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

In the expansion of $(1 + x)^n$,the coefficients of the $p^{th}$ and $(p + 1)^{th}$ terms are respectively $p$ and $q$. Then $p + q = $

Which of the following is a worker bee in a honeybee colony?

Four particles,each of mass $M$,are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is:

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$,they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is

Which of the following octahedral complexes does not exhibit geometric isomerism? ($A$ and $B$ are monodentate ligands.)