A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of \(15^{\circ}\) in time \(t\) sec. The increase in angle through which it rotates in the next \(2 t \mathrm{sec}\) is

The study of photoelectric effect is useful in understanding

To heat the food containing water, the frequency of the microwaves used in microwave oven is

A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by $1\%$ and $3\%$ respectively, the modulation index is changed by

Two particles executing SHM along a straight line have same amplitude 'A' and time period ' \(T\) '. At \(t=0\), one particle is at a displacement \(+A\) and another is at a displacement \(-\frac{A}{2}\) and they are approaching towards each other. They cross each other after a time.

If the amplitude of a lightly damped oscillator decreases by \(1.5 \%\) then the mechanical energy of the oscillator lost in each cycle is

Two polaroids are placed in the path of unpolarised light beam of intensity \(I_0\) such that no light is emitted from the second polaroid. If a third polaroid whose polarisation axis makes an angle \(\theta\) with that of the first polaroid is placed between the polaroids, then intensity of light emerging from the last polaroid is

\(\int x^5 e^{-2 x} d x=\)

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

A random variable \(X\) follows the binomial distribution and \(X \sim B(n, 0.3)\). If the mean of \(X\) is three times as large as the standard deviation of \(X\), then \(n=\)

Which of the following causes "blue baby syndrome"?

If the equation of one asymptote of the hyperbola \(14 x^2+38 x y+20 y^2+x-7 y-91=0\) is \(7 x+5 y-3=0\), then the other asymptote is

In Young's double slit experiment, the wavelengths of red and blue lights used are \(7.5 \times 10^{-5} \mathrm{~cm}\) and \(5 \times 10^{-5} \mathrm{~cm}\) respectively. If \(\mathrm{n}^{\text {th }}\) bright fringe of red color coincides with \((n+1)^{\text {th }}\) bright fringe of blue colour, then the value of ' \(n\) ' is