PYQ Vault

Day 171: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Three Dimensional Geometry. Asked once: 2024 (same type asked 4 times)

    34 (b)
    Find the shortest distance between the lines L1\mathrm{L}_1 & L2\mathrm{L}_2 given below : L1\mathrm{L}_1 : The line passing through (2,−1,1)(2, -1, 1) and parallel to x1=y1=z3\dfrac{x}{1} = \dfrac{\mathrm{y}}{1} = \dfrac{\mathrm{z}}{3} L2:r⃗=i^+(2μ+1)j^−(μ+2)k^\mathrm{L}_2 : \vec{r} = \hat{i} + (2\mu + 1)\hat{j} - (\mu + 2)\hat{k}.

  2. Question 2

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    35 (a)
    Show that the following lines do not intersect each other : x−13=y+12=z−15\dfrac{x-1}{3} = \dfrac{y+1}{2} = \dfrac{z-1}{5}; x+24=y−13=z+1−2\dfrac{x+2}{4} = \dfrac{y-1}{3} = \dfrac{z+1}{-2}

  3. Question 3

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    13
    The value of λ\lambda for which the angle between the lines r⃗=i^+j^+k^+p(2i^+j^+2k^)\vec{r} = \hat{i} + \hat{j} + \hat{k} + p(2\hat{i} + \hat{j} + 2\hat{k}) and r⃗=(1+q)i^+(1+qλ)j^+(1+q)k^\vec{r} = (1 + q)\hat{i} + (1 + q\lambda)\hat{j} + (1 + q)\hat{k} is π2\frac{\pi}{2} is :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    23
    If the equation of a line is x=ay+bx = ay + b, z=cy+dz = cy + d, then find the direction ratios of the line and a point on the line.

  5. Question 5

    Three Dimensional Geometry. Asked once: 2022 (same type asked 4 times)

    5
    If a line makes an angle α\alpha, β\beta, γ\gamma with the coordinate axes, then find the value of cos⁡2α+cos⁡2β+cos⁡2γ\cos 2\alpha + \cos 2\beta + \cos 2\gamma.