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The position of an image for the object $O$ is at a distance $nR$ on the concave side of spherical refracting surface from the point $P$ shown in figure. There are two different media present on both sides of spherical surface. The value of $n$ will be :

($R$ is the radius of curvature of the spherical surface).

Two electrical strain gauges are bonded to a duralumin cantilever as shown in below figure (a) and are connected in a bridge circuit as shown in figure (b). Each gauge has a resistance of $100\Omega$ and a gauge factor of $\mathrm{2.1.}$ The resistance of other two arms of the bridge are also $100\Omega$ each. The input voltage is $4V$ and the modulus of elasticity for duralumin is $70GN/m^2$. The output of the circuit $\left(V_0\right)$ when a stress of $200MN/m^2$ is applied to the cantilever is ___ $mV.$

To raise the temperature of a certain mass of gas by $50{}^{\circ }\text{C}$ at a constant pressure, $160\text{calories}$ of heat is required. When the same mass of gas is cooled by $100{}^{\circ }\text{C}$ at constant volume, $240\text{calories}$ of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

A ball rolls off the top of a staircase with velocity u m/s . If the steps are h metre high and b metre wide, the ball will hit the edge of nth step, when

In the given arrangement, if we replace the copper plate connected to the negative terminal of the battery with a carbon rod, which of the following happens?

Calculate the total torque acting on the body shown in figure (10-E2) about the point O.

An amplitude modulated wave is represented by the equation $V_m=5(1+0.6\cos 6280t)\sin (211\times {10}^{4}t)\text{V}$. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :

A car travels first $\frac{1}{3^{\text{rd}}}$ of the distance $AB$ at $30\text{km/h}$, next $\frac{1}{3^{\text{rd}}}$ of the distance at $40\text{km/h}$, last $\frac{1}{3^{\text{rd}}}$ of the distance at $24\text{km/h}$. Its average speed for the whole journey is -

An insect is at the bottom of a hemispherical ditch of radius $1\text{m}$. It crawls up the ditch but start slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is $0.75,$ then $h$ is : ($g=10{\text{ms}}^{-2}$)

The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is

A disc of radius $2m$ and mass $100kg$ rolls on a horizontal floor. Its centre of mass has a speed of $20cm/s$. How much work is needed to stop it ?

A force $F=(3\hat{i}+c\hat{j}+2\hat{k})\text{N}$ acting on a particle causes a displacement of $\overrightarrow{S}=(-4\hat{i}+2\hat{j}-3\hat{k})\text{m}$. If the work done is $6\text{J}$, then the value of ${}^{\prime }{c}^{\prime }$ is

We have an isolated conducting spherical shell of radius 10 cm. Some positive charge is given to it so that resulting electric field has a maximum intensity of $1.8\times {10}^{6}N{C}^{-1}.$ The same amount of negative charge is given to another isolated conducting spherical shell of radius 20 cm. Now, first shell is placed inside the second so that both are concentric as shown in the figure.

The electric field intensity just inside the outer sphere is

On
an open ground, a motorist follows a track that turns to his left by
an angle of 60° after every 500 m. Starting from a given turn,
specify the displacement of the motorist at the third, sixth and
eighth turn. Compare the magnitude of the displacement with the total
path length covered by the motorist in each case.

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x=a(\theta -sin\theta ),y=a(1+cos\theta )$

A $200\text{W}$ and $100\text{W}$ bulbs, both will operate at $220\text{V}$, are connected in series to a $220\text{V}$ power supply. The power consumed by the combination is-

Seven identical circular planar discs, each of mass $M$ and radius $R$ are welded

symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is

What will be the nature of force between B and C if A and B repel each other while A and C attract each other?

When a ray of light is incident at angle of ${60}^{\circ }$to a medium of refractive index n, it is observed that the angle of refraction is half of the angle of incidence. The value of n is

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