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. 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 3. 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 4. If $nC_{3}=nC_{2}$ then the value of $nC_{4}$ is 2 3 4 5 None 5. The possible out comes when a coin is tossed five times $2^{5}$ $5^{2}$ 10 $\frac{5}{2}$ None 6. If $nP_{r}= 720 (nC_{r})$, then r is equal to 4 5 6 7 None 7. The number of ways selecting 4 players out of 5 is 4! 20 25 5 None 8. The value of n, when $nP_{2} = 20$ is 3 6 5 4 None 9. 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 10. The term containing $x^{3}$ in the expansion of $(x-2y)^{7}$ is 3rd 4th 5th 6th None 11. 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 12. The last term in the expansion of $(3+\sqrt{2})^{8}$ is 81 16 $8\sqrt{2}$ $27\sqrt{3}$ None 13. 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 14. 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 15. 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 16. The number of ways to arrange the letters of the word “ CHEESE ” 120 240 720 6 None 17. The constant term in the expansion of $(x+\frac{2}{x})^{6}$ is 156 165 162 160 None 18. The total number of 9 digit number which have all different digit is 10! 9! 9 × 9! 10 × 10! None 19. 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 20. If $\frac{kx}{(x+4)(2x-1)}=\frac{4}{x+4} +\frac{1}{2x-1}$, the k = 9 11 5 7 None 21. 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 22. Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is 715 78 286 13 None 23. Sum of the binomial coefficients is $2^{n}$ $n^{2}$ 2n n+17 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. 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 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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