Day 89: NDA Maths

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

Question 1
Application of Derivatives. This type asked 2 times: NDA 1 2017, NDA 1 2018. This one: NDA 1 2018
83 $16\sin\theta-12\sin^2\theta$
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Question 2
Functions. This type asked 2 times: NDA 2 2017, NDA 1 2018. This one: NDA 1 2018
72 $f(x)=\frac{x^2}{1+x^2}$
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Question 3
Sequence & Series. This type asked 2 times: NDA 1 2017, NDA 1 2018. This one: NDA 1 2018
31 $What is the sum of all two-digit numbers which when divided by 3 leave 2 as remainder?$
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Question 4
Complex Numbers. This type asked 2 times: NDA 1 2017, NDA 2 2017. This one: NDA 2 2017
30 $\left|z - \dfrac{4}{z}\right| = 2$
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Question 5
Definite Integration. This type asked 2 times: NDA 1 2017, NDA 2 2017. This one: NDA 2 2017
76 $\displaystyle\int_0^{2\pi} \sqrt{1 + \sin\dfrac{x}{2}}\,dx$
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Question 1