PYQ Vault

Day 279: NDA Maths

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

  1. Question 1 (case study, 3 parts)

    Trigonometric Identities. Asked once: NDA 1 2025

    Let p=tan⁡2α−tan⁡αp = \tan 2\alpha - \tan\alpha and q=cot⁡α−cot⁡2αq = \cot\alpha - \cot 2\alpha.
    41
    What is pq\frac{p}{q} equal to?

    Tap an option to check your answer.

    42
    What is (p+q)(p + q) equal to?

    Tap an option to check your answer.

    43
    What is tan⁡2α\tan^2\alpha equal to?

    Tap an option to check your answer.

  2. Question 2

    Vectors. Asked once: NDA 2 2025

    68
    What is the area of the parallelogram whose sides are represented by the vectors i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} and 2i^+j^+2k^2\hat{i}+\hat{j}+2\hat{k}?

    Tap an option to check your answer.

  3. Question 3

    3D Geometry. Asked once: NDA 1 2021

    68
    What is the projection of the line segment joining A(1,7,−5)A(1,7,-5) and B(−3,4,−2)B(-3,4,-2) on yy-axis?

    Tap an option to check your answer.

  4. Question 4

    Application of Derivatives. Asked once: NDA 1 2024

    84
    Let f(x)=xln⁡x  (x>1)f(x)=\dfrac{x}{\ln x}\;(x>1). Consider the following statements: (A) f′′(e)=1ef''(e)=\dfrac{1}{e}. (B) f(x)f(x) attains a local minimum value at x=ex=e. (C) A local minimum value of f(x)f(x) is ee. Which of the statements given above are correct?

    Tap an option to check your answer.

  5. Question 5

    Binomial Theorem. Asked once: NDA 2 2021

    27
    Consider the expansion of (1+x)n(1+x)^{n}. Let pp, qq, rr and ss be the coefficients of first, second, nnth and (n+1)(n+1)th terms respectively. What is (ps+qr)(ps+qr) equal to?

    Tap an option to check your answer.