[" 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 "],[qquad " [JEE (Main)-201"]

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)

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)=

" 6.Find the value of "^(10)C_(5)+2*^(10)C_(4)+^(10)C_(3)

The value of (^21C_1-^10C_1)+(^21C_2-^10C_2)+....+(^21C_(10)-^10C_(10)) is

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

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

"^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*18C_(10)+....^(40)C_(10)*^(10)C_(10) is equal to

"^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*18C_(10)+....^(40)C_(10)*^(10)C_(10) is equal to