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Day 75: NDA Maths

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

  1. Question 1

    Probability. This type asked 2 times: NDA 1 2019, NDA 1 2023. This one: NDA 1 2023

    102
    Let AA and BB be two independent events such that P(Aˉ)=0.7P(\bar{A})=0.7, P(Bˉ)=kP(\bar{B})=k, P(A∪B)=0.8P(A\cup B)=0.8. What is the value of kk?

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  2. Question 2

    Quadratic Equations. This type asked 2 times: NDA 1 2020, NDA 1 2023. This one: NDA 1 2023

    17
    For how many integral values of kk, the equation x2−4x+k=0x^{2}-4x+k=0, where kk is an integer has real roots and both of them lie in the interval (0,5)(0,5)?

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  3. Question 3

    Statistics. This type asked 2 times: NDA 1 2018, NDA 1 2023. This one: NDA 1 2023

    112
    For data −1,1,4,3,8,12,17,19,9,11-1,1,4,3,8,12,17,19,9,11; if MM is the median of first 5 observations and NN is the median of last five observations, then what is the value of 4M−N4M-N?

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  4. Question 4

    Statistics. This type asked 2 times: NDA 1 2021, NDA 1 2023. This one: NDA 1 2023

    110
    A die is thrown 10 times and obtained the following outputs: 1, 2, 1, 1, 2, 1, 4, 6, 5, 4. What will be the mode of data so obtained?

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  5. Question 5 (case study, 2 parts)

    Trigonometric Identities. This type asked 2 times: NDA 2 2018, NDA 1 2023. This one: NDA 1 2023

    Consider the following for the next two (02) items that follow: Let sin⁡?eta\sin?eta be the GM of sin⁡?lpha\sin?lpha and cos⁡?lpha\cos?lpha; tan⁡γ\tan\gamma be the AM of sin⁡?lpha\sin?lpha and cos⁡?lpha\cos?lpha.
    31
    What is cos⁡2β\cos2\beta equal to?

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    32
    What is the value of sec⁡2γ\sec2\gamma?

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