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Day 384: NDA Maths

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

  1. Question 1

    Probability. Asked once: NDA 1 2018

    115
    A,B events with 2P(A)=3P(B), 0<P(A)<P(B)<1. Which ordering is correct?

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  2. Question 2

    Trigonometric Identities. Asked once: NDA 1 2018

    49
    If cos⁡α+cos⁡β+cos⁡γ=0\cos\alpha + \cos\beta + \cos\gamma = 0, where 0<α,β,γ≤π/20 < \alpha, \beta, \gamma \le \pi/2, then what is sin⁡α+sin⁡β+sin⁡γ\sin\alpha + \sin\beta + \sin\gamma?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2018

    35
    Consider the following in respect of matrices A and B of same order: 1. A2−B2=(A+B)(A−B)A^2-B^2=(A+B)(A-B) 2. (A−I)(I+A)=O⇔A2=I(A-I)(I+A)=O \Leftrightarrow A^2=I where I is the identity matrix and O is the null matrix. Which of the above is/are correct?

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  4. Question 4

    Probability. Asked once: NDA 1 2018

    116
    Box has chits 0-9. First drawn, kept aside; second drawn. P(second is '9')?

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  5. Question 5

    Trigonometric Identities. Asked once: NDA 1 2017

    43
    If K=sin⁡ ⁣(π18)sin⁡ ⁣(5π18)sin⁡ ⁣(7π18)K = \sin\!\left(\dfrac{\pi}{18}\right)\sin\!\left(\dfrac{5\pi}{18}\right)\sin\!\left(\dfrac{7\pi}{18}\right), then what is the value of KK?

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