Chapter 2: AlgebraMarch 14, 2024 Maven Leave a Comment Welcome to the Chapter 2: Algebra Name Email 1. 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 2. 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 3. The constant term in the expansion of $(x+\frac{2}{x})^{6}$ is 156 165 162 160 None 4. The total number of 9 digit number which have all different digit is 10! 9! 9 × 9! 10 × 10! None 5. The last term in the expansion of $(3+\sqrt{2})^{8}$ is 81 16 $8\sqrt{2}$ $27\sqrt{3}$ None 6. 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 7. If $\frac{kx}{(x+4)(2x-1)}=\frac{4}{x+4} +\frac{1}{2x-1}$, the k = 9 11 5 7 None 8. The number of ways to arrange the letters of the word “ CHEESE ” 120 240 720 6 None 9. 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 10. 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 11. Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is 715 78 286 13 None 12. Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is 8 7 6 9 None 13. 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 14. 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 15. Sum of the binomial coefficients is $2^{n}$ $n^{2}$ 2n n+17 None 16. The number of ways selecting 4 players out of 5 is 4! 20 25 5 None 17. 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 18. The possible out comes when a coin is tossed five times $2^{5}$ $5^{2}$ 10 $\frac{5}{2}$ None 19. If $nC_{3}=nC_{2}$ then the value of $nC_{4}$ is 2 3 4 5 None 20. 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 21. The greatest positive integer which divide n( n+1) (n+2) (n+3) for all $n\in N$ 2 6 20 24 None 22. The term containing $x^{3}$ in the expansion of $(x-2y)^{7}$ is 3rd 4th 5th 6th None 23. The value of n, when $nP_{2} = 20$ is 3 6 5 4 None 24. If $nP_{r}= 720 (nC_{r})$, then r is equal to 4 5 6 7 None 25. 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 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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