PYQ Vault

Day 60: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 2 times: 2023, 2024. This one: 2024

    25
    Find the vector equation of the line passing through the point (2,3,−5)(2, 3, -5) and making equal angles with the co-ordinate axes.

  2. Question 2

    Three Dimensional Geometry. This type asked 2 times: 2023, 2024. This one: 2024

    34
    The vertices of Δ\Delta ABC are A(1, 1, 0), B(1, 2, 1) and C(−2-2, 2, −1-1). Find the equations of the medians through A and B. Use the equations so obtained to find the coordinates of the centroid.

  3. Question 3

    Vector Algebra. This type asked 2 times: 2023, 2024. This one: 2024

    13
    Let a⃗\vec{a} be any vector such that ∣a⃗∣=a|\vec{a}| = a. The value of ∣a⃗×i^∣2+∣a⃗×j^∣2+∣a⃗×k^∣2|\vec{a} \times \hat{i}|^{2} + |\vec{a} \times \hat{j}|^{2} + |\vec{a} \times \hat{k}|^{2} is :

    Tap an option to check your answer.

  4. Question 4

    Vector Algebra. This type asked 2 times: 2023, 2024. This one: 2024

    12
    The vectors a⃗=2i^−j^+k^\vec{a} = 2\hat{i} - \hat{j} + \hat{k}, b⃗=i^−3j^−5k^\vec{b} = \hat{i} - 3\hat{j} - 5\hat{k} and c⃗=−3i^+4j^+4k^\vec{c} = -3\hat{i} + 4\hat{j} + 4\hat{k} represents the sides of

    Tap an option to check your answer.

  5. Question 5

    Application of Integrals. This type asked 2 times: 2022, 2023. This one: 2023

    33
    The area of the region bounded by the line y = mx (m > 0), the curve x2+y2=4x^2 + y^2 = 4 and the x-axis in the first quadrant is π2\frac{\pi}{2} units. Using integration, find the value of m.