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Day 267: NDA Maths

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

  1. Question 1

    Quadratic Equations. Asked once: NDA 1 2026

    43
    Consider the following statements: I. x+x+1=0\sqrt{x}+x+1=0 has two irrational roots. II. 5x−x−4=05\sqrt{x}-x-4=0 has two rational roots. Which of the statements given above is/are correct?

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  2. Question 2 (case study, 2 parts)

    Sequence & Series. Asked once: NDA 2 2025

    For the following two (02) items: Let (6+10+14+…(6+10+14+\ldots up to mm terms)=(1+3+5+7+…) = (1+3+5+7+\ldots up to nn terms)) where m<25m<25 and n<25n<25.
    33
    What is the relation between mm and nn?

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    34
    How many values of mm are possible?

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  3. Question 3

    Sets & Relations. Asked once: NDA 2 2019

    1
    If both pp and qq belong to the set {1,2,3,4}\{1, 2, 3, 4\}, then how many equations of the form px2+qx+1=0px^{2} + qx + 1 = 0 will have real roots ?

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  4. Question 4

    Statistics. Asked once: NDA 1 2024

    Distribution: xi=1,2,…,nx_i=1,2,\ldots,n with fi=1,2−1,…,2−(n−1)f_i=1,2^{-1},\ldots,2^{-(n-1)}.
    118
    What is the mean of the distribution?

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  5. Question 5

    Trigonometric Equations. Asked once: NDA 2 2023

    29
    If tan⁡(πcos⁡θ)=cot⁡(πsin⁡θ), 0<θ<π/2\tan(\pi\cos\theta)=\cot(\pi\sin\theta),\ 0<\theta<\pi/2; then what is the value of 8sin⁡2 ⁣(θ+π4)8\sin^2\!\left(\theta+\frac{\pi}{4}\right)?

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