Let $f(x)$ be a polynomial of degree $3$ such that $f(-1) = 10$,$f(1) = -6$,$f(x)$ has a critical point at $x = -1$,and $f'(x)$ has a critical point at $x = 1$. Then $f(x)$ has a local minima at $x =$

At a given instant of time,two particles have position vectors $4 \hat{i} + 4 \hat{j} + 57 \hat{k} \text{ m}$ and $2 \hat{i} + 2 \hat{j} + 5 \hat{k} \text{ m}$ respectively. If the velocity of the first particle is $0.4 \hat{i} \text{ ms}^{-1}$,what is the velocity of the second particle in $\text{ms}^{-1}$ if they collide after $10 \text{ s}$?

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc,so as to rotate with angular velocity $\omega$ in time $t$?

Which one of the following is commonly used in the transfer of foreign $DNA$ into crop plants?

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

Consider the following statements $A$ and $B$. Identify the correct choice in the given answer.
$A$. $p-n, p-p$ and $n-n$ forces between nucleons are not equal and charge dependent.
$B$. In a nuclear reactor,the fission reaction will be in an accelerating state if the value of the neutron reproduction factor $k > 1$.