If $\cos ^{-1}\left(\frac{x}{2}\right)+\cos ^{-1}\left(\frac{y}{3}\right)=\theta$,then $9x^2-12xy\cos \theta+4y^2=$

Which of the following compounds is soluble in benzene but almost insoluble in water?

Among the following, the $CORRECT$ combinations are :
$A.$ $IF_3$ $\rightarrow$ $T$-shaped $(sp^3d)$
$B.$ $IF_5$ $\rightarrow$ Square pyramidal $(sp^3d^2)$
$C.$ $IF_7$ $\rightarrow$ Pentagonal bipyramidal $(sp^3d^3)$
$D.$ $ClO_4^-$ $\rightarrow$ Square planar $(sp^3d)$
Choose the correct answer from the options given below :

If a point $P$ moves such that its distances from the point $A(1,1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is

Which among the following is a benzylic halide?

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to