BINOMIAL THEOREM
By Rajput sir ( 9810286256 )
1. Using Binomial Theorem expand. (i) [pic] (ii) [pic].
2. Evaluate the following : (i)[pic]- [pic] (ii) [pic]+ [pic]
3. (i) Find the tenth term of [pic] . (ii) Find the 7th term from the end of [pic].
4. For what value of m the coefficients of (2m+1)th and (4m+5)th terms in the expansion[pic]are equal.
5. The first three terms of the binomial expansion are 1, 10 and 40 find the expansion.
6. In the binomial expansion of[pic] the 5th term is 4 times the 4th term and 4th term is 6 times the 3rd term find n and x.
7. Show that the middle term of the expansion[pic] is [pic].
8. Find the terms independent of x in the following expansion (i) [pic] (ii) [pic]
9. Find the coefficient of[pic] in the following expansion [pic]. By Rajput sir ( 9810286256 )
10. In the binomial expansion of[pic] the coefficients of the 5th, 6th and 7th terms are in AP, find n.
11. In the binomial expansion of[pic] the coefficients of the three consecutive terms are in the ratio 6:33:110, find n.
12. In the binomial expansion [pic] the coefficients of three consecutive terms are 45, 120 and 210 find n.
13. If [pic]and [pic]are the coefficients of 2nd, 3rd, 4th and 5th terms of the binomial expansion of[pic] then prove that [pic]. By Rajput sir ( 9810286256 )
14. Find the coefficient of (i) [pic] in [pic] (ii) [pic] in the expansion [pic]
15. If a and b are distinct integers then using binomial theorem prove that a-b is a factor of [pic]
16. In the binomial expansion of[pic] the coefficients of the [pic], [pic] and [pic] terms are in AP, then prove that [pic].
17. If [pic] is the rth term the binomial expansion of[pic] then prove that [pic]
18. Find numerically greatest term in the expansion(i)[pic]when x =1.(ii) [pic]when[pic]and n=10
19. Find the coefficient of [pic] in the following expansion [pic]....