Mathematics Part 2

11 chapters 15 solved questions

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Chapters

1. 1 Complex Numbers 12 Q
2. 2 Sequences and Series
3. 3 Permutations and Combination
4. 3 Permutations and combinations 2 Q
5. 4 Method of Induction and Binomial theorem
6. 4 Methods of Induction and Binomial Theorem
7. 5 Sets and relations
8. 6 Functions
9. 7 Limits 1 Q
10. 8 Continuity
11. 9 Differentiation

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• The value of \((1+i)^8\) is Answer: C. 16 (1+i)²=2i⇒(1+i)⁸=(2i)⁴=16 . Complex Numbers 1 answer
• If \(\omega\) is a complex cube root of unity, then \((1+\omega-\omega^2)^3=\) Answer: D. −8 1+ω=-ω²⇒(-2ω²)³=-8ω⁶=-8 . Complex Numbers 1 answer
• \(\lim_{x\to0}\frac{1-\cos4x}{x^2}=\) Answer: B. 8 1-cos4x=2sin²2x ; lim2sin²2x/x²=2·4=8 . Limits 1 answer
• The number of distinct arrangements of the letters of the word BANANA is Answer: C. 60 6!/3! 2!=60 (A repeated 3 times, N twice). Permutations and combinations 1 answer
• A committee of 5 is to be formed from 6 men and 4 women. The number of ways in which it contains at least 3 women is Answer: B. 66 binom43binom62+binom44binom61=60+6=66 . Permutations and combinations 1 answer
• z – z¯ = 6i ( z – z¯ = 6i) z – z¯ = (2 + 3i) – (2 – 3i) = 2 + 3i – 2 + 3i = 6i Complex Numbers 1 answer