The major product of the following reaction is

The direction ratios of the two lines $AB$ and $AC$ are $1, -1, -1$ and $2, -1, 1$. The direction ratios of the normal to the plane $ABC$ are

The sound waves of wavelengths $5 ~m$ and $6 ~m$ produce $30$ beats in $3 ~s$. The velocity of sound is: (in $~m/s$)

The acute angle between the two lines whose direction ratios $(l, m, n)$ satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$ is

When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

Considering only the Principal values of inverse functions,the set $A = \{x \geq 0 \mid \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$