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If n is a positive integer, then (sqrt3 ...

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

A

a non-real number

B

a real number

C

a positive real number

D

None of these

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The correct Answer is:
B
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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-2 (CONCEPT APPLICATOR)
  1. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The sum sum(i=0)^(m)""^(10)C(i)xx""^(20)C(m-i)("where " ""^(p)C(q)=0" ...

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