PYQ Vault

Day 68: CBSE Class 10 Maths

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

  1. Question 1

    Coordinate Geometry. Asked once: 2026 (same type asked 4 times)

    29 (b)
    Prove that the point P dividing the line segment joining the points A(−1,7)A(-1, 7) and B(4,−3)B(4, -3) in the ratio 3:23 : 2, lies on the line x−3y=−1x - 3y = -1. Also find length of PA and PB.

  2. Question 2

    Introduction to Trigonometry. Asked once: 2026 (same type asked 4 times)

    22 (b)
    Evaluate : 2cos⁡30∘−cot⁡360∘tan⁡30∘\dfrac{2\cos 30^\circ - \cot^3 60^\circ}{\tan 30^\circ}

  3. Question 3

    Introduction to Trigonometry. Asked once: 2026 (same type asked 4 times)

    25 (a)
    If tan⁡A=43\tan A = \dfrac{4}{3}, find sin⁡A\sin A and cos⁡A\cos A.

  4. Question 4

    Introduction to Trigonometry. Asked once: 2026 (same type asked 4 times)

    28 (a)
    Prove that : sec⁡3θsec⁡2θ−1+cosec⁡3θcosec⁡2θ−1=sec⁡θ⋅cosec⁡θ (sec⁡θ+cosec⁡θ)\dfrac{\sec^3\theta}{\sec^2\theta - 1} + \dfrac{\operatorname{cosec}^3\theta}{\operatorname{cosec}^2\theta - 1} = \sec\theta \cdot \operatorname{cosec}\theta\,(\sec\theta + \operatorname{cosec}\theta)

  5. Question 5

    Introduction to Trigonometry. Asked once: 2026 (same type asked 4 times)

    28 (b)
    If sec⁡αcosec⁡β=p\dfrac{\sec\alpha}{\operatorname{cosec}\beta} = p and tan⁡αcosec⁡β=q\dfrac{\tan\alpha}{\operatorname{cosec}\beta} = q, then prove that (p2−q2)sec⁡2α=p2(p^2 - q^2)\sec^2\alpha = p^2.