Day 259: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1 (case study, 2 parts)
Differentiation. Asked once: NDA 1 2026
For the next two (02) items that follow: Consider the differential equation $e^{x+y}\dfrac{dy}{dx}=e^{x-y}$ .
97 $\dfrac{d^2y}{dx^2}\left(\dfrac{dx}{dy}\right)^2$
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98 $y(0)=0$
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Question 2 (case study, 2 parts)
Functions. Asked once: NDA 2 2025
For the following two (02) items: Consider the function $f(x)=1-\sqrt[3]{(x-1)^2}$ .
81 $What is the domain of the function?$
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82 $The function has$
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Question 3
Height & Distance. Asked once: NDA 1 2019
100 $AB=z$
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Question 4 (case study, 2 parts)
Indefinite Integration. Asked once: NDA 2 2024
Let $2\displaystyle\int\dfrac{x^2-1}{\sqrt{x^2+1}}\,dx = U(x)V(x)-3\ln\{U(x)+V(x)\}+c$ .
99 $|U^2(x)-V^2(x)|$
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100 $U(x)V(x)$
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Question 5
Inverse Trigonometry. Asked once: NDA 1 2025
48 $A man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be 45°. The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?$
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Question 1 (case study, 2 parts)