If the function defined by $f(x) = \begin{cases} \ kx^2 + 1, & \text{if } x \le 1 \\ 2 , & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then k is equal to

If $x = t^2$ and $y = t\sqrt{t}$, then $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{1}{4}$ is :

If $x=4t^3$ and $y=6t^2$ then $\frac{d^2y}{dx^2}$ at $t=1$ is

If $x^2+y^2 = t+\dfrac{1}{t}$ and $x^4+y^4=t^2+\dfrac{1}{t^2}$, then $\dfrac{dy}{dx}$ is equal to

If $f(x) = 2x$ and $g(x) = \frac{x^2}{2} + 1$, then which of the following can be a discontinuous function ?

Match List-I with List-II

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below: