PYQ Vault

Day 159: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2023 (same type asked 2 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : A line through the points (4, 7, 8) and (2, 3, 4) is parallel to a line through the points (−1,−2,1)(-1, -2, 1) and (1, 2, 5). Reason (R) : Lines r⃗=a1⃗+λb1⃗\vec{r} = \vec{a_1} + \lambda \vec{b_1} and r⃗=a2⃗+μb2⃗\vec{r} = \vec{a_2} + \mu \vec{b_2} are parallel if b1⃗⋅b2⃗=0\vec{b_1} \cdot \vec{b_2} = 0.

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked once: 2025 (same type asked 2 times)

    12
    If PQ→×PR→=4i^+8j^−8k^\overrightarrow{PQ} \times \overrightarrow{PR} = 4\hat{i} + 8\hat{j} - 8\hat{k}, then the area (ΔPQR)(\Delta PQR) is

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  3. Question 3

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    24 (a)
    If the vectors a⃗\vec{a} and b⃗\vec{b} are such that ∣a⃗∣=3|\vec{a}| = 3, ∣b⃗∣=23|\vec{b}| = \dfrac{2}{3} and a⃗×b⃗\vec{a} \times \vec{b} is a unit vector, then find the angle between a⃗\vec{a} and b⃗\vec{b}.

  4. Question 4

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    5
    If the vector i^−bj^+k^\hat{i} - b\hat{j} + \hat{k} is equally inclined to the coordinate axes, then the value of b is :

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  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 2 times)

    26 (a)
    If xcos⁡(p+y)+cos⁡psin⁡(p+y)=0x \cos (p + y) + \cos p \sin (p + y) = 0, prove that cos⁡pdydx=−cos⁡2(p+y)\cos p \dfrac{dy}{dx} = -\cos^2 (p + y), where p is a constant.