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Day 178: NDA Maths

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

  1. Question 1

    Permutation & Combination. Asked once: NDA 2 2021 (same type asked 4 times)

    4
    Let S={2,3,4,5,6,7,9}S=\{2,3,4,5,6,7,9\}. How many different 3-digit numbers (with all digits different) from SS can be made which are less than 500?

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  2. Question 2

    Quadratic Equations. Asked once: NDA 2 2021 (same type asked 4 times)

    8
    If pp and qq are the non-zero roots of the equation x2+px+q=0x^{2}+px+q=0, then how many possible values can qq have?

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  3. Question 3 (case study, 2 parts)

    Statistics. Asked once: NDA 2 2021 (same type asked 4 times)

    Direction: Consider the following for the next two (02) items that follow. Two regression lines are given as 3x - 4y + 8 = 0 and 4x - 3y - 1 = 0.
    106
    Consider the following statements: 1. The regression line of yy on xx is y=34x+2y=\frac{3}{4}x+2. 2. The regression line of xx on yy is x=34y+14x=\frac{3}{4}y+\frac{1}{4}. Which of the above statements is/are correct?

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    107
    Consider the following statements: 1. The coefficient of correlations rr is 34\frac{3}{4}. 2. The means of xx and yy are 3 and 4 respectively. Which of the above statements is/are correct?

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  4. Question 4

    Trigonometric Identities. Asked once: NDA 1 2021 (same type asked 4 times)

    16
    If tan⁡x=−34\tan x = -\frac{3}{4} and xx is in the second quadrant, then what is the value of sin⁡x⋅cos⁡x\sin x \cdot \cos x?

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  5. Question 5

    Inverse Trigonometry. Asked once: NDA 1 2019 (same type asked 4 times)

    41
    If tan⁡θ=12\tan\theta = \dfrac{1}{2} and tan⁡φ=13\tan\varphi = \dfrac{1}{3}, then what is the value of (θ+φ)(\theta+\varphi)?

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