A tube of length \(L\) is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is \(2 \mathrm{~m} / \mathrm{s}\), then velocity of water leaving the point (2) will be

A particle of mass \(500 \,gm\) is moving in a straight line with velocity \(v=b x^{5 / 2}\). The work done by the net force during its displacement from \(x=0\) to \(x =4 \,m\) is ...................\(J\) (Take \(b =0.25 \,m ^{-3 / 2} s ^{-1}\) )

In the given figure the blocks \(A , B\) and C weigh \(4 kg, 6 kg\) and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5 . The force \(\overrightarrow{ F }\) required to slide the block C with constant speed is _________ N . (Used \(g =10 m / s ^2\) )

When a long glass capillary tube of radius \(0.015\;cm\) is dipped in a liquid, the liquid rises to a height of \(15\, cm\) within it. If the contact angle between the liquid and glass to clase to \(0^{\circ},\) the surface tension of the liquid, in \(milli\,Newton \;m ^{-1}\) is \(.....\) \(\left[\rho_{\text {(liquid) }}=900\; kg\,m ^{-3}, g =10\, ms ^{-2}\right]\) (Give answer in closest integer)

The ratio of wavelength of spectral lines \(H_\alpha\) and \(H _\beta\) in the Balmer series is \(\frac{x}{20}\). The value of \(x\) is \(...............\)

In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by :

Match List \(I\) with List \(II\).

List \(I\)	List \(II\)
\((A)\) Torque	\((I)\) \(Nms^{-1}\)
\((B)\) Stress	\((II)\) \(J\,kg^{-1}\)
\((C)\) Latent Heat	\((III)\) \(Nm\)
\((D)\) Power	\((IV)\) \(Nm^{-2}\)

Choose the correct answer from the options below.

A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^{\circ}\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio \(v_1^2: v_2^2\) is:

A uniform wire of length \(l\) of weight \(w\) is suspended from the roof with a weight of \(W\) at the other end. The stress in the wire at \(\dfrac{l}{3}\) distance from the top is \(\left(\dfrac{W}{A} + \dfrac{2}{\gamma}\dfrac{w}{A}\right)\), where, \(A\) is the cross sectional area of the wire. The value of \(\gamma\) is _______.

If \({V}_{{A}}\) and \({V}_{{B}}\) are the input voltages (either \(5\, {V}\) or \(0\, {V}\) ) and \({V}_{0}\) is the output voltage then the two gates represented in the following circuit \((A)\) and \((B)\) are:- \((A)\quad\quad\quad\quad(B)\)

There are \(10^{10}\) radioactive nuclei in a given radioactive element, Its half-life time is \(1\, minute.\) How many nuclei will remain after \(30\, seconds?\) \((\sqrt{2}=1.414)\)

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength . If wavelength of red light is \(6600\,\mathop A\limits^o\) , then wavelength of first maximum will be.....\(\mathop A\limits^o \)

A block '\(A\)' takes \(2\,s\) to slide down a frictionless incline of \(30^{\circ}\) and length ' \(l\) ', kept inside a lift going up with uniform velocity ' \(v\) '. If the incline is changed to \(45^{\circ}\), the time taken by the block, to slide down the incline, will be approximately \(........\,s\)