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Day 286: NDA Maths

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

  1. Question 1

    Differential Equations. Asked once: NDA 1 2020

    95
    The function u(x,y)=cu(x,y)=c which satisfies the differential equation x(dx−dy)+y(dy−dx)=0x(dx-dy)+y(dy-dx)=0 is

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  2. Question 2 (case study, 2 parts)

    Differentiation. Asked once: NDA 2 2023

    Consider the following for the next two (02) items that follow: Let f(x)={ax(x+1)+b,x<1x−1,1≤x≤2f(x)=\begin{cases}ax(x+1)+b, & x<1\\ x-1, & 1\leq x\leq 2\end{cases}
    63
    If f(x)f(x) is differentiable at x=1x=1, then what is the value of (a+b)(a+b)?

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    64
    What is lim⁡x→0f(x)\lim_{x\to0}f(x) equal to?

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  3. Question 3 (case study, 2 parts)

    Functions. Asked once: NDA 1 2025

    Let the curve f(x)=∣x−3∣f(x) = |x - 3|.
    85
    What is the domain of the function f(x)f(x)?

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    86
    What is the area bounded by the curve f(x)f(x) and y=3y = 3?

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  4. Question 4

    Indefinite Integration. Asked once: NDA 2 2021

    85
    If ∫1−sin⁡2x dx=Asin⁡x+Bcos⁡x+C\int\sqrt{1-\sin 2x}\,dx=A\sin x+B\cos x+C, where 0<x<π40<x<\frac{\pi}{4}, then which one of the following is correct?

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  5. Question 5

    Inverse Trigonometry. Asked once: NDA 2 2021

    31
    What is the value of cot⁡ ⁣[sin⁡−1 ⁣35+cot⁡−1 ⁣32]\cot\!\left[\sin^{-1}\!\frac{3}{5}+\cot^{-1}\!\frac{3}{2}\right]?

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