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Day 90: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Sets & Relations. This type asked 2 times: NDA 1 2017, NDA 2 2017. This one: NDA 2 2017

    22
    If we define a relation RR on the set N×NN \times N as (a,b) R (c,d)⇔a+d=b+c(a,b)\,R\,(c,d) \Leftrightarrow a+d=b+c for all (a,b),(c,d)∈N×N(a,b),(c,d) \in N \times N, then the relation is

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  2. Question 2

    Trigonometric Identities. This type asked 2 times: NDA 1 2017, NDA 2 2017. This one: NDA 2 2017

    38
    1+sin⁡A=− ⁣(sin⁡A2+cos⁡A2)\sqrt{1+\sin A} = -\!\left(\sin\dfrac{A}{2} + \cos\dfrac{A}{2}\right) is true if

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  3. Question 3

    Lines. Asked once: NDA 1 2021 (same type asked 8 times)

    62
    What is the acute angle between the lines x−2=0x - 2 = 0 and 3x−y−2=0\sqrt{3}x - y - 2 = 0?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2021 (same type asked 8 times)

    11
    If AA and BB are two matrices such that ABAB is of order n×nn \times n, then which one of the following is correct?

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  5. Question 5 (case study, 2 parts)

    Probability. Asked once: NDA 1 2025 (same type asked 7 times)

    The probabilities that A, B and C become managers are 310,12\frac{3}{10}, \frac{1}{2} and 45\frac{4}{5} respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 49,29\frac{4}{9}, \frac{2}{9} and 13\frac{1}{3} respectively.
    111
    What is the probability that the bonus scheme will be introduced?

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    112
    If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?

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