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Day 242: NDA Maths

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

  1. Question 1

    Inverse Trigonometry. Asked once: NDA 1 2026

    34
    Consider the following in respect of inverse circular functions: I. sin⁡−1(−x)=−sin⁡−1x\sin^{-1}(-x)=-\sin^{-1}x II. cos⁡−1(−x)=cos⁡−1x\cos^{-1}(-x)=\cos^{-1}x III. tan⁡−1(−x)=π−tan⁡−1x\tan^{-1}(-x)=\pi-\tan^{-1}x IV. cot⁡−1(−x)=π−cot⁡−1x\cot^{-1}(-x)=\pi-\cot^{-1}x. How many of the above are correct?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 2 2026

    88
    If mm and nn are the roots of the equation x2−px+q=0x^2 - px + q = 0, then what is lim⁡x→mex2−px+q−1(x−m)(x−n)\lim_{x \to m} \frac{e^{x^2 - px + q} - 1}{(x - m)(x - n)} equal to?

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  3. Question 3

    Linear Inequalities. Asked once: NDA 1 2025

    4
    If x+5y=4x + 5y = 4 and y+5x=−4y + 5x = -4, then what is (x+y)(x + y) equal to?

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  4. Question 4

    Lines. Asked once: NDA 2 2026

    54
    What is the equation of the line which is equidistant from the lines 2x−4y−7=02x - 4y - 7 = 0 and 6x−12y+1=06x - 12y + 1 = 0?

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  5. Question 5

    Logarithms. Asked once: NDA 1 2026

    13
    If 1−log⁡102=log⁡10(5x+4x+3x+2x+1)1-\log_{10}2=\log_{10}(5^x+4^x+3^x+2^x+1), then what is a value of xx?

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