On a temperature scale \(X\). The boiling point of water is \(65^{\circ} X\) and the freezing point is \(-15^{\circ} X\). Assume that the \(X\) scale is linear. The equivalent temperature corresponding to \(-95^{\circ} X\) on the Farenheit scale would be \(..........^{\circ} F\)

An object of mass ' \(m\) ' initially at rest on a smooth horizontal plane starts moving under the action of force \(F=2 N\). In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizontal varies as \(\theta= kx\), where \(k\) is a constant and \(x\) is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be \(E =\frac{ n }{ k } \sin \theta\). The value of \(n\) is \(.....\)

Diameter of a steel ball is measured using a Vernier callipers which has divisions of \(0. 1\,cm\) on its main scale \((MS)\) and \(10\) divisions of its vernier scale \((VS)\) match \(9\) divisions on the main scale. Three such measurements for a ball are given as

S.No.	\(MS\;(cm)\)	\(VS\) divisions
\((1)\)	\(0.5\)	\(8\)
\((2)\)	\(0.5\)	\(4\)
\((3)\)	\(0.5\)	\(6\)

If the zero error is \(- 0.03\,cm,\) then mean corrected diameter is  ........... \(cm\)

A player kicks a football with an initial speed of \(25\, {ms}^{-1}\) at an angle of \(45^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g \(=10 \,{ms}^{-2}\) )

Match List - \(I\) with List - \(II\).

List - \(I\) \((Number)\)	List - \(II\) \((Significant figure)\)
\((A)\) \(1001\)	\((I)\) \(3\)
\((B)\) \(010.1\)	\((II)\) \(4\)
\((C)\) \(100.100\)	\((III)\) \(5\)
\((D)\) \(0.0010010\)	\((IV)\) \(6\)

Choose the correct answer from the options given below :

If earth has a mass nine times and radius twice to the of a planet \(P\). Then \(\frac{v_e}{3} \sqrt{x}\; ms ^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(P\), where \(v_e\) is escape velocity on earth. The value of \(x\) is

A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is

When one light ray is reflected from a plane mirror with \(30^{\circ}\) angle of reflection, the angle of deviation of the ray after reflection is \(.....^{\circ}\)

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi\  \mathrm{m}\) and \(R_2=4 \pi\  \mathrm{m}\) carrying current \(I=4 \mathrm{~A}\) as per figure given below is \(\alpha \times 10^{-7} \mathrm{~T}\). The value of \(\alpha\) is___________ (Centre \(\mathrm{O}\) is common for all segments)

A planet takes \(200\) days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

The distance between two consecutive points with phase difference of \(60^{\circ}\) in a wave of frequency \(500\,Hz\) is \(6.0\,m\). The velocity with which wave is traveling is \(.........km / s\)