Force acts for \(20\,s\) on a body of mass \(20\,kg\), starting from rest, after which the force ceases and then body describes \(50\,m\) in the next \(10\,s\). The value of force will be \(..........\,N\)

An engine operates by taking \(n\,moles\) of an ideal gas through the cycle \(ABCDA\) shown in figure. The thermal efficiency of the engine is : (Take \(C_v =1 .5\, R\), where \(R\) is gas constant)

In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).

Visible light of wavelength \(6000 \times 10^{-8}\; \mathrm{cm}\) falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at \(60^{\circ}\) from the central maximum. If the first minimum is produced at \(\theta_{1},\) then \(\theta_{1}\) is close to.....\(^o\)

A bar magnet is demagnetized by inserting it inside a solenoid of length \(0.2\, m\), \(100\, turns\), and carrying a current of \(5.2\, A\). The coercivity of the bar magnet is.....\(A/m\)

The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time \(0\) to \(10\,s\) is

A beam of light consisting of two wavelengths \(7000\; \mathring A\) and \(5500 \;\mathring A\) is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is \(2.5\,mm\) and the distance between the plane of slits and the screen is \(150\,cm\). The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is \(n \times 10^{-5}\,m\). The value of \(n\) is .............

A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load)

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).