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CUET Mathematics 2026 PYQs30 May Shift 2. Free, no login required.

Geometry

past year questions, CUET Mathematics 2026 30 May Shift 2

3D Geometry

past year questions, Geometry, CUET Mathematics 2026 30 May Shift 2

Easy

core

Direction ratios of the line perpendicular to the lines x−32=y+7−3=z−21\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1} and x+21=y+32=z−5−2\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2} are

Solution

✅ Correct Option: 4

The required direction is the cross product of (2,−3,1)(2,-3,1) and (1,2,−2)(1,2,-2).

=((−3)(−2)−(1)(2),  (1)(1)−(2)(−2),  (2)(2)−(−3)(1))=(4,5,7)=\big((-3)(-2)-(1)(2),\;(1)(1)-(2)(-2),\;(2)(2)-(-3)(1)\big)=(4,5,7).

Related questions:

2026: 30 May Shift 1

Let L1L_1 and L2L_2 lines such that L1:r⃗=i^+j^+λ(2i^−j^+k^)L_1:\vec{r}=\hat{i}+\hat{j}+\lambda(2\hat{i}-\hat{j}+\hat{k}), L2:r⃗=2i^+j^−k^+μ(4i^−2j^+2k^)L_2:\vec{r}=2\hat{i}+\hat{j}-\hat{k}+\mu(4\hat{i}-2\hat{j}+2\hat{k}) and θ\theta be the acute angle between L1L_1 and L2L_2, then

Match the LIST-I with LIST-II

LIST-ILIST-II
A.cos⁡θ\cos\thetaI.666\dfrac{\sqrt{66}}{6}
B.sin⁡θ\sin\thetaII.33
C.the shortest distance (in units) between L1L_1 and L2L_2III.11
D.(sum of squares of direction cosines of L1L_1) +2+2IV.00

Choose the correct answer from the options given below:

2025: 2 June Shift 1

The value of λ\lambda so that the lines 1−x3=7y−142λ=z−32\frac{1-x}{3} = \frac{7y-14}{2\lambda} = \frac{z-3}{2} and 7−7x3λ=y−51=6−z5\frac{7-7x}{3\lambda} = \frac{y-5}{1} = \frac{6-z}{5} are at right angle, is:

2022: 17 Aug Shift 2

The direction ratio's of line of intersection of two planes :

2x+y+z+47=02x + y + z + 47 = 0 and 3x−2y−z+41=03x - 2y - z + 41 = 0 are :

2026: 30 May Shift 2

The shortest distance between lines whose vector equations are: r⃗=(1−t)i^+(t−2)j^+(3−2t)k^\vec{r} = (1-t)\hat{i} + (t-2)\hat{j} + (3-2t)\hat{k} and r⃗=(s+1)i^+(2s−1)j^−(2s+1)k^\vec{r} = (s+1)\hat{i} + (2s-1)\hat{j} - (2s+1)\hat{k}, is:

2026: 21 May Shift 2

Match the LIST-I with LIST-II

LIST-I (Line)LIST-II (Direction cosiness)
A. r⃗=(2i^−j^+k^)+λ(3i^+2k^)\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{i} + 2\hat{k})I. ⟨25,15,0⟩\left\langle \dfrac{2}{\sqrt{5}}, \dfrac{1}{\sqrt{5}}, 0 \right\rangle
B. x−12=3−y1=2z−14\dfrac{x-1}{2} = \dfrac{3-y}{1} = \dfrac{2z-1}{4}II. ⟨−13,23,−23⟩\left\langle -\dfrac{1}{3}, \dfrac{2}{3}, -\dfrac{2}{3} \right\rangle
C. x+11=2y+11,z=−1\dfrac{x+1}{1} = \dfrac{2y+1}{1}, z = -1III. ⟨313,0,213⟩\left\langle \dfrac{3}{\sqrt{13}}, 0, \dfrac{2}{\sqrt{13}} \right\rangle
D. 1−x1=y2=1−z2\dfrac{1-x}{1} = \dfrac{y}{2} = \dfrac{1-z}{2}IV. ⟨23,−13,23⟩\left\langle \dfrac{2}{3}, -\dfrac{1}{3}, \dfrac{2}{3} \right\rangle

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

The equation of plane passing through the point of (3, 2, 0) and containing the line x−22=y+34=z−11\frac{x-2}{2} = \frac{y+3}{4} = \frac{z-1}{1} is

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