The velocity acquired by an electron at rest when subjected to a uniform electric field of potential difference 180 V is
(Mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

A proton of velocity a \((3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-1}\) enters field of magnetic induction \((2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\) tesla, the acceleration produced in the proton in \(\mathrm{ms}^{-2}\) is \(\left(\right.\) Specific charge of proton \(=0.96 \times 10^8 \mathrm{Ckg}^{-1}\) )

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

If a transmitting antenna of height \(105 \mathrm{~m}\) is placed on a hill, then its coverage area is

If a current of 15 A passes through a solenoid of length 25 cm, radius 2 cm and number of turns 500, then the magnetic moment of the solenoid is

A particle executes simple harmonic motion between $x=-A$ and $x=+A$. If it takes a time $T_1$ to $g_0$ from $x=0$ to $x=A/2$ and $T_2$ to go from $x=A/2$ to $x=A$. Then

The Solar Radiation is

Two light waves of wavelengths \(600 \mathrm{~nm}\) and \(200 \mathrm{~nm}\) incident on a metal surface. The maximum velocity of photoelectrons produced due to one wavelength is \(\frac{1}{3}\) of the maximum velocity of the photoelectrons produced due to the other wavelength, then the work function of the metal is

The insecticide DDT is considered as ____

If the circle \(x^2+y^2+8 x-4 y+c=0\) touches the circle \(x^2+y^2+2 x+4 y-11=0\) externally and cuts the circle \(x^2+y^2-6 x+8 y+k=0\) orthogonally, then \(\mathrm{k}=\)

Let \(B=\left(\begin{array}{ccc}2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & 1 & -1\end{array}\right)\) and \(C=\left(\begin{array}{ccc}-1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2\end{array}\right)\)
If a matrix \(A\) is such that \(\mathrm{BAC}=\mathrm{I}\), then \(\mathrm{A}^{-1}=\)

In \(\triangle A B C\), if \(A, B, C\) are in arithmetic progression then
\(\sqrt{\mathrm{a}^2-\mathrm{ac}+\mathrm{c}^2} \cdot \cos \left(\frac{\mathrm{~A}-\mathrm{C}}{2}\right)=\)

\(\int_0^{\pi / 2} \log _e(\sin 2 x) d x\)