PYQ Vault

Day 18: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2022, 2025

    24 (b)
    Let a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c} be three vectors such that a⃗⋅b⃗=a⃗⋅c⃗\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} and a⃗×b⃗=a⃗×c⃗\vec{a} \times \vec{b} = \vec{a} \times \vec{c}, a⃗≠0⃗\vec{a} \neq \vec{0}. Show that b⃗=c⃗\vec{b} = \vec{c}.

  2. Question 2

    Vector Algebra. Asked 2 times: 2022*, 2025 (* = numbers or wording changed that year)

    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 ∣a⃗×b⃗∣2+∣a⃗⋅b⃗∣2=256|\vec{a} \times \vec{b}|^2 + |\vec{a} \cdot \vec{b}|^2 = 256 and ∣b⃗∣=8|\vec{b}| = 8, then ∣a⃗∣=2|\vec{a}| = 2. Reason (R) : sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1 and ∣a⃗×b⃗∣=∣a⃗∣ ∣b⃗∣sin⁡θ|\vec{a} \times \vec{b}| = |\vec{a}|\,|\vec{b}|\sin\theta and a⃗⋅b⃗=∣a⃗∣ ∣b⃗∣cos⁡θ\vec{a} \cdot \vec{b} = |\vec{a}|\,|\vec{b}|\cos\theta.

    Tap an option to check your answer.

  3. Question 3

    Vector Algebra. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    2
    The unit vector perpendicular to the vectors i^−j^\hat{i} - \hat{j} and i^+j^\hat{i} + \hat{j} is

    Tap an option to check your answer.

  4. Question 4

    Vector Algebra. Asked 2 times: 2023, 2025

    16
    If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| for any two vectors, then vectors a⃗\vec{a} and b⃗\vec{b} are :

    Tap an option to check your answer.

  5. Question 5

    Application of Derivatives. Asked 2 times: 2023*, 2024 (* = numbers or wording changed that year)

    23
    Show that f(x)=4sin⁡x2+cos⁡x−xf(x) = \dfrac{4 \sin x}{2 + \cos x} - x is an increasing function of xx in [0,π2]\left[0, \dfrac{\pi}{2}\right].