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A Centigrade and Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers a temperature of $140{}^{\circ }\text{F}$. The fall of the temperature as registered by the centigrade thermometer is:

A body is projected up with a speed $V$

along the line of greatest slope of an inclined plane of angle of inclination $\beta$. If the body collides elastically perpendicular to the inclined plane, find the time after which it crosses through its point of projection after collision ?

A straight conducting rod of length $30\text{cm}$ and having a resistance of $0.2\Omega$ is allowed to slide over two parallel thick metallic rails with uniform velocity of $0.2{\text{ms}}^{-1}$ as shown in the figure. The rails are stacked in a horizontal plane. If the horizontal component of earth's magnetic field is $0.3\times {10}^{-4}\text{T}$ and a steady current of $3\mu \text{A}$ is induced through the rod. The angle of dip will be

Train $A$ and train $B$ are running on parallel tracks in the opposite directions with speeds of $36{\text{km h}}^{-1}$ and $72{\text{km h}}^{-1}$, respectively. A person is walking in train $A$ in the direction opposite to its motion with a speed of $1.8{\text{km h}}^{-1}$. The speed $\left({\text{in ms}}^{–1}\right)$ of this person as observed from train $B$ will be close to

A string of length $10\text{cm}$ fixed at one end and free at another end, has its fundamental frequency half that of second overtone for another string fixed at both ends. What will be the length of string fixed at both ends?

(Assume velocity of wave in both strings is same)

What would be the interaction force between two copper spheres each of mass 1 g, separated by distance 1 m, if the total electronic charge in them differed from the total charge of the nuclei by one percent.?

A body of mass m is suspended by two strings making angles $\alpha$ and $\beta$ with the horizontal (as shown in the figure). Find the tensions in the strings?

An observer is moving with one-third of the speed of light towards a stationary microwave source emitting waves at frequency $8\text{GHz}$. What is the frequency of the microwave measured by the observer?

A particle of mass m slides back and forth between the two inclined friction less planes if h is the initial height,then find the time period.

In an L-R circuit connected to a battery of constant e.m.f E, switch S is closed at time t = 0. If e denotes the magnitude of induced e.m.f across inductor and i denotes the current in the circuit at any time t. Then which of the following graphs shows the variation of e with i ?

The relation between speed of sound in moist air $v_m$ and dry air $v_d$ at the same temperature and pressure will be

Find the area of the region bounded by $x^2=16y,y=1,y=4$ and the $y$-axis in the first quadrant.

A block of ice mass 2.0 kg is pushed down an inclined plane of inclination ${37}^{\circ }$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10m/s^2$ If the block started from rest, find the work done$\left(W_f\right)$ by the applied force in the first second, $W_g$ by the weight of the block in the first second and $\left(W_f\right)$ by the frictional force acting on the block in the first second. Take $g=10m/s^2$

The normal reaction $\text{N}$ for a vehicle of $800\text{kg}$ mass, negotiating a turn on a ${30}^{\circ }$ banked road at maximum possible speed without skidding is _____ $\times {10}^3{\text{kg-m/s}}^2$.



Take $\cos {30}^{\circ }=0.87$ and $\mu =0.2$

Four charges $+q,+q,-q\text{and}-q$ are placed respectively at the corners $A,B,C\text{and}D$ of a square of side $a$ arranged in the given order. $E\text{and}F$ are midpoints of side $BC$ and $CD$ respectively. $O$ is the center of the square.



$\left(i\right)$ The electric field at $O$ is



​​​​​​​$[$1 Mark$]$

A
pair of adjacent coils has a mutual inductance of 1.5 H. If the
current in one coil changes from 0 to 20 A in 0.5 s, what is the
change of flux linkage with the other coil?

From a fixed pulley the masses $2\text{kg}$, $1\text{kg}$ and $3\text{kg}$ are suspended as shown in the figure. Find the extension in spring if its stiffness is $k=100\text{N/m}$. Assume the acceleration of $1\text{kg}$ and $3\text{kg}$ to be same.

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

In the equation ΔH=ΔU+PΔV

It is being carried out at constant temperature. How can it be possible that there is no change in pressure but there is change in volume. It also defies Boyle's Law

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair?

A simple pendulum has a time period of 3.0 s. If the point of suspension of the pendulum starts moving vertically upward with a velocity v = Kt where $K=4.4m{s}^{-2}$, the new time period will be (Take $g=10m{s}^{-2}$)

The pressure of an ideal gas varies with volume as $P=\alpha V$, where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes $\text{m}$ times its initial volume. The work done by the gas in the process is

Two identical particles of mass $1\text{kg}$ each go round a circle of radius $R$, under the action of their mutual gravitational attraction. The angular speed of each particle is :

A particle is moving in a straight path with an acceleration $a=bn$, where $b$ is a positive constant $(n\ne -1)$. Assuming particle is at rest at origin at $t=0$, the relation between the velocity and the position$\left(r\right)$ of the particle at time $t=1\text{s}$ is

(Assume SI units)

The power factor of the circuit in below figure is $\frac{1}{\sqrt{2}}$. The capacitance of the circuit is equal to

In the figure shown below, two rods are maintained at the same temperature difference between the ends. As a result, heat is flowing through two rods made of the same material. If the diameters of the rods are in the ratio $1:4$ and their lengths are in the ratio $3:2$, then find the ratio of the rates of flow of heat through them.