[^10C_(0)^(2)-^(10)C_(1)^(2)+^(10)C_(2)^(2)-...-(^(10)C_(9))^(2)+(^(10)C_(10))^(2)," (C) "4^((6)/(4))" are an alled "],[[" (A) "0," (B) "(^(10)C_(5))^(2)+(^(10)C_(10))^(2)=]]

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

"^10(C_0)^2 - "^10(C_1)^2 + "^10(C_2)^2 - ...... - ( "^10C_9)^2 + ( "^10C_10)^2=

"^10(C_0)^2 + "^10(C_1)^2 + "^10(C_2)^2 + ...... + ( "^10C_9)^2 + ( "^10C_10)^2=

Prove that ^10C_(1)(x-1)^(2)-^(10)C_(2)(x-2)^(2)+^(10)C_(3)(x-3)^(2)+...-^(10)C_(10)(x-10)^(2)=

Prove that ""^(10)C_(2)+2xx^(10)C_(3)+^(10)C_(4)=^(12)C_(4)

Evaluate : 2^(10)C_(0)+(2^(2).^(10)C_(1))/(2)+(2^(3).^(10)C_(2))/(3)+ . . .+(2^(11).^(10)C_(10))/(11)

Prove that ^10 C_1(x-1)^2-^(10)C_2(x-2)^2+^(10)C_3(x-3)^2+-^(10)C_(10)(x-10)^2=x^2

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________.

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________.

Evaluate ""^(10)C_(1)+""^(10)C_(2)+ . . .+""^(10)C_(10)