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If C0,C1,C2,........, Cn denote the coef...

If `C_0,C_1,C_2,........, C_n` denote the coefficients in the expansion of `(1+ x)^n`, then the value of : `C_1+2C_2+3 C_3+..... +nC_n` is :

A

`n.2^(n-1)`

B

` (n+1) 2^(n-1)`

C

` (n+1) 2^(n)`

D

`(n+2) 2^(n-1)`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
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  2. Product of any r consecutive natural numbers is always divisible by :

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  3. If C0,C1,C2,........, Cn denote the coefficients in the expansion of (...

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  4. A polygon has 44 diagonals. The number of the sides is :

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  5. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

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  6. Using binomial theorem. the value of (0.999)^3,correct to 3 decimal pl...

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  7. The coefficient of x^n, where n is any positive integer, in the expans...

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  8. If ""^(2n+1)P(n-1): ""^(2n-1)Pn =3:5 then the value of n equals :

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  9. If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-...

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  10. ""^15C0.""^5C5+""^15C1.""^5C4+""^15C2.""^5C3+ ""^15C3.^5C2+""^15C4.""^...

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  11. Every body in a room shakes hand with every body else. The total numbe...

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  12. ""^15C8+""^15C9-""^15C6-""^15C7=

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  13. If the rth term in the expansion of (x/3-2/x^2)^10 contains x^4, then ...

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  14. If 5^(99) is divided by 13, the remainder is

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  15. The total number of terms in the expansion of (x+y)^100 after simplifi...

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  16. If Pm stands for ""^mPm, then : 1+1.P1+2P2+3P3+.........+nPn is equal...

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  17. The number of positive integers satisfying the inequality ""^(n+1)C(n-...

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  18. The number of diagonals of a polygon of 20 sides is :

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  19. he number of ways in which 5 boys and 5 girls can be seated for a phot...

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  20. (""^8C0)/6-""^8C1+""^8C2 .6-""^8C3 .6^2+....+ ""^8C8 .6^7 =

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