Sum of Coefficients of All Terms
Trending Questions
What is the integral of ?
The sum of terms of the series is
none of these
- 10
- 12
- 24
- 6
11C01 + 11C12 + 11C23+.............. 11C1011 =
- 256
- 128
- 512
- 64
If and are the greatest values of , then:
- n⋅2n−1
- n⋅2n−1−n
- n⋅2n+n
- (n−1)⋅2n
If then the value of is equal to
For (the set of all real numbers), , . Then
- n−1
- (−1)n(1+n)
- (−1)n−1(n−1)2
- (−1)n−1 n
- − 20C102
- 20C10
- − 20C10
- 20C102
Let denotes the greatest integer less than or equal of . If then is equal to
is equal to
None of these
If the coefficients of Tr, Tr+1, Tr+2 terms of (1+x)14 are in A.P., then r =
7
6
8
9
The coefficient of the term independent of in the expansion of
- 27
- 28
- 29
- 210
The sum of the series upto terms is
None of these
- 20C102
- − 20C102
- 20C10
- − 20C10
Let r and n be positive integers such that 1≤r≤n. Then prove the following :
(i) nCrnCr−1=n−r+1r
(ii) nn−1Cr−1=(n−r+1)nCr−1
(iii) nCrn−1Cr−1=nr
(iv) nCr+2nCr−1+nCr−2=n+2Cr
If the sum of the coefficients in the expansion of (a+b)n is 4096, then the greatest coefficient in the expansion is
1594
792
924
2924
- 214
- 215
- 213
- 27
If the function is defined by , then is equal to:
- n⋅2n+1
- n⋅2n
- (n+1)2n
- n⋅2n+1
Suppose is a matrix. If for every column vector , and , then the sum of the digits of is:
( where Cr= nCr)
- 2n+1−n(n+1)(n+2)
- 2n−1(n+1)
- 2n+2−n−3(n+1)(n+2)
- 2n+1+1(n+1)(n+2)