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Day 271: NDA Maths

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

  1. Question 1

    Inverse Trigonometry. Asked once: NDA 2 2023

    27
    If sec⁡−1p−csc⁡−1q=0\sec^{-1}p - \csc^{-1}q = 0, where p>0,q>0p>0,q>0, then what is the value of p−2+q−2p^{-2}+q^{-2}?

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  2. Question 2 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 1 2026

    For the next two (02) items that follow: Let f(x)=tan⁡(x2)f(x)=\tan(x^2) and g(x)=x∣x∣g(x)=x|x| for ∣x∣<π/2|x|<\sqrt{\pi/2}.
    99
    If p(x)=f(x)g(x)p(x)=f(x)g(x), then which of the following statements is/are correct? I. p(x)p(x) is continuous at x=0x=0. II. p(x)p(x) is differentiable at x=0x=0. Select the answer using the code given below.

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    100
    If q(x)=f∘g(x)q(x)=f\circ g(x), then which of the following statements is/are correct? I. q(x)q(x) is continuous at x=0x=0. II. q(x)q(x) is differentiable at x=0x=0. Select the answer using the code given below.

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  3. Question 3 (case study, 2 parts)

    Lines. Asked once: NDA 1 2026

    For the next two (02) items that follow: The equation of a straight line which passes through the origin and makes an angle α\alpha (0≤α≤90°0\leq\alpha\leq90°) with the line L: x+3y+33=0x+\sqrt{3}y+3\sqrt{3}=0 is x−3y=0x-\sqrt{3}y=0.
    51
    What is the value of α\alpha?

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    52
    What is the angle made by the line L with positive direction of y-axis?

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  4. Question 4

    Logarithms. Asked once: NDA 1 2024

    28
    For x≥y>1x\geq y>1, let log⁡x ⁣xy+log⁡y ⁣yx=k\log_x\!\dfrac{x}{y}+\log_y\!\dfrac{y}{x}=k, then the value of kk can never be equal to

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2026

    18
    Consider the following statements: I. If n×nn\times n (n>1n>1) matrix is symmetric, then its inverse is also a symmetric matrix. II. If n×nn\times n (n>1n>1) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct?

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