If $f(x) = \frac{x^2-10x+25}{x^2-7x+10}$ and $f$ is continuous at $x = 5$, then $f(5)$ is equal to

$A$ steel wire can withstand a load up to $2940 ~N$. $A$ load of $150 ~kg$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (in $^{\circ}$)

The events $A$ and $B$ have probabilities $0.25$ and $0.50$,respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then,the probability that neither $A$ nor $B$ occurs is:

What are $X$ and $Y$ in the following reactions?

The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$. If $T$ is the time period and the mass of the particle is $2 \text{ g}$,the kinetic energy of the particle when $t=\frac{T}{4}$ is given by (in $J$)

An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to