$10 \ g$ of hydrogen and $64 \ g$ of oxygen were filled in a steel vessel and exploded. The amount of water produced in this reaction will be ........... $mol$.

$A$ radioactive sample consists of two distinct species having an equal number of atoms $N_0$ initially. The mean-life of one species is $\tau$ and of the other is $5\tau$. The decay products in both cases are stable. The total number of radioactive nuclei at $t = 5\tau$ is:

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

$\int(x+1)^2 e^x d x$ is equal to

$A$ ball of mass $m_1$ and another ball of mass $m_2$ are dropped from the same height. If the time taken by the balls to reach the ground is $t_1$ and $t_2$ respectively,then:

For $x \in \mathbb{R}$,the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is