\(n-\) \(moles\) of an ideal gas with constant volume heat capacity \(C_v\) undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

A solid sphere of mass \(1\,kg\) rolls without slipping on a plane surface. Its kinetic energy is \(7 \times 10^{-3}\,J\). The speed of the centre of mass of the sphere is \(.........cm s ^{-1}\).

The diffraction pattern of a light of wavelength \(400\) \(\mathrm{nm}\) diffracting from a slit of width \(0.2 \mathrm{~mm}\) is focused on the focal plane of a convex lens of focal length \(100 \mathrm{~cm}\). The width of the \(1^{\text {st }}\) secondary maxima will be _______.

A steel rail of length \(5\,m\) and area of cross-section \(40\,cm^2\) is prevented from expanding along its length while the temperature rises by \(10\,^oC\). If coefficient of linear expansion and Young's modulus of steel are \(1.2\times10^{-5}\, K^{-1}\) and \(2\times10^{11}\, Nm^{-2}\) respectively, the force developed in the rail is approximately

An object is placed beyond the centre of curvature \({C}\) of the given concave mirror. If the distance of the object is \({d}_{1}\) from \({C}\) and the distance of the image formed is \({d}_{2}\) from \({C}\), the radius of curvature of this mirror is

A circuit to verify \(Ohm's\) law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit

Figure shown a \(DC\) voltage regulator circuit, with a Zener diode of breakdown voltage \(= 6\,V\). If the unregulated input voltage varies between \(10\, V\) to \(16\, V\), then what is the maximum Zener current ?.......\(mA\)

An electron of mass m with an initial velocity \(\overrightarrow{ V }= V_0 \hat i \,(V_0 > 0)\) enters an electric field \(\vec E = -\vec E_0 \hat i \,(E_0 =\) constant \(> 0)\) at \(t = 0.\) If \(\lambda_0\) is its de-Broglie wavelength initially,then its de-Broglie wavelenght at time \(t\) is

A gas mixture consists of \(3\,moles\) of oxygen and \(5\,moles\) or argon at temperature \(T.\) Considering only translational and rotational modes, the total internal  energy of the system is

A red \(LED\) emits light at \(0.1\) watt uniformly around it. The amplitude of the electric field of the light at a distance of \(1\ m\) from the diode is....\( Vm^{-1}\)

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then