In the figure shown, what is the current (in Ampere) drawn from the battery ? You are given \(R_1 = 15\,\Omega \)\(,R _2 = 10\,\Omega ,\)\( R_3 = 20\,\Omega ,\)\( R_4 = 5\,\Omega ,\)\(R_5 = 25\,\Omega ,\)\(R_6 = 30\,\Omega , \)\(E = 15\,V\)

In an experiment a convex lens of focal length \(15\, cm\) is placed coaxially on an optical bench in front of a convex mirror at a distance of \(5\,cm\) from it. It is found that an object and its image coincide, if the object is placed at a distance of \(20\,cm\) from the lens. The focal length of the convex mirror is.......\(cm\)

In the figure given below. a block of mass \(M =490\,g\) placed on a frictionless table is connected with two springs having same spring constant \(\left( K =2 N m ^{-1}\right)\). If the block is horizontally displaced through ' \(X\) 'm then the number of complete oscillations it will make in \(14 \pi\) seconds will be \(.........\)

Six point charges are kept \( 60^{\circ} \) apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is __________ .
(\( \epsilon \) is permittivity of free space)

If one mole of an ideal gas at \(\left( P _{1}, V _{1}\right)\) is allowed to expand reversibly and isothermally (\(A\) to \(B\) ) its pressure is reduced to one-half of the original pressure (see \(figure\)). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value \(( B \rightarrow C ) .\) Then it is restored to its initial state by a reversible adiabatic compression (\(C\) to \(A\)). The net workdone by the gas is equal to  ...... .

A ball rolls off the top of a stairway with horizontal velocity \(\mathrm{u}\). The steps are \(0.1 \mathrm{~m}\) high and \(0.1 \mathrm{~m}\) wide. The minimum velocity \(\mathrm{u}\) with which that ball just hits the step \(5\) of the stairway will be \(\sqrt{\mathrm{x}} \mathrm{ms}^{-1}\) where \(\mathrm{x}=\) _______ [use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ].

If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )

If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______.

A body having specific charge \(8\,\mu {C} / {g}\) is resting on a frictionless plane at a distance \(10\, {cm}\) from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of \(100 \,{V} / {m}\) is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be \(....\, S.\)

Light from a point source in air falls on a convex curved surface of radius \(20 \mathrm{~cm}\) and refractive index \(1.5.\) If the source is located at \(100 \mathrm{~cm}\) from the convex surface, the image will be formed at _______ \(\mathrm{cm}\) from the object.

Consider the \(LR\) circuit shown in the figure. If the switch \(S\) is closed at \(t = 0\) then the amount of charge that passes through the battery between \(t = 0\) and \(t = \frac{L}{R}\) is

Three charged particle \(A, B\) and \(C\) with charges \(-4 q,  2 q\) and \(-2 q\) are present on the circumference of a circle of radius \(d\). the charged particles \(A, C\) and centre \(O\) of the circle formed an equilateral triangle as shown in figure. Electric field at \(O\) along \(x-\)direction is