PYQ Vault

Day 44: CBSE Class 10 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Coordinate Geometry. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    29
    The three vertices of a rhombus PQRS are P(2,−3)P(2, -3), Q(6,5)Q(6, 5) and R(−2,1)R(-2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

  2. Question 2 (case study, 4 parts)

    Coordinate Geometry. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : (−4,2)(-4, 2) Rajasthan High Court Point B : (4,−4)(4, -4) Birla Mandir Point C : (4,3)(4, 3) Heera Bagh Point D : (−5,−2)(-5, -2) Amar Jawan Jyoti Based on the above, answer the following questions :
    38 (i)
    Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?
    38 (ii)
    There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio.
    38 (iii) (a)
    Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer.
    38 (iii) (b)
    Using section formula, show that points A, O and B are not collinear.

  3. Question 3

    Introduction to Trigonometry. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    9
    sec⁡2A−1sin⁡2A\dfrac{\sec^2 A - 1}{\sin^2 A} is same as

    Tap an option to check your answer.

  4. Question 4

    Introduction to Trigonometry. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    10
    If cos⁡A=12\cos A = \dfrac{1}{2}, then the value of sin⁡2A+2cos⁡2A\sin^2 A + 2\cos^2 A is :

    Tap an option to check your answer.

  5. Question 5

    Pair of Linear Equations in Two Variables. This type asked 3 times: 2023, 2024, 2026. This one: 2023

    27
    A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.