Fill in the blanks:
`"^(2)C_2` +`"'^(3)C_2 `+`'" ^(4)C_2` + `"^(5)C_2` +` "^(6)C_2 `+ `"^(7)C_2` is equal to__________

The sum S = ""^(20)C_(2) + 2*""^(20)C_(3) + 3 *""^(20)C_(4) + ...+ 19 * ""^(20)C_(20) is equal to

If C_0+C_1+C_2+…………+C_n=256 , then ^(2n)C_2 is equal to:

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to

^5C_1+^5C_2+^5C_3+^5C_4+^5C_5 is equal to

Prove that : ^2C_1+ ^3C_1+ ^4C_1= "^3C_2+ ^4C_2 .

If m= "^nC_2 , prove that "^m C_2 =3xx ^(n+1)C_4 .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(6) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

Fill in the blanks : If A = [(1,a,3),(2,b,6),(3,c,9)] , then det A is equal to……….

Verify (a + b + c) (a ^(2) +b ^(2) + c ^(2) - ab - b c - ca) = a ^(3) + b ^(2) + c ^(2) - 3 abc