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

10C_1=

10C_0=

Find the sum sum_(k=0)^(10)^(20)C_kdot

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)) .

Find the sum of the series ^15 C_0+^(15)C_1+^(15)C_2++^(15)C_7dot

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

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

The value of "^20 C_0+^(20)C_1+^(20)C_2+^(20)C_3+^(20)C_4+^(20)C_ 12+^(20)C_ 13+^(20)C_14+^(20)C_15 is a. 2^(19)-(( "^(20)C_10 + "^(20)C_9))/2 b. 2^(19)-((^(20)C 10+2xx^(20)C9))/2 c. 2^(19)-(^(20)C 10)/2 d. none of these

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

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