Home
Class 12
MATHS
Let (1+x+x^(2))^(9)=a(0)+a(1)x+a(2)x^(2)...

Let `(1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+......+a_(18)x^(18)`. Then

A

`a_(0)+a_(2)+.......+a_(18)=a_(1)+a_(3)+......+a_(17)`

B

`a_(0)+a_(2)+......+a_(18)` is even

C

`a_(0)+a_(2)+......+a_(18)` is divisible by 9

D

`a_(0)+a_(2)+......+a_(18)` is divisible by 3 but not by 9

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2017 (UNIT-4)|13 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2017 (UNIT-7)|1 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2017 (UNIT-2)|1 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If (1+x+x^(2))^(25)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50).x^(50) , then a_(0)+a_(2)+a_(4)+....+a_(50) is

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+.....+a_(2n)x^(2n)" prove that",a_(0)+a_(2)+a_(4)+.......a_(2n)=(1)/(2)(3^(n)+1) .

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

Let (x+10)^(50)+(x-10)^(50)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50)x^(50) for all x in R , then (a_(2))/(a_(0)) is equal to

If the expansion in power of x of the function (1)/(( 1 - ax)(1 - bx)) is a_(0) + a_(1) x + a_(2) x^(2) + a_(3) x^(3) + …, then a_(n) is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The remainder obtained when a_(1)+5a_(2)+9a_(3)+13a_(4)+…+(8n-3)a_(2n) is divided by (p+2) is (a) 1 (b) 2 (c) 3 (d) 0

If (1+x+2x^(2))^(20) = a_(0) + a_(1)x^() "……" + a_(40)x^(40) , then following questions. The value of a_(0) +a_(2) + a_(4)+ "……" + a_(38) is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The value of a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n) when p=-3 and n in even is

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....