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Day 113: CDS Maths

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

  1. Question 1

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

    82
    ABCABC is a triangle right angled at BB. Let MM and NN be two points on ABAB such that AM=MN=NBAM = MN = NB. Let PP and QQ be two points on ACAC such that PMPM is parallel to QNQN and QNQN is parallel to CBCB. If BC=12BC = 12 cm, then what is (PM+QN)(PM + QN) equal to?

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  2. Question 2

    Trigonometric Ratios and Identities. Asked once: CDS 1 2026 (same type asked 3 times) See all 3 of this type

    43
    If 3sin⁡θ+4cos⁡θ=53\sin\theta + 4\cos\theta = 5, then what is a value of 4tan⁡θ+3cot⁡θ4\tan\theta + 3\cot\theta ?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 1 2025 (same type asked 3 times) See all 3 of this type

    23
    If p=1cosec⁡θ+cot⁡θp = \dfrac{1}{\operatorname{cosec} \theta + \cot \theta} and q=cosec⁡θq = \operatorname{cosec} \theta, then what is p2−2pqp^2 - 2pq equal to ?

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  4. Question 4

    Inequalities. Asked once: CDS 2 2022 (same type asked 3 times) See all 3 of this type

    30
    Consider the question and two statements given below : Let x and y be two real numbers. Question : Is xy>0xy > 0 ? Statement-1 : x8y9<0x^8 y^9 < 0. Statement-2 : x9y10<0x^9 y^{10} < 0. Which one of the following is correct in respect of the question and the statements ?

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  5. Question 5

    Linear Equations. Asked once: CDS 1 2017 (same type asked 3 times) See all 3 of this type

    47
    The system of equations 2x+4y=62x + 4y = 6 and 4x+8y=84x + 8y = 8 is

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