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Day 92: CDS Maths

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

  1. Question 1

    Averages. Asked once: CDS 1 2021 (same type asked 6 times) See all 6 of this type

    27
    Let the average score of a class of boys and girls in an examination be pp. The ratio of boys and girls in the class is 3:13 : 1. If the average score of the boys is (p+1)(p + 1), then what is the average score of the girls?

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  2. Question 2

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022 (same type asked 6 times) See all 6 of this type

    11
    What is the value of the following? 2sin⁡68∘cos⁡22∘−2cot⁡15∘5tan⁡75∘−3tan⁡20∘tan⁡40∘tan⁡45∘tan⁡50∘tan⁡70∘5\frac{2\sin 68^\circ}{\cos 22^\circ} - \frac{2\cot 15^\circ}{5\tan 75^\circ} - \frac{3\tan 20^\circ \tan 40^\circ \tan 45^\circ \tan 50^\circ \tan 70^\circ}{5}

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  3. Question 3

    Circles. Asked once: CDS 2 2025 (same type asked 5 times) See all 5 of this type

    65
    In a circle of radius 14 cm, APBAPB is a shorter arc and PP is the midpoint of the arc. Let CC be the midpoint of the chord ABAB and PC=7PC = 7 cm. What is the length of the chord APAP ?

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  4. Question 4

    Heights and Distances. Asked once: CDS 1 2026 (same type asked 5 times) See all 5 of this type

    44
    At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be 56\frac{5}{6}. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be 98\frac{9}{8}. What is the height of the tower ?

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  5. Question 5

    Mensuration 2D. Asked once: CDS 1 2024 (same type asked 5 times) See all 5 of this type

    39
    The chord AB of a circle with centre at O is 232\sqrt{3} times the height of the minor segment. If P is the area of the sector OAB and Q is the area of the minor segment of the circle, then what is the approximate value of PQ\frac{P}{Q} ? (Take 3=1.7\sqrt{3} = 1.7 and π=3.14\pi = 3.14)

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