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Day 119: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    51
    If AA, BB, CC are acute angles and sin⁡(B+C−A)=cos⁡(C+A−B)=tan⁡(A+B−C)=1\sin(B + C - A) = \cos(C + A - B) = \tan(A + B - C) = 1 then what is (A+B+C)(A + B + C) equal to?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 1 2020 (same type asked 3 times) See all 3 of this type

    90
    Let PQRSPQRS be the diameter of a circle of radius 9 cm. The length PQPQ, QRQR and RSRS are equal. Semi-circle is drawn with QSQS as diameter (as shown in the given figure). What is the ratio of the shaded region to that of the unshaded region ?

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  3. Question 3

    Sequence and Series. Asked once: CDS 2 2020 (same type asked 3 times) See all 3 of this type

    100
    The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic mean ?

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  4. Question 4

    Sequence and Series. Asked once: CDS 1 2021 (same type asked 3 times) See all 3 of this type

    30
    If 11×2+12×3+13×4+⋯+1n(n+1)=99100\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \cdots + \frac{1}{n(n + 1)} = \frac{99}{100} then what is the value of nn ?

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  5. Question 5

    Statistics. Asked once: CDS 2 2018 (same type asked 3 times) See all 3 of this type

    57
    The median of 19 observations is 30. Two more observations are made and the values of these are 8 and 32. What is the median of the 21 observations ?

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