PYQ Vault

Day 48: MH SSC Class 10 Geometry

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

  1. Question 1

    Pythagoras Theorem. Asked once: Mar 2022

    Q5(i)
    If a and b are natural numbers and a>ba > b. If (a2+b2)(a^2 + b^2), (a2−b2)(a^2 - b^2) and 2ab2ab are the sides of the triangle, then prove that the triangle is right angled. Find out two Pythagorean triplets by taking suitable values of a and b.

  2. Question 2

    Similarity. Asked once: Mar 2022

    Q4(i)
    □ABCD\square ABCD is a parallelogram. Point P is the midpoint of side CD. Seg BP intersects diagonal AC at point X, then prove that: 3AX=2AC3AX = 2AC.

  3. Question 3

    Circle. Asked once: Mar 2023

    Q5(1)
    In the given figure, a circle touches side BC of △ABC\triangle ABC at point P from outside the triangle. Lines AC and AB, when extended, are tangents to the circle at points N and M respectively. Prove that AM=12(Perimeter of △ABC)AM = \dfrac{1}{2}(\text{Perimeter of } \triangle ABC).

  4. Question 4

    Mensuration. Asked once: Mar 2016

    Q5(iii)
    Water flows at the rate of 1515 m per minute through a cylindrical pipe having diameter 2020 mm. How much time will it take to fill a conical vessel of base diameter 4040 cm and depth 4545 cm?

  5. Question 5

    Pythagoras Theorem. Asked once: Mar 2019

    Solve the following questions (Any one):
    Q5(ii)
    In △ABC\triangle ABC, ∠ACB=90∘\angle ACB = 90^\circ. Seg CD ⊥\perp side AB and seg CE is the angle bisector of ∠ACB\angle ACB. Prove that ADBD=AE2BE2\frac{AD}{BD} = \frac{AE^2}{BE^2}.