PYQ Vault

Day 79: CBSE Class 10 Maths

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

  1. Question 1

    Surface Areas and Volumes. Asked once: 2025 (same type asked 3 times)

    15
    A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The entire height of the solid is

    Tap an option to check your answer.

  2. Question 2

    Surface Areas and Volumes. Asked once: 2025 (same type asked 3 times)

    34
    From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid. (Use π=227,5=2.2)\left(\text{Use } \pi = \dfrac{22}{7}, \sqrt{5} = 2.2\right)

  3. Question 3

    Triangles. Asked once: 2024 (same type asked 3 times)

    12
    In ΔABC\Delta ABC, DE∥BCDE \parallel BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is :

    Tap an option to check your answer.

  4. Question 4

    Triangles. Asked once: 2025 (same type asked 3 times)

    33 (a)
    The corresponding sides of ΔABC\Delta ABC and ΔPQR\Delta PQR are in the ratio 3 : 5. AD⊥BCAD \perp BC and PS⊥QRPS \perp QR as shown in the following figures : (i) Prove that ΔADC∼ΔPSR\Delta ADC \sim \Delta PSR (ii) If AD = 4 cm, find the length of PS. (iii) Using (ii) find ar (ΔABC)(\Delta ABC) : ar (ΔPQR)(\Delta PQR)

  5. Question 5

    Triangles. Asked once: 2024 (same type asked 3 times)

    21
    Diagonals AC and BD of a trapezium ABCD intersect at O, where AB∥DCAB \parallel DC. If DOOB=12\dfrac{DO}{OB} = \dfrac{1}{2}, then show that AB = 2CD