`10C_1=`

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 ^10 C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9dot

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

Let X=(\ ^(10)C_1)^2+2(\ ^(10)C_2)^2+3(\ ^(10)C_3)^2+\ ddot\ +10(\ ^(10)C_(10))^2 , where \ ^(10)C_r , r in {1,\ 2,\ ddot,\ 10} denote binomial coefficients. Then, the value of 1/(1430)\ X is _________.

Compute 10C1

"^(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

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) .

Let a=111 1(55d igi t s),b=1+10+1=^2++10^4,c=1+10^5+10^(10)+10^(15)++10^(50), then a=b+c b. a=b c c. b=a c d. c=a b

The domain of the function f(x)=1/sqrt((1^10C_(x-1)-3X^10C_x)) contains the points. (a) 9,10,11 (b) 9,10,12 (c) all natural numbers (d) none of these

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