An electron with energy \(0.1\,ke\,V\) moves at right angle to the earth's magnetic field of \(1 \times 10^{-4}\,Wbm ^{-2}\). The frequency of revolution of the electron will be. (Take mass of electron \(=9.0 \times 10^{-31}\,kg\) )

Find the correct combination of A, B, C and D inputs which can cause the LED to glow

In the given figure, a body of mass \(M\) is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant \(k,\) the frequency of oscillation of given body is :

A person moved from \(A\) to \(B\) on a circular path as shown in figure. If the distance travelled by him is \(60 \,m\), then the magnitude of displacement would be\(.....\,m\) (Given \(\left.\cos 135^{\circ}=-0.7\right)\)

A constant Power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time \('t'\) is proportional to

Three conductors of same length having thermal conductivity \(\mathrm{k}_1, \mathrm{k}_2\) and \(\mathrm{k}_3\) are connected as shown in figure.

Area of cross sections of \(1^{\text {st }}\) and \(2^{\text {nd }}\) conductor are same and for \(3^{\text {rd }}\) conductor it is double of the \(1^{\text {st }}\) conductor. The temperatures are given in the figure. In steady state condition, the value of \(\theta\) is _______ \({ }^{\circ} \mathrm{C}\).
(Given : \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1}\mathrm{~m}^{-1}\) \( \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) )

A \(5\) mg particle carrying a charge of \(5\pi\times 10^{-6}\) C is moving with velocity of \((3\hat{i}+2\hat{k})\times 10^{-2}\) m/s in a region having magnetic field \(\vec{B} = 0.1\hat{k}\) Wb/m\(^2\). It moves a distance of \(\alpha\) meter along \(\hat{k}\) when it completes \(5\) revolutions. The value of \(\alpha\) is ________.

Let \( \bar x , M\) and \(\sigma^2\) be respectively the mean, mode and variance of \(n\) observations \(x_1 , x_2,...,x_n\) and \(d_i\, = - x_i - a, i\, = 1, 2, .... , n\), where \(a\) is any number.
Statement \(I\): Variance of \(d_1, d_2,.....d_n\) is \(\sigma^2\).
Statement \(II\) : Mean and mode of \(d_1 , d_2, .... d_n\) are \(-\bar x -a\) and \(- M - a\), respectively

If the line \(\frac{{x - 2}}{3} = \frac{{y + 1}}{2} = \frac{{z - 1}}{1}\) intersects the plane \(2x + 3y -z + 13 = 0\) at a point \(P\) and the plane \(3x + y + 4z = 16\) at a point \(Q\), then \(PQ\) is equal to

At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). The \(n_2\) material is replaced by another material having refractive index \(n_3\) such that the critical angle at the interface between \(n_1\) and \(n_3\) materials is \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is :

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is:

Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be

For the given circuit, in the steady state, \(\left| V _{ B }- V _{ D }\right|=.......V.\)