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A particle is projected from point A on the ground at an angle $\theta$ with horizontal. Another particle is projected from point B simultaneously from height 4H above point A with same velocity. A and B are in the same vertical plane, where H is the maximum height attained by the particle A. Both the particles collide at the same time on the ground. Find the angle at which particle B is projected with horizontal:

A wire of length $2L$, is made by joining two wires $A$ and $B$ of the same length, but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in $B$ is $q$ then the ratio $p:q$ is

What is the need of knowing mean and average or the RMS value of current or voltage in a circuit ????

Ac is dangerous or DC ???

The resultant capacitance between the points $\text{A}$ and $\text{B}$ in figure

The temperature coefficient of resistance of a conductor is

What is the value of linear velocity, if $\overrightarrow{\omega }=3\hat{i}-4\hat{j}+\hat{k}$ and $\overrightarrow{r}=5\hat{i}-6\hat{j}+6\hat{k}$

A metal surface experiences ${10}^{-8}\text{N}$ force due to radiation. If its area exposed to radiations is $2{\text{m}}^2$, calculate the wavelength of the radiation (in $\mu \text{m})$.

$($Given: No. of photons incident per second $=5\times {10}^{12})$

Two uniform solid balls of the same density and radii $r$ and $2r$ are dropped in air and are falling vertically downward. The terminal velocity of the ball of radius $r$ is $1\text{cm/s}$, then the terminal velocity of the ball of radius $2r$ will be

Find the angular fringe width in a Young's double slit experiment with green light of wavelength $6000\mathring{A}$. The separation between the slits is $3\times {10}^{-3}\text{m}$.

A
Saturn year is 29.5 times the earth year. How far is the Saturn from
the sun if the earth is 1.50 ×10⁸
km away from the sun?

Find out the magnitude of electric field intensity, $E$ at point $(2,0,0)$ due to a dipole moment, $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin as shown in the figure and also find the potential, $V$ at that point.



$[k=\frac{1}{4\pi {\epsilon }_0}]$

A pulse is travelling on a stretched string fixed at one end with velocity $2\text{cm/s}$ as shown in the figure. At $t=0\text{s}$, center of pulse is $4\text{cm}$ apart from the fixed end. The shape of string at $t=2\text{s}$ is

Calculate the accurate volume of one molecule of water.

A spring is attached to the bottom of an empty swimming pool with the axis of the spring oriented vertically. A $9\text{kg}$ block of wood $({\rho }_w=900{\text{kg/m}}^3)$ is fixed to the top of the spring and compresses it. Then the pool is filled with water completely covering the block. The spring is now observed to be stretched thrice as much as it had been compressed. Determine the percentage of the volume of block which is hollow. Ignore any air in the hollow space.

Find the average velocity of the position function $s\left(t\right)=2t^2-4t$ on the interval from $t=0\text{sec}$ to $t=5\text{sec}$.

Mercury
has an angle of contact equal to 140° with soda lime glass. A
narrow tube of radius 1.00 mm made of this glass is dipped in a
trough containing mercury. By what amount does the mercury dip down
in the tube relative to the liquid surface outside? Surface tension
of mercury at the temperature of the experiment is 0.465 N m^–1.
Density of mercury = 13.6 × 10³
kg m^–3.

A set of parallel rays are incident on the biconvex lens. If after two refractions and one reflection, final image is formed at 15cm from the lens, then the value of $\frac{x}{18}$ is ____ cm.

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1. 2.5

Which of the following is the same as $\sec 53$?

A uniform chain of length $\text{L}$ and mass $\text{M}$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $\text{g}$ is acceleration due to gravity, the work required to pull the hanging part on the table is

A Pneumatic cylinder has a bore of 200 mm and a piston rod diameter of 140 mm. For an extend speed of 5 m/min, the supply flow rate is

The time taken by the galvanic cell which operates almost ideally under reversible conditions at a current of ${10}^{-16}A$ to deliver 1 mole of electron is :

A charge of $-3\text{C}$ is kept at a distance of $6\text{m}$ from a solid metallic sphere of radius $4\text{m}$ as shown in the figure below. The sphere is grounded. What will be the net charge on the surface of the sphere?

A stone is hung in air from a wire which is stretched over a sonometre. The bridges of the sonometre are $L\text{cm}$ apart when the wire is in unison with a tuning fork of frequency $N$. When the stone is completely immersed in water, the length between the bridges is $l\text{cm}$ for re-establishing unison, the specific gravity of the material of the stone is

Let $n_r$ and $n_b$ be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in one second.

A stone thrown upward with a speed $u$ from the top of a tower reaches the ground with a speed $4u$. The height of the tower is

Two blocks $A$ and $B$ having the same mass collide elastically with each other. the velocity of block $A$ before the collision is $10\text{m/s}$. If block $A$ comes to rest after collision, then what was the velocity of block $B$ before the collision?

A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha }_{c}and{\alpha }_s$. On heating, the temperature of the strip goes up by$\Delta$T and the strip bends to form an arc of radius of curvature R. Then R is

The focal length of a concave mirror is $30cm$. Find the distance of the object in front of the mirror, so that the image is three times the size of the object.

A two bus system is as shown below,







Corresponding Z-bus matrix is $Z=\left[\begin{array}{cc}j0.5& j0.5\\ j0.5& j4.5\end{array}\right]$



If the line between bus 1 and bus 2 is replaced with another line having reactance $\left(j2\right)\Omega$, then modified $Z_{bus}$ is

Which one of the following expression is correct for transconductance $\left(g_m\right)$ of a JFET?

A conducting rod $\text{PQ}$ of length $l=2\text{m}$ is moving at a velocity $v=8{\text{ms}}^{-1}$ making an angle ${30}^{\circ }$ with its length. A uniform magnetic field $B=3\text{T}$ exits in a direction perpendicular to the plane of motion. Then

A particle of charge q and mass m moves in a circular orbit of radius r with angular speed $\omega$ . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on