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In a metre bridge, the gaps are closed by resistances $P$ and $Q$, $P$ being less than $Q$. A balance is obtained when the jockey makes contact at a point of bridge wire $40\text{cm}$ from one end. On shunting the coil $Q$ with a resistance of $50\Omega$, the balance point is moved through $10\text{cm}$. The resistance $P$ and $Q$ are

A vector whose initial and terminal points coincide, is called

Which of the following figure represent the behaviour of diamagnetic substance in presence of external magnetic field?

(Note: Yellow dashed lines represents the direction of magnetic field)

A body of mass m accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time t is:

1. 11.055

The distance between the cathode (filament) and the target in an X-ray tube is 1.5 m. If the cutoff wavelength is 30 pm, find the electric field between the cathode and the target.

In a metre bridge experiment, two unknown resistances X and Y are connected to left and right gaps respectively and the balancing point is obtained at 20 cm from right. What will be the new position of the null point from left if one decides to balance a resistance of 4X against Y? (Assume that length of wire of metre bridge is 120 cm.)

A concave and a convex mirror of focal lengths $10\text{cm}$ each are placed at a distance $d\text{cm}$ apart. An object $\text{AB}$ is placed in between the mirrors at a distance of $10\text{cm}$ from the convex mirror. If first ray is incident on the convex mirror and then on the concave mirror then find the distance $d$ between both the mirrors, so that final image will be formed at the object's position.

A $\text{LCR}$ series combination is connected to an $AC$ source. If voltage across the inductor, capacitor, resistor are $40\text{V},80\text{V}$ and $40\text{V}$ respectively. Then the source voltage of the $AC$ source is

Scientists from Indian Space Research Organisation (ISRO) have indigenously developed world’s lightest synthetic material called ‘silica aerogel’ or ‘blue air’. Consider the following properties of Silica Aerogel:

Calculate the maximum kinetic energy of the $\beta$ particle emitted in the following decay equation in $\text{MeV}$.



${}_7{\text{N}}^{12}\to {}_6{\text{C}}^{{12}^{\ast }}+{}_{+1}{e}^0+\nu$

${}_6{\text{C}}^{{12}^{\ast }}\to {}_6{\text{C}}^{12}+\gamma \left(4.43\text{MeV}\right)$



The atomic mass of ${\text{N}}^{12}$ is $12.018613\text{u}$. The atomic mass of ${\text{C}}^{12}$ is $12\text{u}$.

Two concentric spheres of radii $R$ and $2R$ are charged. The inner sphere has a charge of $1\mu \text{C}$ and the outer sphere has a charge of $2\mu \text{C}$ of the same sign. The potential is $9000\text{V}$ at a distance $3R$ from the common centre. The value of $R$ is

A particle moves along the parabolic path $y=2x-x^2+2$, in such a way that the x-component of velocity vector remains constant ($5m/s$). Find the magnitude of acceleration of the particle.

What are harmonies?

A plane mirror is moving with velocity $4\hat{i}+5\hat{j}+8\hat{k}$ . A point object in front of the mirror moves with a velocity $3\hat{i}+4\hat{j}+5\hat{k}$ . Here, $\hat{k}$ is along the normal to the plane mirror and facing towards the object. The velocity of the image is

A point charge 'q' is placed at a distance 'l' from the centre of a disc of radius 'R' along its axis. The electric flux through the disc is

In the given figure a block of mass M and density $\rho$ is immersed in liquid of density $\sigma$. The block is attached to the spring from top and string from bottom. Elongation in the spring when string is tight is x and spring constant is $\frac{Mg}{3x}$.

$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ & & & \left(Tensiondevelopedinstring\right)& & \left(Forcegeneratedinspring\right)\\ \left(I\right)& If\rho =2g/cc& \left(i\right)& T=\frac{4Mg}{3}& \left(P\right)& F=\frac{Mg}{3}\\ & \sigma =1g/cc& & & & \\ \left(II\right)& If\rho =1g/cc& \left(ii\right)& T=\frac{Mg}{3}& \left(Q\right)& F=0\\ & \sigma =1g/cc& & & & \\ \left(III\right)& If\rho =1g/cc& \left(iii\right)& T=\frac{Mg}{2}& \left(R\right)& F=\frac{Mg}{2}\\ & \sigma =2g/cc& & & & \\ \left(IV\right)& If\rho =1.2g/cc& \left(iv\right)& T=0& \left(S\right)& F=\frac{4Mg}{3}\\ & \sigma =0.8g/cc& & & & \end{array}$
Mark the correct combination.

If $y=x^3+2x^2+7x+8$, then $\frac{dy}{dx}$ will be

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. What is the maximum height attained by the ball?

A stone is projected at time t = 0 with a speed $v_0$ and an angle $\theta$ with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as

An excited atom gives up its excess energy by emitting a photon of certain characteristic frequency. The average time period that elapses between the excitation of an atom and the time it radiates is $1.0\times {10}^{-8}s$. What is the inherent uncertainty in the frequency of the photon?

Two identical sized capacitors $C_1$ and $C_2$ are connected to a battery in series. A dielectric slab of dielectric constant $K=2$ is filled in the half region of both the capacitors as shown in figure.









$(C\to$ capacitance, $q\to$ charge stored, $U\to$ energy stored $)$



Match the following column:

An ideal transformer , rated at $6.6\text{kW}$, is used to step up an alternating voltage having peak value of $220\text{V}$ to $4.4\text{kV}$. If the primary coil has $1,000$ turns, find the current rating of the secondary coil.

In 10 seconds the angular speed of a bike increases from 1000rpm to 1800rpm. The angular acceleration of bike is

A ball of mass $m$ is suspended by the string of length $l=2\text{m}$. Another ball of mass $2m$ collides horizontally with ball of mass $m$ with a speed of $u$ so that it completes vertical circle as depicted in the below figure. Find the initial speed of the ball of mass $2m$ before collision.

[Consider, collision is perfectly elastic, take $g=10{\text{ms}}^{-2}$]