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Day 292: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Inverse Trigonometry. Asked once: NDA 1 2021

    31
    tan⁡−1x+cot⁡−1x=π2\tan^{-1} x + \cot^{-1} x = \frac{\pi}{2} holds, when

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  2. Question 2 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 1 2025

    Let f(x)={x3,x2<1x2,x2≥1f(x) = \begin{cases} x^3, & x^2 < 1 \\ x^2, & x^2 \geq 1 \end{cases}
    79
    What is lim⁡x→0f′(x)\lim_{x \to 0} f'(x) equal to?

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    80
    Consider the following statements: (I). The function is continuous at x=−1x = -1. (II). The function is differentiable at x=1x = 1. Which of the statements given above is/are correct?

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  3. Question 3

    Lines. Asked once: NDA 2 2025

    61
    Which one of the following is the perpendicular form of the straight line 3x+2y=7\sqrt{3}x+2y=7?

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  4. Question 4

    Logarithms. Asked once: NDA 2 2021

    40
    If log⁡102⋅log⁡210+log⁡10(10x)=2\log_{10}2\cdot\log_{2}10+\log_{10}(10^{x})=2, then what is the value of xx?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2026

    23
    Let p=(x+y+z)p=(x+y+z) and q=xyzq=xyz. If ∣x111y111z∣\begin{vmatrix}x&1&1\\1&y&1\\1&1&z\end{vmatrix} is positive, then which one of the following is correct?

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