Home
Class 12
MATHS
Evaluate: (i) .^(12)C(1)+.^(12)C(2)+.^...

Evaluate:
(i) `.^(12)C_(1)+.^(12)C_(2)+.^(12)C_(3)+ . . .+.^(12)C_(12)`
(ii) `.^(19)C_(3)+.^(19)C_(5)+.^(19)C_(7)+ . . .+^(19)C_(19)`.

Text Solution

Verified by Experts

(i) `.^(12)C_(1)+.^(12)C_(2)+.^(12)C_(3)+ . . .+.^(12)C_(12)`
`=.^(12)C_(0)+.^(12)C_(1)+.^(12)C_(2)+.^(12)C_(3)+ . . . .+.^(12)C_(12)-.^(12)C_(0))`
={sum of coefficients in the expansion of `(1+a)^(12)`}`-.^(12)C_(1)`
={sum of coefficient of evenn terms in the expansion of `(1+a)^(19)`}-`.^(19)C_(1)=2^(19-1)-19`
`=2^(18)-19`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Illustration|1 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Try Yourself|20 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise section-J (Aakash Challengers Qestions)|16 Videos

Similar Questions

Explore conceptually related problems

Evaluate (i) ""^(10)C_(4)+""^(10)C_(5) (ii) ""^(13)C_(6)+ ""^(13)C_(5) (iii) ""^(19)C_(17)+ ""^(19)C_(18) .

Evaluate .^(12)C_(7) .

Evaluate the following: (i) .^(10)C_(5) (ii) .^(12)C_(8) (iii) .^(15)C_(12) (iv) .^(n+1)C_(n) (v) .^(14)C_(9)

Evaluate the following : (i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20) (ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9) (iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25) (iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)

The value of |(.^(10)C_(4).^(10)C_(5).^(11)C_(m)),(.^(11)C_(6).^(11)C_(7).^(12)C_(m+2)),(.^(12)C_(8).^(12)C_(9).^(13)C_(m+4))| is equal to zero when m is

Evaluate the following : (i) ""^(8)P_(5) (ii) ""^(10)P_(3) (iii) ""^(12)C_(7) (iv) ""^(9)C_(0) .

If ""^(n)C_(10)= ""^(n)C_(9) , find ""^(n)C_(19) .

Evaluate .^19C_18+^19C_17