The value of $x$ for which $\sin (\cot^{-1} (1 + x)) = \cos(\tan^{-1} x)$ is

Which of the following is a biofertilizer?

If three points $A, B$ and $C$ have position vectors $(1, x, 3), (3, 4, 7)$ and $(y, -2, -5)$ respectively and if they are collinear, then $(x, y)$ is

In an ideal gas at temperature $T$,the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is:

$A$ black body at a temperature of $1640\,K$ has the wavelength corresponding to maximum emission equal to $1.75\,\mu m$. Assuming the moon to be a perfectly black body,the temperature of the moon,if the wavelength corresponding to maximum emission is $14.35\,\mu m$,is.......$K$.

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to