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Day 118: CDS Maths

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

  1. Question 1

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

    85
    In a triangle ABC, the sides AB, AC are produced and the bisectors of exterior angles of ∠ABC\angle ABC and ∠ACB\angle ACB intersect at D. If ∠BAC=50∘\angle BAC = 50^\circ, then ∠BDC\angle BDC is equal to

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2019 (same type asked 3 times) See all 3 of this type

    8
    For x>0x > 0, what is the minimum value of x+x+22xx + \frac{x + 2}{2x} ?

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  3. Question 3

    Number System. Asked once: CDS 2 2019 (same type asked 3 times) See all 3 of this type

    20
    Suppose n is a positive integer such that (n2+48)(n^2 + 48) is a perfect square. What is the number of such n ?

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  4. Question 4

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

    5
    In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics ?

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  5. Question 5

    Time, Speed and Distance. Asked once: CDS 1 2023 (same type asked 3 times) See all 3 of this type

    10
    The time taken by a train to cross a man travelling in another train is 10 seconds, when the other train is travelling in the opposite direction. However, it takes 20 seconds, if both the trains are travelling in the same direction. The length of the first train is 200 m and that of the second train is 150 m. What is the speed of the first train?

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