For the given circuit the current through battery of \(6\,V\) just after closing the switch ' \(S\) ' will be\(.......A\).

A force of \(- P \hat{k}\) acts on the origin of the coordinate system. The torque about the point \((2,-3)\) is \(P(a \hat{i}+b \hat{j})\), the ratio of \(\frac{a}{b}\) is \(\frac{x}{2}\). The value of \(x\) is

Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be _______.

Each of three blocks \(P\), \(Q\) and \(R\) shown in figure has a mass of \(3 \mathrm{~kg}\). Each of the wire \(A\) and \(B\) has cross-sectional area \(0.005 \mathrm{~cm}^2\) and Young's modulus \(2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Neglecting friction, the longitudinal strain on wire \(B\) is _______ \(\times 10^{-4}\). \(\left(\right.\) Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

A faulty thermometer reads \(5^{\circ} C\) in melting ice and \(95^{\circ} C\) in steam. The correct temperature on absolute scale will be. \(.........K\) when the faulty thermometer reads \(41^{\circ} C\).

The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is  ........ \(\times 10^{8}\; Nm ^{-2}\)

In the Young's double slit experiment the intensity produced by each one of the individual slits is \(I_0\). The distance between two slits is 2 mm . The distance of screen from slits is 10 m . The wavelength of light is \(6000\) Å. The intensity of light on the screen in front of one of the slits is _________ .

Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

A particle starts moving from time \(t=0\) and its coordinate is given as \(x(t)=4t^{3}-3t.\)
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point.
C. Acceleration of the particle is non-negative.
D. The particle is 0.5 units away from origin at its turning point.
E. Particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below :

Suppose that the points \((h, k), (1, 2)\) and \((-3, 4)\) lie on the line \(L_1\). If a line \(L_2\) passing through the points \((h, k)\) and \((4, 3)\) is perpendicular to \(L_1\), then \(\frac{k}{h}\) equals

An online exam is attempted by \(50\) candidates out of which \(20\) are boys. The average marks obtained by boys is \(12\) with a variance \(2 .\) The variance of marks obtained by \(30\) girls is also \(2 .\) The average marks of all \(50\) candidates is \(15 .\) If \(\mu\) is the average marks of girls and \(\sigma^{2}\) is the variance of marks of \(50\) candidates, then \(\mu+\sigma^{2}\) is equal to ...... .

An arc lamp requires a direct current of \(10\ A\) at \(80\ V\) to function. If it is connected to a \( 220\ V (rms ), 50\ Hz\ AC\) supply, the series inductor needed for it to work is close to :

Match the List\(-I\) with List\(-II\) 

List \(I\)	List \(II\)
\(A\) Microwaves	\(I\) Radio active decay of the nucleus
\(B\) Gamma rays	\(II\) Rapid acceleration and deceleration of electron in aerials
\(C\) Radio waves	\(III\) Inner shell electrons
\(D\) \(X\)-rays	\(IV\) Klystron valve

Choose the correct answer from the options given below