CUET Mathematics - If the lines x - 5/5 + 2 = 2 - y/5 = 1 - z/-1 and y+1/22 = z - 1/3 are perpendicular, then the value of is equal to | PYQs + Solutions

26 May Shift 2

Which of the following statements are true?

(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector $3\hat{i} + 2\hat{j} - 8\hat{k}$ is $\vec{r} = (5\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(3\hat{i} + 2\hat{j} - 8\hat{k})$

(B) Vector form of the equation of line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is $\vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k})$

(C) The direction cosines of z-axis are (1, 1,0).

(D) If a line has direction ratios 2, -1, -2, then its direction cosines are -2/3, -1/3, -2/3.

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15 May Shift 1

If $\alpha, \beta$ and $\gamma$ are angle of inclinations of a line with x, y and z axes respectively, then the value of $2(\cos 2\alpha + \cos 2\beta + \cos 2\gamma)$ is

14 May Shift 2

Match List-I with List-II

List-I	List-II
Lines	Direction Ratios
(A) $\frac{x - 1}{2} = \frac{2 - y}{1} = z$	(I) 1, 3, -1
(B) $\frac{2x - 1}{2} = \frac{y + 1}{3} = \frac{1 - z}{1}$	(II) 2, -2, 0
(C) $\frac{x + 1}{2} = \frac{3 - y}{2}, z = 2$	(III) 2, -1, 1
(D) $\frac{2x - 3}{4} = \frac{1 - 2y}{2} = \frac{z}{5}$	(IV) 2, -1, 5

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CUET Mathematics 2025 3 June Shift 1 PYQs

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