Two identical thin biconvex lenses of focal length \(15\, cm\) and refractive index \(1.5\) are in contact with each other. The space between the lenses is filled with a liquid of refractive index \(1.25\). The focal length of the combination is \(cm\).

Sun light falls normally on a surface of area \(36\,cm ^{2}\) and exerts an average force of \(7.2 \times 10^{-9}\,N\) within a time period of \(20\) minutes. Considering a case of complete absorption, the energy flux of incident light is.

An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\)

In an experiment the values of two spring constants were measured as \(k _1=(10 \pm 0.2) N / m\)
and \(k _2=(20 \pm 0.3) N / m\). If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

The current flowing through the \(1 \Omega\) resistor is \(\frac{\mathrm{n}}{10} \ A.\) The value of \(n\) is _______.

In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into \(a\) square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
(Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) )

A point source of light \(S\), placed at a distance \(60 \,cm\) infront of the centre of a plane mirror of width \(50 \,cm\), hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance \(1.2\, m\) from it (see in the \(figure\)). The distance between the extreme points where he can see the image of the light source in the mirror is \(\ldots \ldots \ldots\, cm.\)