PYQ Vault

Day 7: CBSE Class 10 Maths

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

  1. Question 1

    Some Applications of Trigonometry. Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    34 (a)
    The angle of elevation of the top of a building from a point A, on the ground, is 30∘30^\circ. On moving a distance of 24 m towards its base to the point B, the angle of elevation changes to 60∘60^\circ. Find the height of the building and distance of point A from the base of the building. (Take 3=1⋅73\sqrt{3} = 1{\cdot}73)

  2. Question 2

    Triangles. Asked 3 times: 2023, 2025, 2026

    22
    D is a point on the side BC of ΔABC\Delta ABC such that ∠CAB=∠CDA\angle CAB = \angle CDA. Show that CA2=CB×CDCA^2 = CB \times CD.

  3. Question 3

    Triangles. Asked 3 times: 2023, 2024, 2026* (* = numbers or wording changed that year)

    33 (b)
    Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that (i) AQ = QR (ii) AP = 2PQ (iii) PR = 2AP

  4. Question 4

    Arithmetic Progressions. Asked 3 times: 2023*, 2024*, 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.
    20
    Assertion (A) : For an A.P., 3,6,9, …, 198, 10th10^{\text{th}} term from the end is 168. Reason (R) : If ‘a’ and ‘ll’ are the first term and last term of an A.P. with common difference ‘d’, then nthn^{\text{th}} term from the end of the given A.P. is l−(n−1)dl - (n - 1)d.

    Tap an option to check your answer.

  5. Question 5

    Coordinate Geometry. Asked 3 times: 2023*, 2024, 2025 (* = numbers or wording changed that year)

    23
    Prove that abscissa of a point P which is equidistant from points with coordinates A(7,1)A(7, 1) and B(3,5)B(3, 5) is 2 more than its ordinate.