Day 173: NDA Maths

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

Question 1
Applications of Integration. Asked once: NDA 2 2022 (same type asked 5 times)
81 $x - |y| = 0$
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Question 2 (case study, 2 parts)
Definite Integration. Asked once: NDA 1 2024 (same type asked 5 times)
Let $f(x)=|x-1|$ , $g(x)=[x]$ and $h(x)=f(x)\cdot g(x)$ where $[\cdot]$ is the greatest integer function.
93 $\displaystyle\int_{-1}^{0}h(x)\,dx$
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94 $\displaystyle\int_{0}^{2}h(x)\,dx$
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Question 3
Differential Equations. Asked once: NDA 1 2022 (same type asked 5 times)
57 $1+\left(\frac{dy}{dx}\right)^2=\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}$
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Question 4
Sequence & Series. Asked once: NDA 2 2024 (same type asked 5 times)
11 $x>1,\; y>1,\; z>1$
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Question 5
3D Geometry. Asked once: NDA 2 2022 (same type asked 5 times)
64 $A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?$
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Question 1