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Day 239: CDS Maths

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

  1. Question 1

    Lines, Angles and Polygons. Asked once: CDS 1 2020

    96
    In the given figure PQPQ is parallel to RSRS, ∠AEF=95∘\angle AEF = 95^\circ, ∠BHS=110∘\angle BHS = 110^\circ, and ∠ABC=x∘\angle ABC = x^\circ. Then what is the value of xx?

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  2. Question 2

    Logarithms. Asked once: CDS 1 2025

    20
    If log⁡10(100001−4x)5−x=1\dfrac{\log_{10}(100001 - 4^x)}{5 - x} = 1, then what is xx equal to ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 2 2024

    48
    A square is drawn inside a square of side 14 cm in such a way that the corners of the inner square coincide with the mid points of the sides of the outer square. What is the area lying between the two squares ?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 1 2026

    69
    The volume of a cube is 88 cm3\text{cm}^3 and is equal to the volume of a cuboid of length x, breadth y and height z, where x, y and z are natural numbers (x>y>z)(x > y > z). Let n be the number of such cuboids with different dimensions. What is the value of n ?

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  5. Question 5

    Number System. Asked once: CDS 1 2026

    28
    Consider the following statements : I. Two consecutive natural numbers are always co-prime. II. If m and n are relatively prime, then m×nm \times n is always even. Which of the statements given above is/are correct ?

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