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Find the coefficient of x^5 in (1+2x+3x^...

Find the coefficient of `x^5` in `(1+2x+3x^2...........)^(-3/2)`

A

15

B

21

C

12

D

30

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The correct Answer is:
B
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Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-2 (CONCEPT APPLICATOR)
  1. In the binomial expansion (a+bx)^(-3) = ( 1)/( 8 ) + (9)/( 8)x +"…….."...

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  2. What is the last digit of 3^(3^(4n)) +1, where n is a natural number?

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  3. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

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  4. If f(x)=(x-1)(x-2)(x-3).......(x-50) find coeff. of x^50 and x^49

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  5. If n is a positive integer, then (sqrt3 +i)^n+(sqrt3 -i)^n is

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  6. Prove that (C0+C1)(C1+C2)(C2+C3)(C(n-1)+Cn)=(n+1)^n/(n!).c0.C1.C2........

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  7. If (1 + ax)^n= 1 +8x+ 24x^2 +..... then the value of a and n is

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  8. The sum of the series (2)/(1!) + (4)/(3!) + (6)/(5!) + ……. "to" oo ...

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  9. If coefficient of a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0) , t...

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  10. The number of dissimilar terms in the expansion of (a+b)^(n) is n+1, ...

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  11. The sum of rational term in (sqrt(2)+3 3+5 6)^(10) is equal to 12632 b...

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  12. If the 7th tern in the binomial expansion of (3/((84)^(1/3)) +sqrt(3) ...

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  13. If (+x)^n=sum(r=0)^n ar x^r&br=1+(ar)/(a(r-1))&prod(r=1)^n br=((101)^...

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  14. The coefficients of x^(13) in the expansion of (1 - x)^(5) (1 + x...

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  15. If x is so small that x^3 and higher powers of x may be neglectd, then...

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  16. If (r+1)^(th) term is (3.5...(2r-1))/(r!) (1/5)^(r), then this is th...

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  17. The the term independent in the expansion of [(t^(-1)-1)x+(t^(-1)+1)^(...

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  18. If the third in the expansion of [x + x^(log 10x)]^(6) is 10^(6) ,...

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  19. For what value of x is the ninth term in the expansion of (3^(log3 sqr...

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  20. The middle term in the expansion of (1+(1)/(x^(2)))^n ( 1+x^(2))^(n) i...

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