`10C_0=`

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)) .

Column I, Column II The coefficient of the two consecutive terms in the expansion of (1+x)^n will be equal, then n can be, p. 9 If 15^n+23^n is divided, by 19, then n can be, q. 10 ^10 C_0^(20)C_(10)-^(10)C_1^(18)C_(10)+^(10)C_2^(16)C_(10)- is divisible by 2^n ,t h e nn can be, r. 11 If the coefficients of T_r , T_(r+1),T_(r+2) terms of (1+x)^(14) are in A.P., then r is less than, s. 12

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(r-1)) is equal to

The value of underset(r=0)overset(10)sumr^(10)C_(r),3^(r).(-2)^(10-r) is -

If |{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0 , then the value of r is equal to

Find the sum ^10 C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9dot

Prove that (cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0

The sum of series ^(20)C_0-^(20)C1+^(20)C2-^(20)C3++^(20)C 10 is

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