CUET Mathematics 2025 21 May Shift 1 PYQs

Which of the following statements are true?

(A) The function $f(x) = \frac{x^4}{4} - \frac{4}{3}x^3 + \frac{x^2}{2} + 6x$ has 3 critical points.

(B) The function $f(x) = |x| + 3$ has no minimum value.

(C) A local maximum value is always the absolute maximum value.

(D) $f(x) = x^2$ has minima at $x=0$.

Choose the correct answer from the options given below:

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(C) The minimum value of the function is $2$

(D) The maximum value of the function is $\frac{3}{4}$

Choose the correct answer from the options given below :

The equation of the tangent line to the curve $y = x^2 - 2x + 5$ which is parallel to the line $4x - y + 1 = 0$ is