PYQ Vault

Day 184: 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)

    7
    Direction cosines of a line perpendicular to both x-axis and z-axis are :

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  2. Question 2

    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) : The lines r⃗=a⃗1+λb⃗1\vec{r} = \vec{a}_1 + \lambda \vec{b}_1 and r⃗=a⃗2+μb⃗2\vec{r} = \vec{a}_2 + \mu \vec{b}_2 are perpendicular, when b⃗1⋅b⃗2=0\vec{b}_1 \cdot \vec{b}_2 = 0. Reason (R) : The angle θ\theta between the lines r⃗=a⃗1+λb⃗1\vec{r} = \vec{a}_1 + \lambda \vec{b}_1 and r⃗=a⃗2+μb⃗2\vec{r} = \vec{a}_2 + \mu \vec{b}_2 is given by cos⁡θ=b⃗1⋅b⃗2∣b⃗1∣∣b⃗2∣\cos\theta = \dfrac{\vec{b}_1 \cdot \vec{b}_2}{|\vec{b}_1||\vec{b}_2|}.

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  3. Question 3

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

    6
    If ∣a⃗×b⃗∣=3|\vec{a} \times \vec{b}| = \sqrt{3} and a⃗⋅b⃗=−3\vec{a} \cdot \vec{b} = -3, then angle between a⃗\vec{a} and b⃗\vec{b} is

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  4. Question 4

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

    30 (a)
    If x30y20=(x+y)50x^{30} y^{20} = (x + y)^{50}, prove that dydx=yx\dfrac{dy}{dx} = \dfrac{y}{x}.

  5. Question 5

    Integrals. Asked once: 2024 (same type asked 2 times)

    27 (b)
    Find : ∫1x [(log⁡x)2−3log⁡x−4] dx\displaystyle\int \dfrac{1}{x\,[(\log x)^2 - 3 \log x - 4]}\, dx