` 2.^(10)C_(0)-^(10)C_(1)-^(10)C_(2)+2*^(10)C_(3)-^(10)C_(4)-^(10)C_(5)+2*^(10)C_(6)-^(10)C_(7)-^(10)C_(8)` `+2*^(10)C_(9)-^(10)C_(10)=`

Find the sum ^10C_(1)+^(10)C_(3)+^(10)C_(5)+^(10)C_(7)+^(10)C_(9)

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)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)

^10(C_(0))^(2)-^(10)(C_(1))^(2)+^(10)(C_(2))^(2)-......-(^(10)C_(9))^(2)+(^(10)C_(10))^(2)=

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10)) is (A) 2^(21) - 2^(11) (B) 2^(21) - 2^(10) (C) 2^(20) - 2^(9) (D) 2^(20) - 2^(10)

(1+x)^(10)*(1+(1)/(x))^(20)is1^(30)C_(5)(2)^(10)C_(5)-3)^(20)C_(5)-4)^(30)

In the expansion off (1+x)^(10)=.^(10)C_(0)+.^(10)C_(1)x+.^(10)C_(2)x^(2)+ . . .+.^(10)C_(10)x^(10) , then value of 528[(.^(10)C_(0))/(2)-(.^(10)C_(1))/(3)+(.^(10)C_(2))/(4)-(.^(10)C_(3))/(5)+ . . .+(.^(10)C_(10))/(12)] is equal to________.

C(10,8)+C(10,1)=

C_(2)H_(4),C_(4)H_(10), C_(3)H_(8),CH_(4)