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Statement-1 The number of terms in the e...

Statement-1 The number of terms in the expansion of
` (x + (1)/(x) + 1)^(n) " is " (2n +1)`
Statement-2 The number of terms in the expansion of
` (x_(1) + x_(2) + x_(3) + …+ x_(m))^(n) "is " ^(n + m -1)C_(m-1)`.

A

`""^(n+1)C_(r)`

B

`""^(n+r-1)C_(r-1)`

C

`""^(n+r+1)C_(r+1)`

D

`""^(n+r-1)C_(r)`

Text Solution

Verified by Experts

The correct Answer is:
B
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MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-EXERCISE (LEVEL 1 Single Correct Answer Type Questions)
  1. The expansion of (x + y + z)^(n) is given by

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  2. The number of terms in the expansion of (x + y + x)^(10), is

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  3. Statement-1 The number of terms in the expansion of (x + (1)/(x) +...

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  4. Find the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx...

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  5. If x+y= 1, then value of sum(r=0)^(n)(r)(""^(n)C(r))x^(n-r)y^(r) is

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  6. If sum of the coefficients in the expansion of (x+1/x)^(n) is 128, the...

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  7. In the binomial expansion (a-b)^n, nge5 the sum of 5th and 6th terms i...

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  8. 2C0+2^2/2 C1+2^3/3 C2+.............+2^11/11 C10 =?

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  9. C1/C0+2C2/C1+3C3/C2+............+nCn/C(n-1)=(n(n+1))/2

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  10. If (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r),(1 + (C(1))/(C(0))) (1 + (C(...

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  11. lf C(r)=""^(n)C(r), then C(0)-1/3C(1)+1/5C(2)…… upto (n+1) terms equal

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  12. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

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  13. Find the sum sum(j=0)^n(^(4n+1)Cj+^(4n+1)C(2n-j)) .

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  14. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  15. Third term in expression of (x + x^(log(10)x))^(5) is 10^(6) than poss...

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  16. The numerically greatest term in the expansion of (1 + x)^(10) when...

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  17. The greatest term in the expansion of (3 + 5x)^(15), when x=1/5, is

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  18. If sum of the coefficients of x^(7) and x^(4) in the expansion of ((x^...

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  19. The value of (19^(3)+6^(3)+(3)(19)(6)(25))/(3^(6)+6(243)(2)+(15)(81)(4...

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  20. In the expansion of (x+a)^n if the sum of odd terms is P and the sum o...

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