Match List-I with List-II.

List-I	List-II
(A) Mass density	(I) [ML2T-3]
(B) Impulse	(II) [MLT-1]
(C) Power	(III) [ML2T0]
(D) Moment of inertia	(IV) [ML-3T0]

Choose the correct answer from the options given below :

In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

Glycerine of density \(1.25 \times 10^3\,kg\,m ^{-3}\) is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is \(10\,cm ^2\) and \(5\,cm ^2\) and pressure drop across its length is \(3\,Nm ^{-2}\). The rate of flow of glycerine through the pipe is \(x \times 10^{-5} m ^3 s ^{-1}\). The value of \(x\) is \(..............\).

Given below are two statements: one is labelled as Assertion \(\mathrm{A}\) and the other is labelled as Reason \(\mathrm{R}\) Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is \(\frac{1}{2} \mathrm{mgR}\), where R is the radius of earth.
Reason \(\mathrm{R}\) : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below

Suppose two planets (spherical in shape) of radii \({R}\) and \(2 {R}\), but mass \({M}\) and \(9\, {M}\) respectively have a centre to centre separation \(8\, {R}\) as shown in the figure. A satellite of mass \('{m}'\) is projected from the surface of the planet of mass \('M'\) directly towards the centre of the second planet. The minimum speed \('v'\) required for the satellite to reach the surface of the second planets is \(\sqrt{\frac{a}{7} \frac{G M}{R}}\) then the value of \('a'\) is \(....\) [Given: The two planets are fixed in their position]

Photons of an electromagnetic radiation has an energy \(11\, keV\) each. To which region of electromagnetic spectrum does it belong ?

An electron revolving in \(\mathrm{n}^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n\) \(\alpha\) \(n^x\), the value of \(x\) is _______.

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
(Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) )

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

Electrons are accelerated through a potential difference \(V\) and protons are accelerated through a potential difference \(4\, V\). The de-Broglie wavelengths are \(\lambda_e \) and \(\lambda_p \) for electrons and protons respectively. The ratio of \(\frac{{{\lambda _e}}}{{{\lambda _p}}}\) is given by : (given \(m_e\) is mass of electron and \(m_p\) is mass of proton).

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will be