PYQ Vault

Day 209: CBSE Class 10 Maths

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

  1. Question 1

    Arithmetic Progressions. Asked once: 2023

    27
    If pthp^{\text{th}} term of an A.P. is q and qthq^{\text{th}} term is p, then prove that its nthn^{\text{th}} term is (p+q−n)(p + q - n).

  2. Question 2

    Circles. Asked once: 2025

    31
    In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ=15∘\angle OPQ = 15^\circ and ∠PTQ=θ\angle PTQ = \theta, then find the value of sin⁡2θ\sin 2\theta.

  3. Question 3

    Coordinate Geometry. Asked once: 2025

    27
    If (a,b)(a, b) is the mid-point of the line segment joining the points A(10,−6)A(10, -6) and B(k,4)B(k, 4) and a−2b=18a - 2b = 18, then find the value of k.

  4. Question 4

    Introduction to Trigonometry. Asked once: 2023

    21 (a)
    If sin⁡θ+sin⁡2θ=1\sin\theta + \sin^2\theta = 1, then prove that cos⁡2θ+cos⁡4θ=1\cos^2\theta + \cos^4\theta = 1.

  5. Question 5

    Pair of Linear Equations in Two Variables. Asked once: 2025

    21 (b)
    In a pair of supplementary angles, the greater angle exceeds the smaller by 50∘50^\circ. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.