If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

If $\vec{a} + \vec{b} + \vec{c} = 0$,$|\vec{a}| = 3$,$|\vec{b}| = 5$,and $|\vec{c}| = 7$,then the angle between $\vec{a}$ and $\vec{b}$ is

Which of the following statements is $NOT$ consistent with the rules of nomenclature?

$A$ galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \text{ V}$ along with a resistance of $2950 \Omega$ in series. $A$ full-scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions,the total resistance in series should be: (in $Omega$)

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $C$ is equal to (in $^{\circ}$)

The major product in the following reaction is: