the same vessel the pressure increases by 10%. The value of t is.

In this question, we are adding 273 to T₁ and T₂ to convert it to Kelvin scale as it is in Celsius scale.
(1)Then why did we convert it again in the end when we got the answer for T? Isn't it already in the Kelvin scale?
(2) and why has the -ve sign
​​​​emerged in the answer for T?

A uniform rod of length $5\text{m}$ is placed along $x$ - axis as shown in the figure. The position of centre of mass of the rod from the origin is

A proton and an α particle enter perpendicular to a uniform magnetic field with the same speed. The ratio of the radii of their trajectories is

A spherical shell of radius Ra and a solid metal sphere of radius Rb(Ra>Rb)are kept apart and each is given a charge +Q

If the two are connected by a metal wire what is the relation between electric field on their surfaces and ratio between surface charge density

The edges of a parallelepiped are given by the vectors $(3\hat{i}+3\hat{j}+6\hat{k}),4\hat{j}$ and $8\hat{j}+m\hat{k}.$ What should be the value of $m$ in order that the volume of the parallelepiped be 60?

A process exhibits oscillations for a critical gain setting of 10 in a time period of 30 minute. The setting of ziegler-Nichols for $P+I$ controller mode respectively are:

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $\left|\overrightarrow{a}\right|=3,\text{and}\left|\overrightarrow{b}\right|=\frac{\sqrt{2}}{3}.$ If $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector, then the angle between $\overrightarrow{a}$ and$\overrightarrow{b}$ is

Three rods of identical cross - section and lengths are made of three different materials of thermal conductivity $K_1,K_2\text{and}{K}_3,$ respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at ${100}^{\circ }\text{C}$ and the other at $0^{\circ }\text{C}$ (see figure). If the joints of the rod are at ${70}^{\circ }\text{C}$ and ${20}^{\circ }\text{C}$ in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $K_1,K_2\text{and}{K}_3$ is :

Four metallic plates each with a surface area of one side A are placed at a distance d from each other as shown in figure. The capacitance of the system is

1. 97

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ respectively from the horizontal, then answer the following questions: If $v_{1}cos{\theta }_1$ = $v_{2}cos{\theta }_2$, then choose the incorrect statement

The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it

A disc is having an initial angular velocity of $4\text{rad/sec}$ and angular acceleration of $8{\text{rad/sec}}^2$. Find the angle rotated (in radian) by disc in $3\text{sec}$.

Starting from the origin at time $t=0$, with initial velocity $5\hat{j}{\text{ms}}^{-1}$, the particle moves in the $x-y$ plane with a constant acceleration of $(10\hat{i}+4\hat{j}){\text{m/s}}^2$. At time $t$, its coordinates are $(20\text{m},y_0\text{m})$. The values of $t$ and $y_0$ are, respectively:

A spherical cavity of radius $\frac{R}{2}$ is removed from a solid sphere of radius $R$ and the sphere is placed on a rough horizontal surface as shown in the figure. The sphere is given a gentle push and the friction is large enough to prevent slipping. Find the time period of oscillation of the sphere.