Match the LIST-I with LIST-II.

LIST-I	LIST-II
(A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
(B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
(C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
(D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

Choose the correct answer from the options given below :

A sportsman runs around a circular track of radius \(r\) such that he traverses the path \(A B A B\). The distance travelled and displacement, respectively, are

A solid circular disc of mass \(50 \mathrm{~kg}\) rolls along a horizontal floor so that its center of mass has a speed of \(0.4 \mathrm{~m} / \mathrm{s}\). The absolute value of work done on the disc to stop it is _______ \(\mathrm{J}\).

For the circuit shown below, calculate the value of \({I}_{{z}}\) : (In \({mA}\))

In \(SI\, units\), the dimensions of \(\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} \) is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, \(\mathrm{PV}=\) constant, while in adiabatic process \(\mathrm{PV}^\gamma=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below :

Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

A Carnot engine \((\mathrm{E})\) is working between two temperatures 473 K and 273 K . In a new system two engines - engine \(E_1\) works between 473 K to 373 K and engine \(E_2\) works between 373 K to 273 K .If \(\eta_{12}, \eta_1\) and \(\eta_2\) are the efficiencies of the engines \(E, E_1\) and \(E_2\), respectively, then

If \(\alpha = \displaystyle\int_0^{2\sqrt{3}} \log_2(x^2 + 4)\,dx + \displaystyle\int_2^4 \sqrt{2^x - 4}\,dx\), then \(\alpha^2\) is equal to _______.

Let the foot of perpendicular of the point \(P (3,-2,-9)\) on the plane passing through the points \((-1,-2,-3),(9,3,4),(9,-2,1)\) be \(Q(\alpha, \beta, \gamma)\). Then the distance of \(Q\) from the origin is:

Let \(S\) be the set of all values of \(\theta \in[-\pi, \pi]\) for which the system of linear equations \(x+y+\sqrt{3} z=0\) \(-x+(\tan \theta) y+\sqrt{7} z=0\) \(x+y+(\tan \theta) z=0\) has non-trivial solution. Then \(\frac{120}{\pi} \sum_{\theta \in s} \theta\) is equal to

The number of strictly increasing functions f from the set {1, 2, 3, 4, 5, 6} to the set {1, 2, 3,...,9} such that \( f(i)\ne i \) for \( 1\le i\le6, \) is equal to:

The logic gate equivalent to the given circuit diagram is: