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Day 233: NDA Maths

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

  1. Question 1

    Probability. Asked once: NDA 2 2018 (same type asked 7 times)

    106
    In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?

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  2. Question 2

    Sequence & Series. Asked once: NDA 2 2017 (same type asked 7 times)

    4
    If Sn=nP+n(n−1)Q2S_n = nP + \dfrac{n(n-1)Q}{2}, where SnS_n denotes the sum of the first nn terms of an AP, then the common difference is

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  3. Question 3

    Application of Derivatives. Asked once: NDA 2 2017 (same type asked 7 times)

    93
    Consider the following statements: Statement I: x>sin⁡xx > \sin x for all x>0x > 0. Statement II: f(x)=x−sin⁡xf(x) = x - \sin x is an increasing function for all x>0x > 0. Which one of the following is correct in respect of the above statements?

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  4. Question 4

    Probability. Asked once: NDA 1 2017 (same type asked 7 times)

    119
    Let AA and BB are two mutually exclusive events with P(A)=13P(A)=\dfrac{1}{3} and P(B)=14P(B)=\dfrac{1}{4}. What is the value of P(Aˉ∩Bˉ)P(\bar{A}\cap\bar{B})?

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  5. Question 5

    Definite Integration. Asked once: NDA 1 2018 (same type asked 6 times)

    92
    What is ∫−π/4π/4(sin⁡x−tan⁡x) dx\int_{-\pi/4}^{\pi/4}(\sin x-\tan x)\,dx?

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