If $f(x) = \begin{cases} \frac{x-1}{2x^2-7x+5}, & \text{for } x \neq 1 \\ -\frac{1}{3}, & \text{for } x=1 \end{cases}$, then $f'(1)$ is equal to:

$A$ parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. $A$ slab of dielectric is then inserted between the plates. Which of the following three quantities change?
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates

The solution of the differential equation $\frac{dy}{dx} - y \tan x = e^x \sec x$ is

The energy-releasing metabolic process in which substrate is oxidized without an external electron acceptor is called:

Which of the following are not electromagnetic waves?

If the equation whose roots are $p$ times the roots of $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ is a reciprocal equation,then $|p| = $