\(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______.

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body is \(...........\,\%\)

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

To establish an instantaneous current of \(2\,A\) through a \(1\,\mu F\) capacitor ; the potential difference across the capacitor plates should be changed at the rate of

An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to

An electron of mass \(m _{ e }\) and a proton of mass \(m _{ p }=1836 m _{ e }\) are moving with the same speed. The ratio of their de Broglie wavelength \(\frac{\lambda_{\text {electron }}}{\lambda_{\text {proton }}}\) will be ....... .

Glycerine of density \(1.25 \times 10^3\,kg\,m ^{-3}\) is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is \(10\,cm ^2\) and \(5\,cm ^2\) and pressure drop across its length is \(3\,Nm ^{-2}\). The rate of flow of glycerine through the pipe is \(x \times 10^{-5} m ^3 s ^{-1}\). The value of \(x\) is \(..............\).

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from \(420\, Hz\) to \(490\, Hz ,\) when he hears it after it gets reflected from the wall. Find the speed of the bus (in \(kmh^{-1}\)) if speed of the sound is \(330\, ms ^{-1}\).