Given below are two statements : Statement \(I\) : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \(\mathrm{P}_1-\mathrm{P}_2=\rho \mathrm{g}\left(\mathrm{h}_2-\mathrm{h}_1\right)\) Statement \(II\) : In ventury tube shown \(2 \mathrm{gh}=v_1^2-v_2^2\) In the light of the above statements, choose the most appropriate answer from the options given below.

Following plots show Magnetization \((M)\) \(vs\) Magnetising field \((H)\) and Magnetic susceptibility \((\chi)\) vs temperature \((T)\) graph : Which of the following combination will be represented by a diamagnetic material?

A plane electromagnetic wave propagating in \(\mathrm{x}\)-direction is described by \(\mathrm{E}_{\mathrm{y}}=\left(200\  \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\  \mathrm{x}\right] \text {; }\) The intensity of the wave is :(Use \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) )

Two ideal polyatomic gases at temperatures \(T _{1}\) and \(T _{2}\) are mixed so that there is no loss of energy. If \(F _{1}\) and \(F _{2}, m _{1}\) and \(m _{2}, n _{1}\) and \(n _{2}\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is

In an experiment, a set of reading are obtained \(-1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm\). The expected least count of the instrument used in recording these readings is ___________ mm.

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 body cools from \(80^{\circ}\,C\) to \(60^{\circ}\,C\) in \(5\) minutes. The temperature of the surrounding is \(20^{\circ} C\). The time it takes to cool from \(60^{\circ}\,C\) to \(40^{\circ}\,C\) is........... \(s\)

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.

The resistive network shown below is connected to a \(D.C.\) source of \(16\, V\). The power consumed by the network is \(4\, Watt\). The value of \(R\) is ............. \(\Omega\)

Tangent and normal are drawn at \(P(16, 16)\) on the parabola \({y^2} = 16x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points  \(P, A\) and \(B\) and \(\angle CPB = \theta \) , then a value of \(\tan \theta \;\)is :

Let \(\vec{a}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{ c }=2 \hat{ i }-3 \hat{ j }+3 \hat{k}\). If \(\vec{b}\) is \(a\) vector such that \(\vec{a}=\vec{b} \times \vec{c}\) and \(|\vec{b}|^2=50\), then \(|72-| \vec{b}+\left.\vec{c}\right|^2 \mid\) is equal to \(..........\).

If the sum of the deviations of \(50\) observations from \(30\) is \(50\), then the mean of these observations is

Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is