CUET Mathematics 2026 19th May Shift 2 PYQs

A function $f(x)$ is defined as:

$f(x) = x^3-6x^2+9x+15$

For the function $f(x)$, which of the following statements are correct ?

(A) The critical points are $x=1$ and $x=3$.

(B) $x=1$ is a point of local minimum.

(C) The local maximum value is 19.

(D) $x=3$ is a point of local minimum.

Choose the correct answer from the options given below:

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm, is:

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