The area (in square units) of the triangle formed by the lines $x=0$,$y=0$ and $3x+4y=12$ is:

Which one of the following pairs is mismatched?

If $\frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5}$,then $(A, B, C)$ equals to

If $x > 0, y > 0, z > 0, xy + yz + zx < 1$ and if $\tan^{-1} x + \tan^{-1} y + \tan^{-1} z = \pi$,then $x + y + z$ equals to

For the reaction sequence given below, the correct statement$(s)$ is$($are$)$
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$($In the options, $X$ is any atom other than carbon and hydrogen, and it is different in $P , Q$ and $R )$

All the pairs $(x, y)$ that satisfy the inequality $2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \leq 1$ also satisfy the equation: