CUET Mathematics 2026 21st May Shift 2 PYQs

A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector $3\hat{i} + 2\hat{j} - 2\hat{k}$ is $\frac{x-1}{3} = \frac{y-2}{2} = \frac{y-3}{-2}$.

B. Equation of line passing through (1, 2, 3) and parallel to the line given by $\frac{x+3}{3} = \frac{4-y}{5} = \frac{z+8}{6}$ is $\frac{x-1}{3} = \frac{y-2}{5} = \frac{z+3}{6}$.

C. Equation of line passing through the origin and (5, -2, 3) is $\frac{x}{5} = \frac{y}{-2} = \frac{z}{3}$.

D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is $2(x-1)+3(y-2)-1(z-3) = 0$.

E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is $2x + 3y + 4z = 1$.

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Match List-I with List-II

List-I	List-II
(A) Line : $x = 2y + 1 = z - 1$	(I) Crosses $xz$ plane at (1, 0, 1)
(B) Line : $x + 1 = 2y + 1 = z$	(II) Crosses $xz$ plane at (0, 0, 1)
(C) Line : $x - 1 = 2y = z + 1$	(III) Crosses $xz$ plane at (1, 0, -1)
(D) Line : $x - 1 = 2y = z - 1$	(IV) Crosses $xz$ plane at (1, 0, 2)

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Match the LIST-I with LIST-II

	LIST-I Equation of line		LIST-II Point on the line, direction ratios of the line
A.	$\dfrac{x-5}{3} = \dfrac{y-2}{2} = \dfrac{z+4}{-8}$	I.	$(-3, -2, 8), \langle 5, 2, -4 \rangle$
B.	$\dfrac{x+5}{3} = \dfrac{y+2}{2} = \dfrac{z-4}{-8}$	II.	$(3, 2, -8), \langle 5, 2, -4 \rangle$
C.	$\dfrac{x-3}{5} = \dfrac{y-2}{2} = \dfrac{z+8}{-4}$	III.	$(-5, -2, 4), \langle 3, 2, -8 \rangle$
D.	$\dfrac{x+3}{5} = \dfrac{y+2}{2} = \dfrac{z-8}{-4}$	IV.	$(5, 2, -4), \langle 3, 2, -8 \rangle$

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