If $\frac{x^3 - 6x^2 + 10x - 2}{x^2 - 5x + 6} = f(x) + \frac{A}{(x - 2)} + \frac{B}{(x - 3)}$,then $f(x) =$ ?

The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0$ for $x>0$ is equal to:

$A$ solid sphere is rolling on a frictionless surface with a translational velocity $v \ m/s$,as shown in the figure. If it is to climb the inclined surface to a height $h$,then $v$ should be:

At identical temperature and pressure,the rate of diffusion of hydrogen gas is $3\sqrt{3}$ times that of a gaseous hydrocarbon having molecular formula $C_nH_{2n-2}$. What is the value of $n$?

Let a random variable $X$ have a Binomial distribution with mean $8$ and variance $4$. If $P(X \leq 2) = \frac{k}{2^{16}}$,then $k$ is equal to:

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is