PYQ Vault

Day 298: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Matrices & Determinants. Asked once: NDA 2 2025

    For the following two (02) items: Let A=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)A=\begin{pmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{pmatrix}.
    39
    What is the value of the determinant of the matrix A4A^4?

    Tap an option to check your answer.

    40
    What is [adj A]−1[\text{adj}\,A]^{-1} equal to?

    Tap an option to check your answer.

  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2023

    27
    Consider the following statements for a fixed natural number nn: 1. C(n,r)C(n,r) is greatest if n=2rn=2r 2. C(n,r)C(n,r) is greatest if n=2r−1n=2r-1 and n=2r+1n=2r+1 Which of the statements given above is/are correct?

    Tap an option to check your answer.

  3. Question 3

    Probability. Asked once: NDA 2 2025

    105
    An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and a blue ball are drawn?

    Tap an option to check your answer.

  4. Question 4 (case study, 2 parts)

    Properties of Triangle. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: The perimeter of a triangle ABCABC is 6 times the AM of sine of angles of the triangle. Further BC=3BC=\sqrt{3} and CA=1CA=1.
    35
    What is the perimeter of the triangle?

    Tap an option to check your answer.

    36
    Consider the following statements: 1. ABCABC is right angled triangle 2. The angles of the triangle are in AP Which of the statements given above is/are correct?

    Tap an option to check your answer.

  5. Question 5

    Quadratic Equations. Asked once: NDA 1 2024

    45
    Under which one of the following conditions does the equation (cos⁡β−1)x2+(cos⁡β)x+sin⁡β=0(\cos\beta-1)x^2+(\cos\beta)x+\sin\beta=0 in xx have a real root for β∈[0,π]\beta\in[0,\pi]?

    Tap an option to check your answer.