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Day 175: CDS Maths

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

  1. Question 1

    Triangles. Asked once: CDS 2 2017 (same type asked 3 times) See all 3 of this type

    68
    In triangle ABC, ∠C=90∘\angle C = 90^\circ and CD is the perpendicular from C to AB. If (CD)−2=(BC)−2+(CA)−2(CD)^{-2} = (BC)^{-2} + (CA)^{-2}, then which one of the following is correct ?

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  2. Question 2

    Trigonometric Ratios and Identities. Asked once: CDS 2 2020 (same type asked 3 times) See all 3 of this type

    46
    If cosec⁡θ−sin⁡θ=m\operatorname{cosec}\theta - \sin\theta = m and sec⁡θ−cos⁡θ=n\sec\theta - \cos\theta = n, then what is m43n23+m23n43m^{\frac{4}{3}} n^{\frac{2}{3}} + m^{\frac{2}{3}} n^{\frac{4}{3}} equal to ?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 2 2018 (same type asked 3 times) See all 3 of this type

    65
    Consider the following statements : 1. If cos⁡θ1−sin⁡θ+cos⁡θ1+sin⁡θ=4\frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, where 0<θ<90∘0 < \theta < 90^\circ, then θ=60∘\theta = 60^\circ. 2. If 3tan⁡θ+cot⁡θ=5cosec⁡θ3 \tan \theta + \cot \theta = 5 \operatorname{cosec} \theta, where 0<θ<90∘0 < \theta < 90^\circ, then θ=60∘\theta = 60^\circ. Which of the statements given above is/are correct ?

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  4. Question 4

    Algebraic Identities and Simplification. Asked once: CDS 1 2017 (same type asked 3 times) See all 3 of this type

    33
    If a+b=5a + b = 5 and ab=6ab = 6, then what is the value of a3+b3a^3 + b^3 ?

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  5. Question 5

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

    86
    Let PABPAB be a secant to a circle intersecting the circle at AA and BB. Let PTPT be the tangent segment. If PA=9PA = 9 cm and PT=12PT = 12 cm, then what is ABAB equal to?

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