The diffraction pattern of a light of wavelength \(400\) \(\mathrm{nm}\) diffracting from a slit of width \(0.2 \mathrm{~mm}\) is focused on the focal plane of a convex lens of focal length \(100 \mathrm{~cm}\). The width of the \(1^{\text {st }}\) secondary maxima will be _______.

In the figure shown below, the charge on the left plate of the \(10\, \mu F\) capacitor is \(-30\,\mu C.\) The charge on the right place of the \(6\,\mu F\) capacitor is.....\(\mu C\)

A wire of resistance \(160\,\Omega\) is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be \(......\Omega\)

If two glass plates have water between them and are separated by very small distance ( see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by

A solution containing active cobalt \({}_{27}^{60}Co\) having activity of \(0.8\,\mu Ci\) and decay constant \(\lambda \) is injected in an animal's body. If \(1 \,cm^3\) of blood is drawn from the animal's body after \(10\, hrs\) of injection, the activity found was \(300\, decays\) per minute. What is the volume of blood that is flowing in the body?..........\(litres\) ( \(ICi = 3.7 \times 10^{10}\) decay per second and at \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

A ball of radius r and density \(\rho\) dropped through a viscous liquid of density \(\sigma\) and viscosity \(\eta\) attains its terminal velocity at time t , given by \(t = A \rho^{ a } r ^{ b } \eta^{ c } \sigma^{ d }\), where A is a constant and a , b c and d are integers. The value of \(\frac{b+c}{a+d}\) is ___________.

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity \(\omega\) as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, \(I_A-I_B\), for the given Amperian loops is:

Mach List-\(I\) with List - \(II\) :

List - \(I\)	List - \(II\)
\((a)\) Ultraviolet rays	\((a)\) Study crystal structure
\((b)\) Microwaves	\((b)\) Greenhouse
\((c)\) Infrared waves	\((c)\) sterilizing surgical instrument
\((d)\) \(x\)-rays	\((d)\) Radar system

Choose the correct answer from the options given below

The ratio of heat dissipated per second through the resistance \(5 \Omega\) and \(10 \Omega\) in the circuit given below is _______.

The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as _______.

A screw gauge with a pitch of \(0.5 \ mm\) and a circular scale with \(50\) divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the \(45^{th} \)division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in \(mm\)) if the main scale reading is \(0.5\ mm\) and the \(25^{th}\) division coincides with the main scale line 

Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length is