Day 72: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1
Probability. This type asked 2 times: NDA 1 2022, NDA 2 2023. This one: NDA 2 2023
106 $Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?$
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Question 2 (case study, 2 parts)
Quadratic Equations. This type asked 2 times: NDA 2 2021, NDA 2 2023. This one: NDA 2 2023
Consider the equation $(1-x)^4+(5-x)^4=82$ .
31 $What is the number of real roots of the equation?$
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32 $What is the sum of all the roots of the equation?$
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Question 3 (case study, 2 parts)
Trigonometric Identities. This type asked 2 times: NDA 1 2020, NDA 2 2023. This one: NDA 2 2023
Let $p=\dfrac{1}{3}-\dfrac{\tan 3x}{\tan x}$ and $q=1-3\tan^2 x,\ 0<x<\pi,\ x\neq\dfrac{\pi}{2}$ .
75 $pq$
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76 $x$
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Question 4 (case study, 2 parts)
Trigonometric Identities. This type asked 2 times: NDA 1 2020, NDA 2 2023. This one: NDA 2 2023
Let $p=\cos\frac{\pi}{5}\cos\frac{2\pi}{5}$ and $q=\cos\frac{4\pi}{5}\cos\frac{8\pi}{5}$ .
73 $p+q$
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74 $pq$
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Question 5
Binary Numbers. This type asked 2 times: NDA 1 2018, NDA 1 2023. This one: NDA 1 2023
3 $What is the binary number equivalent to decimal number 1011?$
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Question 1