The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$, is discontinuous at

If $x^2y^2 = a^{\pi/2}$, then $\dfrac{d^2y}{dx^2} =$

If $f(x) = \begin{cases} \dfrac{1}{|x|}, & x \geq 1 \\ ax^2+b, & x < 1 \end{cases}$ is differentiable at $x=1$ then

The given function $f(x) = [x]$ is discontinuous at :

If $x = a\left(\cos t + \log \tan\frac{t}{2}\right), y = a\sin t$, then value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is

If the function

$f(x) = \begin{cases} ax + 2, & x \leq 1 \\ x^2 + 3x + b, & x > 1 \end{cases}$

is differentiable at $x = 1$, then the value of $(2a + b)$ is

At $x = 2$, $f(x) = [x]$ is

[where [.] is greatest integer function]