If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then :

Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :

The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds of motion is :

For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by