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Day 324: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Matrices & Determinants. Asked once: NDA 1 2025

    25
    Consider the following in respect of a non-singular matrix MM: (I). M2=∣M∣2M^2 = |M|^2 (II). ∣M∣=M−1|M| = M^{-1} (III). ∣M∣=MT|M| = M^T How many of the above are correct?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 2 2021

    17
    If C(n,4)C(n,4), C(n,5)C(n,5) and C(n,6)C(n,6) are in AP, then what is the value of nn?

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  3. Question 3

    Probability. Asked once: NDA 2 2024

    107
    A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may miss?

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  4. Question 4

    Properties of Triangle. Asked once: NDA 1 2020

    30
    Consider the following statements: 1. If in a triangle ABC, A=2BA=2B and b=cb=c, then it must be an obtuse-angled triangle. 2. There exists no triangle ABC with A=40°A=40°, B=65°B=65° and ac=sin⁡40°csc⁡15°\frac{a}{c}=\sin 40°\csc 15°. Which of the above statements is/are correct?

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  5. Question 5

    Quadratic Equations. Asked once: NDA 1 2023

    23
    α\alpha and β\beta are distinct real roots of the quadratic equation x2+ax+b=0x^{2}+ax+b=0. Which of the following statements is/are sufficient to find α\alpha? 1. α+β=0\alpha+\beta=0, α2+β2=2\alpha^{2}+\beta^{2}=2 2. αβ2=−1\alpha\beta^{2}=-1, a=0a=0

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