PYQ Vault

Day 249: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2026

    18
    Let A=[cos⁡θ−sin⁡θsin⁡θcos⁡θ]A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} What is the least value of θ\theta for which A+AT=IA + A^T = I, where II is the identity matrix of order 2?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2026

    9
    What is the greatest value of rr satisfying the inequality 15Cr+1>2× 15Cr^{15}C_{r+1}>2\times\,^{15}C_r?

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  3. Question 3

    Probability. Asked once: NDA 2 2026

    107
    A committee has 6 men and 4 women. One member is selected randomly which is woman only. What is the probability that she belongs to a subgroup of 2 senior women?

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  4. Question 4

    Properties of Triangle. Asked once: NDA 1 2026

    37
    In a triangle ABC, if aa, bb and cc are the lengths of the sides opposite to the angles A, B and C respectively, then what is sin⁡(A−B)sin⁡(A+B)\dfrac{\sin(A-B)}{\sin(A+B)} equal to?

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  5. Question 5

    Quadratic Equations. Asked once: NDA 2 2026

    45
    If x2−2xcos⁡θ+1=0x^2 - 2x\cos\theta + 1 = 0, then what is the magnitude of xx?

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