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### High School Mathematics - 27.4 General Term (Tr+1)

 Suppose we have to find the (r+1)th term in the expansion of (x+y)n In its expansion we find that T3 = nC2 xn-2y2 T4 = nC3 xn-3y3 We can see that all these terms have the following properties. The suffix of C is one less than the number of terms. The power of the first factor x is equal to the difference of the upper and lower suffixes of C. The power of the second factor y and the suffix of C are same. The sum of the power of x and y is equal to the index of the given binomial. Hence (r+1)th term is given by Tr+1 = nCrxn-ryr Example: Find the tenth term in the expansion of (2x-y)11. Solution: T10 = T9+1 = 11C9(2x)11-9(-y)9 = 11C2(2x)2(-y)9 Answer: -220x2y9 Directions: Answer the following.
 Q 1: Find the term independent of x in the expansion of (x2+1/x)9.Answer: Q 2: find the value of (2x2-1/x)1/2Answer: Q 3: In the expansion of (1+x)11, the fifth term is 24 times the third term. Find the value of x.Answer: Q 4: Find the sixth term of (2x-1/x2)7Answer: Q 5: Find the fifth term in (2a+3b)12. Evaluate it when a = 1/3, b = 1/4Answer: Q 6: Find the middle term of (a/x+x/a)10Answer: Q 7: Find the term independent of x in the expansion of (x2-2/x3)5Answer: Q 8: Find the middle term of (2x-1/y)8Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!