A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN.

A short bar magnet placed with its axis at \(30^{\circ}\) with an external field of 800 Gauss, experiences a torque of \(0.016 N . m\). The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3} J\). The value of \(\alpha\) is _________ .

Equivalent resistance of the following network is _______ \(\Omega\).

A parallel plate air capacitor has a capacitance \(C\). When it is half filled as show in figure with a dielectric constant \(K = 5\), the percentage increase in the capacitance is _______.

A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\)

How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?

A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

The magnetic field vector of an electromagnetic wave is given by \({B}={B}_{o} \frac{\hat{{i}}+\hat{{j}}}{\sqrt{2}} \cos ({kz}-\omega {t})\); where \(\hat{i}, \hat{j}\) represents unit vector along \({x}\) and \({y}\)-axis respectively. At \(t=0\, {s}\), two electric charges \(q_{1}\) of \(4\, \pi\) coulomb and \({q}_{2}\) of \(2 \,\pi\) coulomb located at \(\left(0,0, \frac{\pi}{{k}}\right)\) and \(\left(0,0, \frac{3 \pi}{{k}}\right)\), respectively, have the same velocity of \(0.5 \,{c} \hat{{i}}\), (where \({c}\) is the velocity of light). The ratio of the force acting on charge \({q}_{1}\) to \({q}_{2}\) is :-

A body of mass \(m\)  starts moving from rest along \(x-\) axis so that its velocity varies as \(v = a\sqrt s\) where \(a\) is a constant and \(s\)  is the distance covered by the body. The total work done by all the forces acting on the body in the first second after the start of the motion is

Let \(\mathrm{f}: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) be a function satisfying \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}\) for all \(x, y, f(y) \neq 0\). If \(f^{\prime}(1)=2024\) then

\(\lim\limits _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}\) is equal to :

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below.