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The coefficient of x^r[0lt=rlt=(n-1)] in...

The coefficient of `x^r[0lt=rlt=(n-1)]` in the expansion of `(x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+....` `+(x+2)^(n-1)` is `a.^n C_r(3^r-2^n)` `b.^n C_r(3^(n-r)-2^(n-r))` `c.^n C_r(3^r+2^(n-r))` d. none of these

A

`""^(n)C_(r) (3^(r) - 2^(n))`

B

`""^(n)C_(r) (3^(n-r) - 2 ^(n-r))`

C

`(""^(n)C_(r) (3^(r) + 2 ^(n-r))`

D

none of these

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The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. If the coefficient of the middle of term in the expansion of (1+x)^(2n...

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  2. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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  3. The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+...

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  4. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

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  5. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

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  6. the coefficient of x^(7) in (ax - b^(-1) x^(-2))^(11) is

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  7. Find the coefficient of x^5 in the expansion of (1+x^2)^5(1+x)^4.

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  8. Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)...

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  9. If T0,T1, T2, ,Tn represent the terms in the expansion of (x+a)^n , t...

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  10. about to only mathematics

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  11. If the coefficients of three consecutive terms in the expansion of (1+...

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  12. The second, third and fourth terms in the binomial expansion (x+a)^na...

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  13. The value of tan75

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  14. If the coefficients of the (2r+4)t h ,(r+2)t h term in the expansion o...

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  15. Write the middle term in the expansion of (x+1/x)^(10)dot

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  16. The 14^(th) term from the end in the expansion of (sqrt(x ) - sqrt(y)...

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  17. If [x] denotes the greatest less than or equal to x and F = R - [R]...

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  18. If [x] denotes the greatest integer less then or equal to x, then ...

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  19. If n in N such that (7 + 4 sqrt(3))^(n) = I + F , then IF is

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  20. Find n in the binomial (2^(1/3)+1/(3^(1/ 3)))^n , if the ration 7th te...

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