Two beams of light having intensities \(I\) and \(4\,I\) interfere to produce a fringe pattern on a screen. The phase difference between the two beams are \(\pi / 2\) and \(\pi / 3\) at points \(A\) and \(B\) respectively. The difference between the resultant intensities at the two points is \(x I\). The value of \(x\) will be.

Current measured by the ammeter \((A)\) in the reported circuit when no current flows through \(10\,\Omega\) resistance. will be________\(A\)

One main scale division of a vernier callipers is \(a\) \(cm\) and \(n ^{\text {th }}\) division of the vernier scale coincide with \(( n -1)^{\text {th }}\) division of the main scale. The least count of the callipers in \(mm\) is

Refer to the logic circuit given below. For two inputs \((A=1, B=1)\) and \((A=0, B=1)\), output \((Y)\) will be __________.

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi\  \mathrm{m}\) and \(R_2=4 \pi\  \mathrm{m}\) carrying current \(I=4 \mathrm{~A}\) as per figure given below is \(\alpha \times 10^{-7} \mathrm{~T}\). The value of \(\alpha\) is___________ (Centre \(\mathrm{O}\) is common for all segments)

A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\)

For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})\), \(\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0\), them value of \(\mathrm{x}\) is _______.

Consider a frame that is made up of two thin massless rods \(AB\) and \(AC\) as shown in the figure. \(A\) vertical force \(\overrightarrow{ P }\) of magnitude \(100 \;N\) is applied at point \(A\) of the frame. Suppose the force is \(\overrightarrow{ P }\) resolved parallel to the arms \(AB\) and \(AC\) of the frame. The magnitude of the resolved component along the arm \(AC\) is \(xN\). The value of \(x\), to the nearest integer, is ............ [Given : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :-

Two liquids A and B have \(\theta_{\mathrm{A}}\) and \(\theta_{\mathrm{B}}\) as contact angles in a capillary tube. If \(K=\cos \theta_A / \cos \theta_B\). then identify the correct statement:

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ___________ .
\(\left(\tan ^{-1}(1.52)=57.7^{\circ}\right.\), refractive indices of air and glass are 1.00 and 1.52 , respectively)

In a linear simple harmonic motion \((SHM)\) \((A)\) Restoring force is directly proportional to the displacement. \((B)\) The acceleration and displacement are opposite in direction. \((C)\) The velocity is maximum at mean position. \((D)\) The acceleration is minimum at extreme points. Choose the correct answer from the options given below :