Chapter 2: AlgebraMarch 14, 2024 Maven Leave a Comment Welcome to the Chapter 2: Algebra Quiz! Name Email 1. The greatest positive integer which divide n( n+1) (n+2) (n+3) for all $n\in N$ 2 6 20 24 None 2. For all $n> 0$, $nC_{1}+nC_{2}+nC_{3}+...nC_{n}$ is equal to $2^{n}$ $2^{n}-1$ $n^{2}$ $n^{2}-1$ None 3. If n is a positive integer, then the number of terms in the expansion $(x+a)^{n}$ is n n+1 n-1 2n None 4. The number of diagonals in a polygon of n sides is equal to $nC_{2}$ $nC_{2}-2$ $nC_{2}-n$ $nC_{2}-1$ None 5. The possible out comes when a coin is tossed five times $2^{5}$ $5^{2}$ 10 $\frac{5}{2}$ None 6. If $nC_{3}=nC_{2}$ then the value of $nC_{4}$ is 2 3 4 5 None 7. If $nP_{r}= 720 (nC_{r})$, then r is equal to 4 5 6 7 None 8. The number of ways selecting 4 players out of 5 is 4! 20 25 5 None 9. The term containing $x^{3}$ in the expansion of $(x-2y)^{7}$ is 3rd 4th 5th 6th None 10. The value of n, when $nP_{2} = 20$ is 3 6 5 4 None 11. The number of ways to arrange the letters of the word “ CHEESE ” 120 240 720 6 None 12. The constant term in the expansion of $(x+\frac{2}{x})^{6}$ is 156 165 162 160 None 13. There are 10 true or false questions in an examination. Then these questions can be answered in 240 ways 120 ways 1024 ways 100 ways None 14. The middle term in the expansion $(x+\frac{1}{x})^{10}$ is $10C_{4}(\frac{1}{x})$ $10C_{5}$ $10C_{6}$ $10C_{7} x^{4}$ None 15. The total number of 9 digit number which have all different digit is 10! 9! 9 × 9! 10 × 10! None 16. If $\frac{kx}{(x+4)(2x-1)}=\frac{4}{x+4} +\frac{1}{2x-1}$, the k = 9 11 5 7 None 17. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is 18 12 9 6 None 18. The last term in the expansion of $(3+\sqrt{2})^{8}$ is 81 16 $8\sqrt{2}$ $27\sqrt{3}$ None 19. The value of $(5C_{0}+5C_{1)}+(5C_{1}+5C_{2)}+ (5C_{2}+5C_{3)}+ (5C_{3}+5C_{4)}+(5C_{4}+5C_{5)}$ is $2^{6}-2$ $2^{5}-1$ $2^{8}$ $2^{7}$ None 20. The number of 3 letter words that can be formed from the letters of the word number when the repetition is allowed are 206 133 216 300 None 21. The number of permutation of n different things taken r at a time, when the repetition is allowed is $r^{n}$ $n^{r}$ $\frac{n!}{(n-r)!}$ $\frac{n!}{(n+r)!}$ None 22. Number of words with or without meaning that can be formed using letters of the word “EQUATION” , with no repetition of letters is 7! 3! 8! 5! None 23. Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is 715 78 286 13 None 24. Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is 8 7 6 9 None 25. Sum of the binomial coefficients is $2^{n}$ $n^{2}$ 2n n+17 None Time's upRelated Posts:Chapter 1: Introduction to Micro EconomicsChapter 2. Consumption AnalysisChapter 3: Production AnalysisChapter 4: Cost and Revenue Analysis
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