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Day 58: NDA Maths

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

  1. Question 1

    Statistics. This type asked 2 times: NDA 2 2023, NDA 1 2026. This one: NDA 1 2026

    112
    If the mean of 20 observations, namely x1,x2,x3,…,x20x_1,x_2,x_3,\ldots,x_{20} is 1.414, then what is the value of ∑i=120100(2xi+4)\sum_{i=1}^{20}100(2x_i+4)?

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  2. Question 2 (case study, 2 parts)

    Statistics. This type asked 2 times: NDA 2 2022, NDA 1 2026. This one: NDA 1 2026

    For the next two (02) items that follow: The frequency distribution of marks obtained by 100 students in a certain subject is given below: Marks: 0-10, 10-20, 20-30, 30-40; No. of students: 10, 20, f, 40.
    119
    What is the mean deviation about the arithmetic mean?

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    120
    What is the standard deviation?

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  3. Question 3

    Trigonometric Equations. This type asked 2 times: NDA 1 2021, NDA 1 2026. This one: NDA 1 2026

    38
    What is the smallest positive xx satisfying log⁡sin⁡xcos⁡x+log⁡cos⁡xsin⁡x=2\log_{\sin x}\cos x+\log_{\cos x}\sin x=2?

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  4. Question 4

    Trigonometric Identities. This type asked 2 times: NDA 1 2017, NDA 1 2026. This one: NDA 1 2026

    30
    cos⁡x+3sin⁡x\cos x+\sqrt{3}\sin x is maximum when xx is equal to

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  5. Question 5

    Trigonometric Identities. This type asked 2 times: NDA 1 2019, NDA 1 2026. This one: NDA 1 2026

    28
    If x=sec⁡θ−tan⁡θx=\sec\theta-\tan\theta and y=csc⁡θ+cot⁡θy=\csc\theta+\cot\theta, then which one of the following is correct?

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