Binomial Theorem for Any Index
Trending Questions
Q.
If nC12=nC8, then n is equal to
(a) 20 (b) 12 (c) 6 (d) 30
Q.
If nC8= nC2, find nC2.
Q.
The number of integral terms in the expansion of
(512+716)642 is
103
106
108
109
Q. If (1−x)−n=a0+a1x+a2x2+........+arxr+....., then a0+a1+a2+......+ar is equal to
- n(n+1)(n+2)....(n+r)r!
- (n+1)(n+2)....(n+r)r!
- n(n+1)(n+2)....(n+r−1)r!
- None of the above
Q. 10.Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Q.
If nCx= nCy and n≠y then prove that x+y=n.
Q. Prove that the coefficient of x n in the expansion of (1 + x ) 2 n is twice the coefficient of x n in the expansion of (1 + x ) 2 n –1 .
Q. Find the expansion of using binomial theorem.
Q. 13. Show that 9#l- 8n 9 is divisible by 64, whenever n is a positive integer.
Q.
If X={4n−3n−1:n∈N} and Y={9(n−1):n∈N}, then show that X∩Y=X.
Q. If a and b are distinct integers, prove that a – b is a factor of a n – b n , whenever n is a positive integer. [ Hint: write a n = ( a – b + b ) n and expand]
Q. 8. (101)4
Q. Find the coefficient of x5 in the product (1+2x)6(1−x)7 using binomial theorem.
Q. Find a if the coefficients of x 2 and x 3 in the expansion of (3 + ax ) 9 are equal.
Q.
From given A.P i.e., a b2 c3, a2 b3 c4, a3 b4 c5, get the value of abc
Q. The coefficient of t4 in the expansion of (1−t61−t)3 is :
- 12
- 10
- 15
- 14
Q.
Evaluate nCr+2nCr−1+nCr−2.
Q. 11. Find (a by - (a - by. Hence, evaluate 32)- (3 - V2)
Q.
The expansion (1+x)n = 1 + nx + n(n−1)2!(x)2........... is valid if |x| > 1.
True
False
Q. (1-2r)5
Q. 46. Find the value of a2+Va1aVa2 -1
Q. 5. Evaluate (J34./2f-(, f-љуV3 V2
Q. 1. xi(x 3)8
Q. The approximate value of (1.0002)3000 is
- 1.4
- 1.8
- 1.2
- 1.6
