Day 278: NDA Maths

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

Question 1 (case study, 2 parts)
Quadratic Equations. Asked once: NDA 2 2025
For the following two (02) items: Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^2+(\log_{0.5}(a^2))x+(\log_{0.5}(a^2))^4=0$ where $a^2\neq 1$ and $\log_{0.5}(a^2)>0$ . Further, $\beta^2=\alpha(\log_{a^2}(0.5))$ .
21 $\beta$
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22 $\alpha$
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Question 2 (case study, 2 parts)
Sequence & Series. Asked once: NDA 2 2023
Let $a_1,a_2,a_3,\ldots$ be in AP such that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{25}+a_{30}+a_{34}=300$ .
71 $a_1+a_5-a_{10}-a_{15}-a_{20}-a_{25}+a_{30}+a_{34}$
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72 $\sum_{n=1}^{34}a_n$
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Question 3
Sets & Relations. Asked once: NDA 1 2019
2 $X = \{1, 2, 3, 4\}$
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Question 4
Statistics. Asked once: NDA 2 2023
108 $1,2,3,\ldots,10$
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Question 5
Trigonometric Equations. Asked once: NDA 1 2022
38 $\tan\alpha+\tan\beta=1-\tan\alpha\cdot\tan\beta$
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Question 1 (case study, 2 parts)