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Day 272: NDA Maths

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

  1. Question 1

    Permutation & Combination. Asked once: NDA 1 2025

    29
    What is the number of selections of at most 3 things from 6 different things?

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  2. Question 2

    Probability. Asked once: NDA 1 2026

    118
    Three events A, B and C are such that A and B are disjoint, A and C are independent, B and C are independent. If 4P(A)=2P(B)=P(C)4P(A)=2P(B)=P(C) and P(A∪B∪C)=5P(A)P(A\cup B\cup C)=5P(A), then what is the value of P(C)?

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  3. Question 3

    Properties of Triangle. Asked once: NDA 2 2024

    25
    In a triangle ABCABC, ∠A=75∘\angle A=75^\circ and ∠B=45∘\angle B=45^\circ. What is 2a−b2a-b equal to?

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  4. Question 4

    Quadratic Equations. Asked once: NDA 1 2026

    12
    Let α\alpha and β\beta be the roots of the quadratic equation x2−2bx+c2=0x^2-2bx+c^2=0 where bb, cc are positive real numbers. Let A be the arithmetic mean of α\alpha and β\beta; and G be the geometric mean of α\alpha and β\beta. What are the roots of the quadratic equation x2−(b+c)x+bc=0x^2-(b+c)x+bc=0?

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2025

    2
    The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r≠1r \neq 1 is the common ratio, then what is the number of possible real values of rr?

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