An electron is accelerated through a potential difference of \(45.5 \mathrm{~V}\). The velocity acquired by it is \(\left(\right.\) in \(\mathrm{ms}^{-1}\) )

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed \(v\), the net force on the particle (directed towards centre) will be ( \(T\) represents the tension in the string)

In a \(L-C-R\) circuit the potential diffcrcnce between the terminals of the inductance is \(60 \mathrm{~V}\), between the terminals of the capacitor is \(30 \mathrm{~V}\) and that between the terminals of resistance is \(40 \mathrm{~V}\). The supply voltage will be equal to

A particle of mass \(m\) is moving in a horizontal circle of radius \(R\) under a centripetal force equal to \(-\frac{A}{R^{2}}(A=\) constant \()\). The total energy of the particle is

The thickness of a metallic plate is 0.4 cm . The temperature between its two surfaces is \(20^{\circ} \mathrm{C}\). The quantity of heat flowing per second is 50 cal from \(5 \mathrm{~cm}^2\) area. In CGS system, the coefficient of thermal conductivity will be

\(\mathrm{H-}\)polaroid is prepared by

How many \(6 \mu \mathrm{F}, 200 \mathrm{~V}\) condensers are needed to make a condenser of \(18 \mu \mathrm{F}, 600 \mathrm{~V}\) ?\

The magnetic flux linked with a coil satisfies the relation \(\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}\), where \(t\) is time in second. The emf induced in the coil at \(t=2 \mathrm{~s}\) is

Match the reactions in Column I with the correct products given in Column II:
\(\begin{array}{|l|l|l|l|} \hline \text{S.N.} & \text{Column I} & \text{S.No.} & \text{Column II} \\ \hline \text{A} & 1- \text{Chloropropane} + (\mathrm{Zn} / \mathrm{HCl}) \rightarrow & \text{P} & \text{Propanone + Methanal} \\ \hline \text{B} & n- \text{Hexane + (anh.} \left.\mathrm{AlCl}_3 / \mathrm{HCl}_{(\mathrm{g})}\right) \rightarrow & \text{Q} & \text{Propanone} \\ \hline \text{C} & 2- \text{Methylpropene} + ( \left.\mathrm{O}_3 ~\&~ \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\right) \rightarrow & \text{R} & \text{Propane} \\ \hline \text{D} & \text{Propyne} +\left(\mathrm{HgSO}_4 / \mathrm{H}_2 \mathrm{SO}_4\right. at 333 K) \rightarrow & \text{S} & \text{2-Methylpentane + 3-Methylpentane} \\ \hline \end{array}\)

If \(A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]\), then \(A^{-1}=\)

If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then \(\frac{d y}{d x}=\)

Which of the following artificial sweeteners can be used in soft drinks only?

Two unlike charges of the same magnitude \(Q\) are placed at a distance \(d\). The intensity of the electric field at the middle point is the line joining the two charges is