PYQ Vault

Day 108: CBSE Class 12 Maths

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

  1. Question 1

    Probability. Asked once: 2025 (same type asked 4 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : If A and B are two events such that P(A∩B)=0P(A \cap B) = 0, then A and B are independent events. Reason (R) : Two events are independent if the occurrence of one does not effect the occurrence of the other.

    Tap an option to check your answer.

  2. Question 2

    Three Dimensional Geometry. Asked once: 2025 (same type asked 4 times)

    30 (a)
    Find the distance of the point P(2, 4, −1)P(2,\ 4,\ -1) from the line x+51=y+34=z−6−9\dfrac{x + 5}{1} = \dfrac{y + 3}{4} = \dfrac{z - 6}{-9}.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2025 (same type asked 4 times)

    34 (b)
    Find a point P on the line x+51=y+34=z−6−9\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9} such that its distance from point Q(2, 4, -1) is 7 units. Also, find the equation of line joining P and Q.

  4. Question 4

    Three Dimensional Geometry. Asked once: 2025 (same type asked 4 times)

    29 (a)
    Verify that lines given by r⃗=(1−λ)i^+(λ−2)j^+(3−2λ)k^\vec{r} = (1 - \lambda)\hat{i} + (\lambda - 2)\hat{j} + (3 - 2\lambda)\hat{k} and r⃗=(μ+1)i^+(2μ−1)j^−(2μ+1)k^\vec{r} = (\mu + 1)\hat{i} + (2\mu - 1)\hat{j} - (2\mu + 1)\hat{k} are skew lines. Hence, find shortest distance between the lines.

  5. Question 5

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

    32
    Find the value of p for which the lines r⃗=λi^+(2λ+1)j^+(3λ+2)k^\vec{r} = \lambda\hat{i} + (2\lambda + 1)\hat{j} + (3\lambda + 2)\hat{k} and r⃗=i^−3μj^+(pμ+7)k^\vec{r} = \hat{i} - 3\mu\hat{j} + (p\mu + 7)\hat{k} are perpendicular to each other and also intersect. Also, find the point of intersection of the given lines.