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Day 150: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 1 2020 (same type asked 2 times)

    27
    What is the value of 8cos⁡10°⋅cos⁡20°⋅cos⁡40°8\cos 10°\cdot\cos 20°\cdot\cos 40°?

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  2. Question 2

    Binary Numbers. Asked once: NDA 1 2018 (same type asked 2 times)

    17
    The binary number expression of the decimal number 31 is

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  3. Question 3

    Binomial Distribution. Asked once: NDA 1 2020 (same type asked 2 times)

    118
    Consider a random variable X which follows Binomial distribution with parameters n=10n=10 and p=15p=\frac{1}{5}. Then Y=10−XY=10-X follows Binomial distribution with parameters nn and pp respectively given by

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  4. Question 4

    Complex Numbers. Asked once: NDA 1 2017 (same type asked 2 times)

    9
    If 1,ω,ω21, \omega, \omega^2 are the cube roots of unity, then (1+ω)(1+ω2)(1+ω3)(1+ω+ω2)(1+\omega)(1+\omega^2)(1+\omega^3)(1+\omega+\omega^2) is equal to

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  5. Question 5

    Complex Numbers. Asked once: NDA 1 2018 (same type asked 2 times)

    5
    Let α\alpha and β\beta be real numbers and zz be a complex number. If z2+αz+β=0z^2 + \alpha z + \beta = 0 has two distinct non-real roots with Re(z)=1\text{Re}(z) = 1, then it is necessary that

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