Day 76: NDA Maths

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

Question 1 (case study, 3 parts)
Binomial Theorem. This type asked 2 times: NDA 1 2018, NDA 2 2022. This one: NDA 2 2022
Consider the following for the next three (03) items that follow: Consider the binomial expansion of $(p + qx)^9$ :
22 $x^3$
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23 $What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?$
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24 $x^2$
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Question 2
Binomial Theorem. This type asked 2 times: NDA 1 2020, NDA 2 2022. This one: NDA 2 2022
2 $\sum_{r=0}^{n} 2^r C(n,r)$
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Question 3
Definite Integration. This type asked 2 times: NDA 2 2021, NDA 2 2022. This one: NDA 2 2022
94 $\int_0^1 \ln\!\left(\frac{1}{x}-1\right)dx$
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Question 4
Indefinite Integration. This type asked 2 times: NDA 2 2017, NDA 2 2022. This one: NDA 2 2022
75 $\int e^x\{1+\ln x + x\ln x\}\,dx$
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Question 5
Limits & Continuity. This type asked 2 times: NDA 2 2018, NDA 2 2022. This one: NDA 2 2022
84 $\lim_{x\to 0}\frac{x}{\sqrt{1-\cos4x}}$
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Question 1 (case study, 3 parts)