\(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) )

Figure shows the variation in temperature \(\left( {\Delta T} \right)\) with the amount of heat supplied \((Q)\) in an isobaric process corresponding to a monoatomic \((M)\), diatomic \((D)\) and a polyatomic \((P)\) gas. The initial state of all the gases are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines \(a, b\) and \(c\) respectively correspond to

In a Young's double slit experiment, the intensities at two points, for the path difference \(\frac{\lambda}{4}\) and \(\frac{\lambda}{3}\) ( \(\lambda\) being the wavelength of light used) are \(I_1\) and \(I_2\) respectively. If \(I_0\) denotes the intensity produced by each one of the individual slits, then \(\frac{ I _1+ I _2}{ I _0}=..............\)

A force \(\overrightarrow{ F }=(\hat{ i }+2 \hat{ j }+3 \hat{ k }) N\) acts at a point \((4 \hat{ i }+3 \hat{ j }-\hat{ k }) m \cdot\) Then the magnitude of torque about the point \((\hat{i}+2 \hat{j}+\hat{k}) m\) will be \(\sqrt{ x } N - m .\) The value of \(x\) is\(........\)

The average translational kinetic energy of \({N}_{2}\) gas molecules at \(\ldots \ldots \ldots . .{ }^{\circ} {C}\) becomes equal to the \({K} . {E}\). of an electron accelerated from rest through a potential difference of \(0.1\) \(volt.\) \(\left(\right.\) Given \(\left.{k}_{{B}}=1.38 \times 10^{-23} \, {J} / {K}\right)\) (Fill the nearest integer).

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason \(R\): For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below

Two concentric circular coils, \(C _{1}\) and \(C _{2}\), are placed in the \(XY\) plane. \(C _{1}\) has \(500\) turns, and a radius of \(1\; cm . C _{2}\) has \(200\) turns and radius of \(20\, cm . C _{2}\) carries a time dependent current \(I(t)=\left(5 t^{2}-2 t+3\right) \;A\) where \(t\) is in \(s\). The \(emf\) nduced in \(C _{1}\) (in \(mV\) ), at the instant \(t =1\; s\) is \(\frac{4}{ x }\). The value of \(x\) is

If microwaves, \(X\) rays, infrared, gamma rays, ultraviolet, radio waves and visible parts of the electromagnetic spectrum by are denoted \(M, X, I, G, U, R\) and \(V\) then which of the following is the arrangement in ascending order of wavelength ?

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

To find the focal length of a convex mirror, a student records the following data

Object Pin	Convex Lens	Convex Mirror	Image Pin
\(22.2\,cm\)	\(32.2\,cm\)	\(45.8\,cm\)	\(71.2\,cm\)

The focal length of the convex lens is \(f_1\)  and that of mirror is \(f_2\). Then taking index correction to be negligibly small, \(f_1\)  and  \(f_2\) are close to

A Carnot engine absorbs \(1000\,J\) of heat energy from a reservoir at \(127\,^oC\) and rejects \(600\,J\) of heat energy during each cycle. The efficiency of engine and temperature of sink will be

In the experiment for measurement of viscosity ' \(\eta\) ' of given liquid with a ball having radius \(R\), consider following statements.
A. Graph between terminal velocity V and R will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \(\eta\) will change.
Choose the correct answer from the options given below: