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A particle is projected from a point O with a velocity u in a direction making an angle $\alpha$ upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is

A square frame of side a in a B - field is reshaped into a ring in T seconds. Find ${ϵ}_{ind}$.

A projectile is to be launched at an angle ${45}^{\circ }$ so that it falls beyond the pond of length $13.6$ $\text{m}$ as shown in the figure and distance between both the points $O$ to $P$ and $M$ to $N$ is $6$ $\text{m}$. What is the range of values of initial velocity (in $m/s$) so that the projectile falls between points $M$ and $N$.

The figure shows the velocity - time graph of a ball of mass $20\text{g}$ moving along a straight line on a table. How much average force does the table exert on the ball to bring it to rest?

In the figure shown, for an angle of incidence 45^{\circ}at the top surface, what is the minimum refractive index needed for total internal reflection at vertical face

An object of mass 1 kg is moving at a speed of 10 m/s. A constant force acts on the object for 4 seconds due to which the speed of object becomes 2 m/s in opposite direction after the force applied is removed. What can be said about the force acting on the object?

A and B are two identical rods of internal resistance $r=1\Omega .$ If $R=2\Omega ,V_A=4m/s,V_B=3m/s$, length of rods is 1 m, then current in R is (Magnetic field is 2T)

A solid sphere of radius $R$ made of a material of bulk modulus $B$ is surrounded by a liquid in a cylindrical container. A massless piston of area $A$ floats on the surface of the liquid. Find the fractional decrease in the radius of the sphere $\left(\frac{\Delta R}{R}\right)$, when a mass $M$ is placed on the piston to compress the liquid.

If C(n,4) = 495. Find n.

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $k$. A mass $m$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $A$ and $Y$ respectively. If the mass is slightly pulled down and released, it will oscillate with a time period $T$ equal to
[Assume that , within the elastic limit, wire behaves as a spring]

Find out the value of resistance $R$ in figure.

The equation of motion of a projectile is given by $y=12x-\frac{3}{4}{x}^2$. The horizontal component of velocity is $3\text{m/s}$. Given that $g=10{\text{m/s}}^2$, what is the range of the projectile?

A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm². 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is

Amplitude of vibrations remains constant in case of
(i) Free vibrations
(ii) Damped vibrations
(iii) Maintained vibrations
(iv) Forced vibrations

The resultant of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. Magnitude of resultant $\overrightarrow{R}$ is equal to $\frac{\sqrt{3}}{2}$ times of the magnitude of $\overrightarrow{B}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}.$

Two trains $A$ and $B$ are moving on same track in opposite direction with velocity $25\text{m/s}$ and $15\text{m/s}$ respectively. When separation between them becomes 225 m, drivers of both the trains apply brakes producing uniform retardation in train $A$ while retardation of train $B$ increases linearly with time at the rate of $0.3{\text{m/s}}^3$. The minimum retardation of train $A$ to avoid collision will be

The maximum longitudinal pitch in bolted joints, subjected to tensile forces will be mm. [Take thickness of plate = 20 mm]

1. 200

A series $LCR$ circuit containing a resistor of resistance $120\Omega$ has resonant frequency $4\times {10}^5\text{rad/s}$. At resonance, the voltage across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively. Find the value of $C$.

A body started with velocity of $10{\text{ms}}^{–1}$ and moving with an acceleration of $1{\text{ms}}^{–2}$. The distance covered by the body in $7^{th}$ second is

A liquid is in
equilibrium with its vapour in a sealed container at a fixed
temperature. The volume of the container is suddenly increased.

a) What is the initial
effect of the change on vapour pressure?

b) How do rates of
evaporation and condensation change initially?

c) What happens when equilibrium is restored finally and what will
be the final vapour pressure?

A particle of mass ${10}^{-2}\text{kg}$ is moving along the positive $x$-axis under the influence of a force $F\left(x\right)=-\frac{\alpha }{8x^2}$, where $\alpha ={10}^{-2}{\text{N.m}}^2$. At time $t=0$, it is at $x=1.0\text{m}$ and velocity is $v=0$. Find the velocity when it reaches $x=0.5\text{m}$. Consider the magnitude along with sign to represent the velocity.

The equation of motion of a projectile are given by x = 36 t metre and 2y = 96 t – 9.8 $t^2$ metre. The angle of projection is

Light is incident on a transparent plastic block at an angle of ${45}^{\circ }$ from air. The speed of light in the plastic is $\frac{c}{\sqrt{2}}$, where $c$ is the speed of light in the vacuum. Find the angle of refraction.

The position vector of a particle changes with time according to the relation $\overrightarrow{r}\left(t\right)=15t^2\hat{i}+(4-20t^2)\hat{j}$. What is the magnitude of the acceleration at $t=1$?

The gravitational force between two particles with masses m and M, initially at rest at great separation, pulls them together. When their separation becomes d, then speed of either particle relative to the other will be :

A nucleus at rest splits into two nuclear parts having mass number in the ratio $1:2$. Their velocities are in the ratio