In a Wheatstone bridge (see figure) Resistance \(P\) and \(Q\) are approximately equal. When \(R = 400\,\Omega ,\) the bridge is balanced. On interchanging \(P\) and \(Q,\) the value of \(R,\) for balance is \(405\,\Omega .\) The value of \(X\) is close to ................. \(ohm\)

A soap bubble of surface tension \(0.04 N / m\) is blown to a diameter of 7 cm . If \((15000- x ) \mu J\) of work is done in blowing it further to make its diameter 14 cm , then the value of x is _________ .\((\pi=22 / 7)\)

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns \((\mathrm{N})\) to its double \((2 \mathrm{~N})\), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

A small ball of mass \(m\) is thrown upward with velocity \(u\) from the ground. The ball experiences a resistive force \(mkv ^{2}\) where \(v\) is its speed. The maximum height attained by the ball is 

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

The current flowing through a conductor connected across a source is \(2\,A\) and \(1.2\,A\) at \(0^{\circ}\,C\) and \(100^{\circ}\,C\) respectively. The current flowing through the conductor at \(50^{\circ}\,C\) will be \(......\times 10^2\,mA\).

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

The surface tension of a soap bubble is \(0.03\) N/m. The work done in increasing the diameter of bubble from \(2\) cm to \(6\) cm is \(\alpha \pi \times 10^{-4}\) J. The value of \(\alpha\) is _______. (Take \(\pi = 3.14\))

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

An ac current is represented as
\(\mathrm{i}=5 \sqrt{2}+10 \cos \left(650 \pi \mathrm{t}+\frac{\pi}{6}\right) \mathrm{Amp}\)
The r.m.s value of the current is