CUET Mathematics 2025 26 May Shift 2 PYQs

Let $L_1$ and $L_2$ be two lines, represented as,

$L_1: \vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})$ and $L_2: \vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(4\hat{i} - 2\hat{j} + 2\hat{k})$, where $\lambda$ and $\mu$ are scalars. Then which of the following are true?

(A) $L_1$ is perpendicular to $L_2$.

(B) $L_1$ is parallel to $L_2$.

(C) $L_1$ passes through the point (1, 1, 0)

(D) $L_2$ passes through the point (2, 1, -1)

Choose the correct answer from the options given below:

If the lengths of the three sides of a trapezium other than the base are $10 \mathrm{~cm}$ each, then the maximum area of the trapezium is:

The angle between the line $2x = 3y = z$ and $x$- axis is: