Day 102: NDA Maths

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

Question 1
Trigonometric Identities. Asked once: NDA 2 2022 (same type asked 4 times)
52 $\sec x = \frac{25}{24}$
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Question 2
Inverse Trigonometry. Asked once: NDA 1 2019 (same type asked 4 times)
39 $\sin^{-1}\dfrac{4}{5} + \sec^{-1}\dfrac{5}{4} - \dfrac{\pi}{2}$
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Question 3
Matrices & Determinants. Asked once: NDA 1 2023 (same type asked 4 times)
8 $x+2y+z=4$
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Question 4
Permutation & Combination. Asked once: NDA 1 2023 (same type asked 4 times)
2 $What is the number of 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisible by 6?$
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Question 5 (case study, 2 parts)
Quadratic Equations. Asked once: NDA 2 2024 (same type asked 4 times)
The roots of the quadratic equation $a^2(b^2-c^2)x^2+b^2(c^2-a^2)x+c^2(a^2-b^2)=0$ are equal, $a^2\neq b^2\neq c^2$ .
47 $Which one of the following statements is correct?$
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48 $Which one of the following is a root of the equation?$
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Question 1