Among the following the charge that does not exist on any type of charged body is

A body is projected at an angle of \(45^{\circ}\) with the horizontal with a velocity of \(60 \sqrt{2} \mathrm{~ms}^{-1}\). Then the angle made by its velocity with the horizontal after \(6 \mathrm{~s}\) is

Match the following List I with List II.
\(\begin{array}{|c|c|c|}
\hline & \text { List I } & \text { List II } \\
\hline \text { (A) } & \text { Transverse wave (i) } & \begin{array}{l}
\text {Vibrations parallel to the } \\
\text {direction of propagation }
\end{array} \\
\hline \text { (B) } & \begin{array}{l}
\text {Longitudinal wave }
\end{array} & \begin{array}{l}
\text {Vibrations perpendicular to } \\
\text {the direction of propagation }
\end{array} \\
\hline \text { (C) } & \text { Beats } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in the opposite directions }
\end{array} \\
\hline \text { (D) } & \text { Stationary waves (iv) } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in same direction }
\end{array} \\
\hline
\end{array}\)
The correct answer is

A radioactive sample has an activity \(A\) in air. If the sample is kept inside water, then its activity \(A^{\prime}\)

A tuned circuit of a transistor oscillator unit has an inductance of \(5 \mathrm{mH}\) and a capacitance of \(5 \mathrm{pF}\). The natural frequency of the oscillator is

Two coherent sources \(\mathrm{O}_1\) and \(\mathrm{O}_2\) in Young's double slit experiment are illuminated with monochromatic light of wavelength \(5000 Å\). If a second order dark fringe is formed at a point \(\mathrm{R}\) on the screen, the path difference \(\mathrm{O}_1 \mathrm{R} \sim \mathrm{O}_2 \mathrm{R}\) is

If the breaking strength of a rope is \(\frac{4}{3}\) times the weight of a person, then the maximum acceleration with which the person can safely climb up the rope is (g - accelereation due to gravity)

Which of the following orders is not correct about the property shown against it?

A particle of mass \(m\) is under an influence of a force \(\mathbf{F}=\left(-k \mathbf{x}+\mathbf{F}_0\right) \mathrm{N}\). The particle when disturbed will oscillate

In any triangle \(\mathrm{ABC}, a(b \cos C-c \cos B)=\)

The compound which does not respond to iodoform test is

A point mass oscillates along \(\mathrm{x}\)-axis according to \(x=x_0 \sin \left(\omega t-\frac{\pi}{6}\right)\). If the acceleration of the point mass is written as \(\mathrm{a}=\mathrm{A} \sin (\omega \mathrm{t}+\delta)\) then

The general solution of the differential equation \(\frac{d y}{d x}=\frac{2 x y-4 x+y-2}{2 x y+x-4 y-2}\) is