In Thomson's experiment to determine \(\frac{e}{m}\) of an electron, it is found that an electron beam having a kinetic energy of \(45.5 \mathrm{eV}\) remains undeflected, when subjected to crossed electric and magnetic fields. If \(E=1 \times 10^3 \mathrm{Vm}^{-1}\), the value of \(B\) is (mass of the electron is \(9.1 \times 10^{-31} \mathrm{~kg}\) )

The value of \(Y_1\) and \(Y_2\), respectively in the following logic circuit if both \(A\) and \(B\) are 1.

The variation of potential energy of a harmonic oscillator is as shown in the figure. Then, find the spring constant.

A body projected from the ground reaches a point \(X\) in its path after 3 seconds and from there it reaches the ground after further 6 seconds. The vertical distance of the point \(X\) from the ground is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

A solenoid of one meter length and 3.55 cm inner diameter carries a current of 5 A. If the solenoid consists of five closely packed layers each with 700 turns along its length, then the magnetic field at its centre is

In the Uranium radioactive series, the initial nucleus is \({ }_{92}^{238} \mathrm{U}\) and final nucleus is \({ }_{82}^{206} \mathrm{~Pb}\). When the Uranium nucleus decays to lead, the number of \(\alpha\)-particles emitted is .......... and the number of \(\beta\)-particles emitted is ____.

Four capacitors marked with capacitances and breakdown voltages are connected as shown in the figure. The maximum emf of the source, so that no capacitor breaks down is

Which of the following property is less for \(\mathrm{D}_2 \mathrm{O}\) than \(\mathrm{H}_2 \mathrm{O}\) ?

Which of the following statements regarding centre of mass is NOT true?

\(\tan ^{-1} 2+\tan ^{-1} 3=\)

An electric dipole with dipole moment \(2 \times 10^{-10} \mathrm{C} \mathrm{m}\) is aligned at an angle \(30^{\circ}\) with the direction of uniform electric field of \(10^4 \mathrm{~N} \mathrm{C}^{-1}\). The magnitude of the torque acting on the dipole is

If \(\sec ^{-1} \frac{x}{a}-\sec ^{-1} \frac{x}{b}=\sec ^{-1} b \sec ^{-1} a\), then \(x\) is equal to

From the following, identify the reactions which are responsible for depletion of ozone layer.
\(\begin{aligned}
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{NO}_2(g) \rightarrow \mathrm{ClONO}_2(g) \\
& \mathrm{CF}_2 \mathrm{Cl}_2(g) \xrightarrow{\text { uv }} \mathrm{Cl}(g)+\dot{\mathrm{CF}}_2 \mathrm{Cl}(g) \\
& \dot{\mathrm{Cl}}(g)+\mathrm{CH}_4(g) \rightarrow \mathrm{HCl}(g)+\dot{\mathrm{C}} \mathrm{H}_3(g) \\
& \dot{\mathrm{C}} \mathrm{l}(\mathrm{g})+\mathrm{O}_3(g) \rightarrow \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}_2(g) \\
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}(g) \rightarrow \dot{\mathrm{C}} \mathrm{l}(g)+\mathrm{O}_2(g)
\end{aligned}\)