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Day 135: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Quadratic Equations. Asked once: NDA 2 2018 (same type asked 2 times)

    10
    If α\alpha and β\beta (≠0)(\neq 0) are the roots of the quadratic equation x2+αx−β=0x^2 + \alpha x - \beta = 0, then the quadratic expression −x2+αx+β-x^2 + \alpha x + \beta where x∈Rx \in \mathbb{R} has

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  2. Question 2

    Sets & Relations. Asked once: NDA 1 2017 (same type asked 2 times)

    2
    Let A={1,2,3,4,5,6,7,8,9,10}A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}. Then the number of subsets of AA containing two or three elements is

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  3. Question 3

    Statistics. Asked once: NDA 2 2023 (same type asked 2 times)

    102
    If Xˉ=20\bar{X}=20 is the mean of 10 observations x1,x2,…,x10x_1, x_2, \ldots, x_{10}, then what is the value of ∑i=110(3xi−45)\displaystyle\sum_{i=1}^{10}\left(\frac{3x_i-4}{5}\right)?

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  4. Question 4 (case study, 3 parts)

    Statistics. Asked once: NDA 2 2022 (same type asked 2 times)

    Consider the following for the next three (03) items that follow: Consider the following grouped frequency distribution:
    Class0-1010-2020-3030-4040-5050-60
    Frequency124643
    118
    What is the median of the distribution?

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    119
    What is mean deviation about the median?

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    120
    What is the mean deviation about the mean?

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  5. Question 5

    Trigonometric Equations. Asked once: NDA 1 2021 (same type asked 2 times)

    2
    The value of xx, satisfying the equation log⁡cos⁡xsin⁡x=1\log_{\cos x} \sin x = 1, where 0<x<π20 < x < \frac{\pi}{2}, is

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