Two blocks of masses \(\mathrm{m}\) and \(2 \mathrm{~m}\) kept on a frictionless horizontal surface are connected by a massless string. Two horizontal forces \(F_1=(4.2 t) N\) and \(F_2=(7.5 t) N\), where ' \(t\) ' is time in seconds, are acting on the system as shown in the figure. The time at which the tension in the string between the two blocks becomes \(10.6 \mathrm{~N}\) is s.

Two springs A and B fixed at the top and are stretched by \(8 \mathrm{~cm}\) and \(16 \mathrm{~cm}\) respectively, when loads of \(20 \mathrm{~N}\) and \(10 \mathrm{~N}\) are suspended at the lower ends. The ratio of the spring constants of the springs \(A\) and \(B\) is

The process that mainly place in stars to produce energy

Four positive point charges \(+q\) are kept at the four corners of a square of side \(l\). The net electric field at the mid-point of any one side of the square is
\[
\left(\text { Take, } \frac{1}{4 \pi \varepsilon_0}=k\right)
\]

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists
\(\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}\)
\(\begin{array}{llll}A & B & C & D\end{array}\)

A cylinder has a piston at temperature of $30°\mathrm{C}$. There is all round clearance of $0.08 \mathrm{mm}$ between the piston and cylinder wall if internal diameter of the cylinder is $15 \mathrm{cm}$. What is the temperature at which piston will fit into the cylinder exactly? $\left({\alpha }_p=1.6\times {10}^{-5}/{}^{\circ }\mathrm{C}\right.$ and $\left.{\alpha }_c=1.2\times {10}^{-5}/{}^{\circ }\mathrm{C}\right)$

The length of a potentiometer wires is l. A cell of emf \(E\) is balanced at a length \(\left(\frac{l}{3}\right)\) from positive end of the wire. If the length of the wire is increased by \(\left(\frac{l}{2}\right)\), the distance at which the same cell gives the balancing point is
(Cell in the primary is ideal and no series resistance is present in the primary circuit.)

A projectile with speed $50 \mathrm{m} {\mathrm{s}}^{-1}$ is thrown at an angle of $60°$ with the horizontal. The maximum height that can be reached is,
(acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The radius of orbit of an electron and the speed of electron in the ground state of hydrogen atom are \(5.5 \times 10^{-11} \mathrm{~m}\) and \(4 \times 10^6 \mathrm{~ms}^{-1}\) respectively. Then, the orbital period of this electron in the first excited state will be
......... .

The equivalent capacitance between \(\mathrm{A}\) and \(\mathrm{B}\) in the given figure is

If \(x \sin (\alpha+y)=\sin y\) and \(y=\frac{m}{x^2+2 n x+1}\) then \(m^2=\)

At \(T(K)\), the equilibrium constant for the reaction \(\mathrm{H}_2(\mathrm{~g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g})\) is \(1.6 \times 10^5\). If 10 bar ' of HBr is introduced into a sealed vessel at \(\mathrm{T}(\mathrm{K})\), the equilibrium pressure of HBr (in bar) is approximately

The product formed when formaldehyde reacts with ammonia is