Day 177: NDA Maths

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

Question 1 (case study, 2 parts)
Properties of Triangle. Asked once: NDA 2 2023 (same type asked 4 times)
The angles $A$ , $B$ and $C$ of triangle $ABC$ are in the ratio $3:5:4$ .
79 $a+b+\sqrt{2}\,c$
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80 $a^2:b^2:c^2$
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Question 2
Statistics. Asked once: NDA 1 2021 (same type asked 4 times)
109 $If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?$
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Question 3
Definite Integration. Asked once: NDA 1 2024 (same type asked 4 times)
78 $\displaystyle\int_0^{\pi/2}\dfrac{a+\sin x}{2(a+\sin x+\cos x)}\,dx$
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Question 4 (case study, 2 parts)
Functions. Asked once: NDA 2 2023 (same type asked 4 times)
Let $f$ be defined on $\mathbb{R}\setminus\{0\}$ and $2f(x)+f\!\left(\frac{1}{x}\right)=x+3$ .
43 $f(0.5)$
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44 $f$
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Question 5
Height & Distance. Asked once: NDA 1 2018 (same type asked 4 times)
43 $2\sqrt{3}$
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Question 1 (case study, 2 parts)