In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength \(5000 Å\). Without disturbing the set up of the experiment, the source of light is replaced by a source of wavelength \(6400 Å\). The fringe width will

Considering interference between two sources of intensities ' I ' and ' 4 I ', the intensity at a point where the phase difference is \(\pi\) is \((\cos \pi=-1)\).

When the observer moves towards the stationary source with velocity \(V_1\), the apparent frequency of the emitted note is \(F_1\). When the observer moves away from the source with velocity \(V_1\), the apparent frequency is \(F_2\). If \(V\) is the velocity of sound in air and \(\frac{F_1}{F_2}=2\) then \(\frac{V}{V_1}=\) ?

An uniform rod \(\mathrm{AB}\) of mass \(m\) and length \(l\) is at rest on a smooth horizontal surface. An impulse \(P\) applied to the end \(B\). The time taken by the rod to turn through a right angle is

The core used in transformer and other electromagnetic devices is laminated to

Two solid spheres (A and B) are made of metals having densities \(\rho_A\) and \(\rho_B\) respectively. If there masses are equal then ratio of their moments of inertia \(\left(\frac{I_B}{I_A}\right)\) about their respective diameter is

Two wires A and B of equal lengths are connected in left and right gap of a metre bridge, null point is obtained at \(40 \mathrm{~cm}\) from left end. Diameters of the wires \(\mathrm{A}\) and \(\mathrm{B}\) are in the ratio \(3: 1\). The ratio of specific resistance of \(A\) to that of \(B\) is

\(\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=\)

A problem in statistics is given to three students \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\). Their chances of solving
the problem are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. If all of them try independently, then the
probability that the problem is solved, is

If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the system

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for first order reaction if rate constant is \(1.386 \times 10^{-3} \mathrm{~s}^{-1}\)

A line makes an angle of \(45^{\circ}\) with \(x\) -axis and congruent angles with \(y\) and \(z\) -axes, then the direction cosines of the line are

If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors and \(\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \quad\) then \(2 \overline{\mathrm{a}} \cdot \overline{\mathrm{p}}+\overline{\mathrm{b}} \cdot \overline{\mathrm{q}}+\overline{\mathrm{c}} \cdot \overline{\mathrm{r}}=\)