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(1 + x)^(n) = p(0) + p(1) x + p(2) x^(2)...

`(1 + x)^(n) = p_(0) + p_(1) x + p_(2) x^(2) + … + p_(n) x^(n) ` , then `p_(0) + p_(3) + p_(6) + …..` =

A

`(1)/(3) [ 2^(n-1) + cos "" (n pi)/(3)]`

B

`(2)/(3) [ 2^(n-1) + cos "" (npi)/(3)]`

C

` (1)/(3) [2^(n-2) + sin "" (npi)/(3)]`

D

`(2)/(3) [2^(n-2) + sin"" (npi)/(6)]`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
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  2. Match the items of List - I with those of List-II

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  3. If z = x +iy and P represents z in the Argand plane and mod (2z-3) = 4...

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  4. If z = (lambda + 3) + isqrt( 5 - lambda^(2)) , then the locus of z is...

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  5. If z=(x+iy) and if the point P in the Argarand plane represent z, then...

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  6. If z1=1+2i,z2=2+3i,z3=3+4i, " then " z1,z2and z3 represents the vertic...

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  7. If z is a complex number with |z|ge 5 . Then the least value of |z +...

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  8. (1 + x)^(n) = p(0) + p(1) x + p(2) x^(2) + … + p(n) x^(n) , then p(0)...

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  9. The cube roots of unity when represented on the Argand diagram form th...

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  10. If a , b , c in R such that a + b + c= 0 and az(1) + bz(2) + cz(3) = ...

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  11. In the Argand plane the area in square units of the triangle formed by...

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  12. If the area of the triangle on the complex plane formed by the point z...

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  13. If |z-2/z|=2 then the greatest value of |z| is

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  14. If |z| ge 3 , then the least value of |z + (1)/(z)| is

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  15. The value of (i)^(i) is

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  16. Log(e) ((1 + i)/(1- i))=

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  17. The real and imaginary points of log (1 + isqrt3) are

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  18. Assertion (A) : If 3 + iy is a root of x^(2) + ax + b = 0 then a = -6 ...

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  19. If log((1)/(sqrt(3))){(|z|^(2)-|z|+1)/(2+|z|)}gt -2 , then z lies insi...

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  20. If omega is a complex cube root of unity , then for any n gt 1 unde...

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