In a Young's double slit experiment, the intensity at a point is \(\left(\frac{1}{4}\right)^{\text {th }}\) of the maximum intensity, the minimum distance of the point from the central maximum is _______ \(\mu \mathrm{m}\). (Given : \(\lambda=600 \mathrm{~nm}, d=1.0 \mathrm{~mm}, \mathrm{D}=1.0 \mathrm{~m}\) )

A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

In the arrangement shown in figure \(a _{1}, a _{2}, a _{3}\) and \(a _{4}\) are the accelerations of masses \(m _{1}, m _{2}, m _{3}\) and \(m _{4}\) respectively. Which of the following relation is true for this arrangement?

An electron, moving along the \(x-\) axis with an initial energy of \(100\, eV\), enters a region of magnetic field \(\vec B = (1.5\times10^{-3}T)\hat k\) at \(S\) (See figure). The field extends between \(x = 0\) and \(x = 2\, cm\). The electron is detected at the point \(Q\) on a screen placed \(8\, cm\) away from the point \(S\). The distance \(d\) between \(P\) and \(Q\) (on the screen) is :......\(cm\) (electron's charge \(= 1.6\times10^{-19}\, C\), mass of electron \(= 9.1\times10^{-31}\, kg\))

An automobile of mass \('m'\) accelerates starting from origin and initially at rest, while the engine supplies constant 10.Power \(P\). The position is given as a function of time by:

When two resistance \(R_1\) and \(R_2\) connected in series and introduced into the left gap of a meter bridge and a resistance of \(10 \Omega\) is introduced into the right gap, a null point is found at \(60 cm\) from left side. When \(R_1\) and \(R_2\) are connected in parallel and introduced into the left gap, a resistance of \(3 \Omega\) is introduced into the right-gap to get null point at 40 cm from left end. The product of \(R_1 R_2\) is \(.............\Omega\)

Consider \(\mathrm{I}_1\) and \(\mathrm{I}_2\) are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If \(\mathrm{L}_1=\) self inductance of coil \(1, \mathrm{M}_{12}=\) mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be ________.

A rectangular coil (Dimension \(5\,cm\times 2\,cm\) ) with \(100\,turns,\) carrying a current of \(3\,A\) in the clock-wise direction, is kept centered at the origin and in the \(X-Z\) plane. A magnetic field of \(1\,T\) is applied along \(X-\) axis. If the coil is tilted through \(45^o\) about \(Z-\) axis, then the torque on the coil is.....\(Nm\)

A point source of \(100\,W\) emits light with \(5 \%\) efficiency. At a distance of \(5\,m\) from the source, the intensity produced by the electric field component is :

A small square loop of wire of side \(\ell\) is placed inside a large square loop of wire of side \(L\) \(\left(\mathrm{L}=\ell^2\right)\). The loops are coplanar and therr centers coinside. The value of the mutual inductance of the system is \(\sqrt{\mathrm{x}} \times 10^{-7} \mathrm{H}\), where X = _______.

A \(1\) kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of \(25\) m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is _____ J.

Two wires \(A\) and \(B\) are carrying currents \(I_1\) and \(I_2\) as shown in the figure. The separation between them is \(d\). A third wire \(C\) carrying a current \(I\) is to be kept parallel to them at a distance \(x\) from \(A\) such that the net force acting on it is zero. The possible values of \(x\) are