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An air bubble in a glass slab $(\mu =1.5)$ appears $3cm$ deep when viewed from one face and $4cm$ when viewed from opposite face, then real thickness of glass slab is

If $\overrightarrow{P}$ and $\overrightarrow{Q}$ are two non-zero vectors, what is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$ ?

A triode valve operates at $V_p=225V$ and $V_R$ = -0.5 V.
The plate current remains unchanged if the plate voltage is increased to 250 V and the grid voltage is decreased to - 2.5 V calculate the amplifiation factor.

The reading of a centigrade thermometer coincides with that of Fahrenheit thermometer for a liquid. The temperature of the liquid $\left(\text{in}{C}^{\circ }\right)$ is

A photon is completely reflected by a surface. If $4\times {10}^{12}$ such photons, having a wavelength of $0.8\text{nm}$ are bouncing back from the surface, the change in momentum of the surface is,

In an electromagnetic wave, the electric and magnetising fields are $100V{m}^{-1}$ and $0.265A{m}^{-1}$. The maximum energy flow is

Figure (8-E7) shows a spring fixed at the bottom end of Ae:.. an incline of inclination. ${37}^{\circ }$ A small block of mass 2 kg starts slipping down the incline from a point 4.8 m away from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 in up the incline. Find (a) the friction : coefficient between the plane and the block and (b) the v spring constant of the spring. Take$g=10m/s^2$

A body is projected into air with a velocity $(8\hat{i}+6\hat{j}){\text{ms}}^{-1}$. If $g=10{\text{ms}}^{-2}$, find the time of flight.

For cubic coordination the value of radius ratio is

Body $A$ of mass $m$ and body $B$ of mass $3m$ move towards each other with velocities $V$ and $2V$ respectively from the positions as shown, along a smooth horizontal circular track of radius $r$. After the first elastic collision, they will collide again after the time

A ball of mass $2.0\text{kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\text{m}$ while applying the force and the ball goes up to $2\text{m}$ height further, find the magnitude of the force. (Consider $g=10{\text{m/s}}^2$)

Moment of inertia of a uniform rod $AB$ about axis $Y{Y}^{\prime }$ as shown in figure is

A car travelling at 36km/h^-1 due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?

A long straight wire is parallel to one edge as shown in figure. If the current in the long wire varies in time as $i=I_0{e}^{-t/\tau }$, what will be the induced emf in the loop ?

A person is standing at a distance $x$ from a jet, its sound level heard by the person is $140\text{dB}.$ If the person moves to a location $10x$ away from the source , then find the loudness intensity of the sound detected by the person at new location (Assume jet as point sized).

A ball is projected upwards from the top of tower with a velocity $50m{s}^{-1}$ making angle ${30}^{\circ }$ with the horizontal. The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground

Light of the wavelength $550\text{nm}$ falls normally on a slit of width $22.0\times {10}^{-5}\text{cm}$. The angular position of the second minima from the central maxima will be :

A ray of light parallel to $x-$axis is incident on a circle $x^2+y^2=R^2$ polished from inside as shown in the figure. Find the co-ordinate of $x\text{and}y$ of the point at which the incident ray should fall such that the reflected ray deviated by ${60}^{\circ }$ after reflection.

The displacement x of a body moving in a straight line is related to time t as $2x^2+3x=t$. If v is the velocity of the body at a certain instant of time, its acceleration will be

The amplitude of a wave represented by displacement equation $y=\frac{1}{\sqrt{a}}sin\omega t\pm \frac{1}{\sqrt{b}}cos\omega t$ will be

What are the coherent sources of light and why do we need coherent sources for the production of interference pattern ?

A 100 Ω
resistor is connected to a 220 V, 50 Hz ac supply.

(a) What is the
rms value of current in the circuit?

(b) What is the
net power consumed over a full cycle?

The angular position of a particle is given by $\theta =2t^2+2t-3$. Find the angular velocity at $t=2\text{sec}$.

The minimum magnifying power of a simple microscope is $19$. What will be its maximum magnifying power?

A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

A metallic bob of weight $100\text{gm}$ is suspended in air. If it is immersed in a liquid at temperature of ${30}^{\circ }\text{C}$, it weighs $90\text{gm}$. When the temperature of the liquid is raised to ${100}^{\circ }\text{C}$, it weighs $90.2\text{gm}$. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is $15\times {10}^{-6}/{}^{\circ }\text{C}$