If the function $f(x) = x^4 - 62x^2 + ax + 9$ attains its local maximum value at $x = 1$, then a is equal to :

Match List-I with List-II

The function $f(x) = 2x^3 - 15x^2 + 36x + 5$ for $x \in [2,5]$ has

Choose the correct answer from the options given below:

The function $f(x) = x^2e^{-2x}$ increases on

The function $f(x) = \frac{x}{3} + \frac{3}{x}$ is increasing in the interval:

If $f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right)$, then $f(x)$ is :

The rate of change in area of a triangle having sides 10cm and 12cm when the variable angle between them at an angle $60°$, is:

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval: