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A particle slides on the surface of a fixed smooth sphere starting from the topmost point. Find the angle subtended by the motion of particle from top to the point when it leaves contact with the sphere.

A stone is dropped from the top of a tower and travels 24.5m in the last second of its journey . What is the height of the tower ?

A block of mass $m$ slides without friction down a fixed inclined board of inclination $\alpha$ with the horizontal. After leaving the inclined, the block falls on a cart of mass $M$ filled with sand as shown.
Initial height of the block above the level of the cart is $h$ as shown. The velocity of cart when block drops on it will be

(Assume that block and cart move together, when block drops on to the cart)

Number of visible lines when an electron returns from 5th Orbit upto ground state in H spectrum:

A.5 B. 4. C. 3. D.10

A spherical tungsten piece of radius 1.0 cm is suspended in an evacuated chamber maintained at 300 K. The piece is maintained at 1000 K by heating it electrically. Find the rate at which the electrical energy must be supplied. The emissivity of tungsten is 0.30 and the Stefan constant \sigma is 6.0 $\times {10}^{-8}W{m}^{-2}{K}^{-4}$.

Find the maximum and minimum values of function $y=2x^3-15x^2+36x+11$

A block of mass $5\text{kg}$ is released from rest when compression in spring is $2\text{m}$. Block is not attached with the spring of spring constant $k$, natural length of the spring is $4\text{m}$. The maximum height of the block from the ground is:

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

A simple pendulum of length $l$ has a bob of mass $m$ with a charge $q$ on it. A vertical sheet with surface charge density $\sigma$ passes through the point of suspension $O$. At equilibrium, the string makes an angle $\theta$ with the vertical, then -

The area(in $\text{sq.units}$) included by the curve $x=2y-y^2$ and $y-$ axis is

If $\overrightarrow{A}$ and $\overrightarrow{B}$ acting in such a way that they satisfy the relation,

$|\overrightarrow{A}\times \overrightarrow{B}|=\overrightarrow{A}.\overrightarrow{B}$. Then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

From a canon mounted on a wagon at a height $H$ from the ground, a shell is fired horizontally with a velocity $v_0\text{m/s}$ with respect to canon. The canon and wagon have a combined mass of $M\text{kg}$ and can move freely on the frictionless, horizontal surface. Find the horizontal distance (in $\text{metres}$) between shell and canon, when the shell touches ground.

The binding energy per nucleon for a deuteron and an alpha particle, are $x_1$ and $x_2$ respectively. What will be the energy released in the following reaction?

${}_1{H}^2+{}_1{H}^2\to {}_{2}H{e}^4$

Two trains are coming from opposite directions with speeds of $75\text{km/hr}$ and $100\text{km/hr}$ on two parallel tracks. At some moment, the distance between them is $100\text{km}.$ After $\text{T}$ hours, the distance between them is again $100\text{km}.$ Then $\text{T}$ is equal to

Figure 5.17 shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body? What is the magnitude of each impulse?

Five conducting parallel plates having area $A$ and separation between them $d$ are placed as shown in figure. Plate number $2$ and $4$ are connected and between points $\text{A}$ and $\text{B}$ a cell of emf $E$ is connected. The charge flow through the cell is

If we add vectors A & E. Which of these is the correct result?

A uniform electric field $\left(\overrightarrow{E}\right)$ and magnetic field $\left({\overrightarrow{B}}_0\right)$ exist in a region as shown in figure. Both the fields are mutually perpendicular.



A positively charged particle having charge $q$ and mass $m$ is projected vertically upward, and it's crossed the line $\text{AB}$ after time $t_0$. Find the speed of projection, if the particle moves with constant velocity after time $t_0$.

$($Given, $g$ is acceleration due to gravity, and $qE=mg)$ $($ Here, the electric field and gravity exist everywhere but the magnetic field starts only after crossing the line $AB)$

A rod of length $50\text{cm}$ moves with a speed of $10\text{cm/s}$ in a uniform magnetic field of strength $10\text{G}$ at an angle of ${30}^{\circ }$ with the field. The emf induced across the ends of the rod is -

Can a ball move in hollow semicircular track which is smooth (means no friction)???

The maximum frequency of X-rays produced in an X-ray tube is $v$ when the operating voltage is $V$. What is the maximum frequency of the X-rays when the operating voltage is $\frac{V}{2}$?

A particle of mass $m$ and charge $q$ is projected vertically upwards. A uniform electric field $E$ is acted vertically downwards. The most appropriate graph between potential energy $U$ (gravitational plus electrostatic) and height $h$ ($<<$ radius of earth) is

(Assume $U$ to be zero on surface of earth.)

For the system shown in below figure, all quantities are per phase and are in per unit. If magnitude of voltage at bus-2 is 1 p.u, then the reactive power supplied by the capacitor, $Q_{G2}$ is _________pu.(Answer up to three decimals)

1. 0.268

Two point charges placed at a distance $r$ in the air experiences a certain force, then the distance at which they will experience the same force in the medium of dielectric constant $K$ is.

If ${\lambda }_v,{\lambda }_x,{\lambda }_m$ represent the wavelengths of visible light, $X$-rays and microwaves respectively, then

Find the
unit vector in the direction of the vector.

According to corpuscular theory of light, the different colours of light are due to

Find the slope of the tangent to curve $y=x^3-x+1$ at the point whose x- coordinate is 2.