Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Product of Pressure \((P)\) and time \((t)\) has the same dimension as that of coefficient of viscosity. Reason \(R\) : Coefficient of viscosity \(=\frac{\text { Force }}{\text { Velocity gradient }}\) Question : Choose the correct answer from the options given below 

Resistance of the wire is measured as \(2\,\Omega\) and \(3\,\Omega\) at \(10^{\circ}C\) and \(30^{\circ}C\) respectively. Temperature cocoefficient of resistance of the material of the wire is............\(^{\circ}C ^{-1}\)

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5 \,m ,\) while the distance between one crest and one trough is \(1.5 \,m\) The possible wavelengths (in \(m\) ) of the waves are

A point particle of mass, moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). The particle is released, from rest, from the point \(P\) and it comes to rest at a point \(R\). The energies, lost by the ball, over the parts, \(PQ\) and \(PR\), of the track, are equal to each other, and no energy is lost when particle changes direction from \(PQ\) to \(QR\). The values of the coefficient of friction \(\mu\) and the distance \(x(=QR)\) are, respecitvely close to

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

A proton with a kinetic energy of \(2.0\,eV\) moves into a region of uniform magnetic field of magnitude \(\frac{\pi}{2} \times 10^{-3}\,T\). The angle between the direction of magnetic field and velocity of proton is \(60^{\circ}\). The pitch of the helical path taken by the proton is \(..........cm\) (Take, mass of proton \(=1.6 \times 10^{-27}\,kg\) and Charge on proton \(=1.6 \times 10^{-19}\,kg)\)

As per given figure \(A , B\) and \(C\) are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths \(\left(\right.\) i.e. \(\left.\frac{\lambda_1}{\lambda_2}\right)\) is \(\frac{7}{4 n}\), then the value of \(n\) will be

If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

lf  \(f(x)\)  is a differentiable function in the interval \((0,\infty )\)  such that \(f(1) = 1\) and \(\mathop {\lim }\limits_{t \to x} \frac{{{t^2}f(x) - {x^2}f(t)}}{{t - x}} = 1,\) for each \(x > 0,\)  then \(f (\frac {3}{2})\) is equal to

The current flowing through \(R _2\) is:

Cross-section view of a prism is the equilateral triangle \({ABC}\) in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from midpoint of \({BC}\) to \({A}\) is \(.....\times 10^{-10}\, {s}\). \((\) Given, speed of light in vacuum \(=3 \times 10^{8} \,{m} / {s}\) and \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)\)