CUET Mathematics 2026 31st May Shift 2 PYQs

Let $y = \log(x + \sqrt{x^2+1})$, and $a\frac{d^2y}{dx^2} + b\frac{dy}{dx} = c$. Then identify the correct statements about the values of $a$, $b$ and $c$ :

(A) $a = 1 + x^2$

(B) $b = 0$

(C) $c = 0$

(D) $b = x$

(E) $c = 2$

Choose the correct answer from the options given below :

Consider the following statements for the curve $f(x) = x|x|$ and find that which of the following(s) are/is correct :

(A) $f(x) = x|x|$ is differentiable at $x = 0$.

(B) $f(x) = x|x|$ is continuous at $x = 0$ but not differentiable at $x = 0$.

(C) $f(x) = x|x|$ has point of infection at $x = 0$.

(D) $f(x) = x|x|$ is symmetrical about y-axis.

Choose the correct answer from the options given below :

If $x^m y^n = (x + y)^{m+n}$, then $\frac{d^2y}{dx^2}$ is equal to: