Day 65: NDA Maths

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

Question 1 (case study, 2 parts)
Applications of Integration. This type asked 2 times: NDA 1 2022, NDA 2 2024. This one: NDA 2 2024
The area bounded by the parabola $y^2=kx$ and the line $x=k$ , where $k>0$ , is $\dfrac{4}{3}$ square units.
87 $k$
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88 $What is the area of the parabola bounded by the latus rectum?$
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Question 2
Binomial Theorem. This type asked 2 times: NDA 1 2024, NDA 2 2024. This one: NDA 2 2024
36 $7^n-6n$
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Question 3 (case study, 2 parts)
Differential Equations. This type asked 2 times: NDA 1 2017, NDA 2 2024. This one: NDA 2 2024
Let $y\,dx+(x-y^3)\,dy=0$ be a differential equation.
89 $What are the order and degree respectively of the differential equation?$
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90 $What is the solution of the differential equation?$
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Question 4 (case study, 2 parts)
Differentiation. This type asked 2 times: NDA 2 2023, NDA 2 2024. This one: NDA 2 2024
Let $f:(-1,1)\to\mathbb{R}$ be a differentiable function with $f(0)=-1$ and $f'(0)=1$ . Let $h(x)=f(2f(x)+2)$ and $g(x)=(h(x))^2$ .
95 $h'(0)$
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96 $g'(0)$
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Question 5
Limits & Continuity. This type asked 2 times: NDA 2 2017, NDA 2 2024. This one: NDA 2 2024
84 $f(x) = [x]^2 - [x^2]$
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Question 1 (case study, 2 parts)