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Day 296: CDS Maths

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

  1. Question 1

    Quadrilaterals. Asked once: CDS 1 2019

    40
    Let PQRSPQRS be a parallelogram whose diagonals PRPR and QSQS intersect at OO. If triangle QRSQRS is an equilateral triangle having a side of length 10 cm, then what is the length of the diagonal PRPR ?

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  2. Question 2

    Ratio, Proportion and Variation. Asked once: CDS 1 2017

    22
    The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:41 : 2 : 3 : 4. If the loss in total value of the diamond was Rs. 70,000, what was the price of the original diamond ?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 1 2020

    4
    Which one of the following is a set of solutions of the equation xx=xxnx^{\sqrt{x}} = \sqrt[n]{x^{x}}, if nn is a positive integer ?

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  4. Question 4

    Triangles. Asked once: CDS 2 2024

    100
    In a right triangle ABCABC, ∠A=90∘\angle A = 90^\circ and ADAD is perpendicular to BCBC. If ∠CAD=60∘\angle CAD = 60^\circ and BC=6BC = 6 cm, then what is ABAB equal to ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2024

    54
    Consider the following statements : 1. In a triangle ABC, if sin⁡A+sin⁡B+sin⁡C=332\sin A + \sin B + \sin C = \frac{3\sqrt{3}}{2}, then the triangle can be equilateral. 2. In a triangle ABC, if cos⁡A+cos⁡B+cos⁡C=32\cos A + \cos B + \cos C = \frac{3}{2}, then the triangle can be equilateral. Which of the statements given above is/are correct ?

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