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Day 30: CDS Maths

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

  1. Question 1

    Quadrilaterals. This type asked 3 times: CDS 2 2020, CDS 1 2022, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    51
    In a cyclic quadrilateral ABCD, ∠A=(4x+3)∘\angle A = (4x + 3)^\circ, ∠B=(3y+9)∘\angle B = (3y + 9)^\circ, ∠C=(4y−3)∘\angle C = (4y - 3)^\circ, ∠D=(5x−10)∘\angle D = (5x - 10)^\circ. What is ∠A+∠B\angle A + \angle B equal to ?

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  2. Question 2

    Quadrilaterals. This type asked 3 times: CDS 2 2020, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    64
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : ABCD is a quadrilateral with AB = 6 cm, BC = 8 cm, CD = 454\sqrt{5} cm, DA = 252\sqrt{5} cm and inscribed in a circle. What is the diameter of the circle ? Statement I : The area of the quadrilateral is 44 cm2\text{cm}^2. Statement II : ∠ABC=90∘\angle ABC = 90^\circ. Which one of the following is correct in respect of the above Question and Statements ?

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  3. Question 3

    Ratio, Proportion and Variation. This type asked 3 times: CDS 1 2024, CDS 2 2024, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    25
    An alloy (X) of gold and silver is taken in the ratio 1 : 2 and another alloy (Y) of gold and silver is taken in the ratio 2 : 3. How many parts of X and Y must be taken to obtain a new alloy Z consisting of gold and silver in the ratio 4 : 7 ?

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  4. Question 4

    Statistics. This type asked 3 times: CDS 2 2025, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    97
    If the mean of 15 observations, namely x1,x2,x3,…,x15x_1, x_2, x_3, \ldots, x_{15} is 2.5, then what is the value of ∑i=115[5(4xi+1)]\sum_{i=1}^{15} [5(4x_i + 1)] ?

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  5. Question 5

    Statistics. This type asked 3 times: CDS 2 2022, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    93
    Consider the observations x, x + 4, 30, 33, 74, 78, 49, 52, 98, 85. If the median of the data is 67, then what is the value of x ?

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