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The value ofunderset(r=0)overset(10)sumr...

The value of`underset(r=0)overset(10)sumr^(10)C_(r),3^(r).(-2)^(10-r)` is -

A

20

B

10

C

300

D

30

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(r=0)overset(10)sumr^(10)C_(r)3^(r)(-2)^(10-r)= 10 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r)(-2)^(10-r)`
`= 10 xx 3 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r-1)(-2)^(10-r)`
`= 30(3-2)^(9) = 30`
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  5. If (1+x)^n=C0+C1x+C2x^2++Cn x^n ,t h e nC0C2+C1C3+C2C4++C(n-2)Cn= ((2...

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  6. ^404C4-^303C4.^4C1+^202C4.^4C2-^101C4.^4C3=

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  7. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is

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  8. The value of sum(r=0)^(50)(-1)^r(^(50)Cr)/(r+2) is equal to 1/(50xx51)...

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  10. The value of sum(r=0)^(50)(-1)^r(^(50)Cr)/(r+2) is equal to 1/(50xx51)...

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  11. sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...

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  13. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...

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  14. Iff(x) =.^(40)C(1).x(1-x)^(39) + 2..^(40)C(2)x^(2)(1-x)^(38)+3..^(40)C...

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  16. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

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  17. Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...

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  19. The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...

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