$\int \frac{3^x dx}{\sqrt{9^x-1}}$ is equal to

The angle between the tangents drawn to the parabola $y^2=4x$ from the point $(1,4)$ is

Benzene and toluene form an ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at $T \ K$ are $50 \ mm \ Hg$ and $40 \ mm \ Hg$ respectively. What is the mole fraction of toluene in vapour phase when $117 \ g$ of benzene is mixed with $46 \ g$ of toluene? (molar mass of benzene and toluene are $78 \ g \ mol^{-1}$ and $92 \ g \ mol^{-1}$ respectively)

$A$ sinusoidal carrier voltage of frequency $1.5\,MHz$ and amplitude $50\,V$ is amplitude modulated by a sinusoidal voltage of frequency $10\,kHz$ producing $50\%$ modulation. The lower and upper side-band frequencies in $kHz$ are:

If $3 \sin x + 4 \cos x = 5$,then $6 \tan \frac{x}{2} - 9 \tan^2 \frac{x}{2}$ is equal to

Choose the wrong statement: