Day 268: NDA Maths

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

Question 1 (case study, 2 parts)
Trigonometric Identities. Asked once: NDA 2 2025
For the following two (02) items: Let $p = \csc 20°$ and $q = \csc 70°$ .
27 $\left(\dfrac{\sqrt{3}p}{4}-\dfrac{q}{4}\right)$
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28 $\dfrac{p^2+q^2}{p^2 q^2}$
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Question 2 (case study, 2 parts)
Vectors. Asked once: NDA 1 2026
For the next two (02) items that follow: Let $\vec{a}$ , $\vec{b}$ , $\vec{c}$ , $\vec{a}+\vec{b}$ , $\vec{b}+\vec{c}$ , $\vec{a}+\vec{b}+\vec{c}$ be unit vectors.
65 $\vec{a}$
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66 $\vec{a}$
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Question 3
3D Geometry. Asked once: NDA 2 2021
62 $Consider the following statements: 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain line that the sum of the squares of direction cosines can be equal to sum of its direction cosines. Which of the above statements is/are correct?$
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Question 4
Application of Derivatives. Asked once: NDA 1 2024
91 $f(x)$
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Question 5
Binary Numbers. Asked once: NDA 2 2019
40 $(cdccddcccddd)_{2}$
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Question 1 (case study, 2 parts)