निम्नलिखित के मान ज्ञात कीजिए :
`.^(30)C_(1)+.^(30)C_(2)+.^(30)C_(3)+......+.^(30)C_(30)`.

If the value of the sum 29(.^(30)C_(0))+28(.^(30)C_(1))+27(.^(30)C_(2))+…….+1(.^(30)C_(28))-(.^(30)C_(30)) is equal to K.2^(32) , then the value of K is equal to

If the value of the sum 29(.^(30)C_(0))+28(.^(30)C_(1))+27(.^(30)C_(2))+…….+1(.^(30)C_(28))+0.(.^(30)C_(29))-(.^(30)C_(30)) is equal to K.2^(32) , then the value of K is equal to

the value of r for which .^(30)C_r.^(20)C_0+^(30)C_(r-1).^(20)C_1.....+^(30)C_0.^(20)C_r is maximum (A) 10 (B) 15 (C) 20 (D) 25

The sum of 30C_(0)+30C_(4)+30C_(8)+.....+30C_(28) is equal to

(1+x)^(10)*(1+(1)/(x))^(20)is1^(30)C_(5)(2)^(10)C_(5)-3)^(20)C_(5)-4)^(30)

The value of sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r) is (a) 40.^(69)C_(29) (b) 40.^(70)C_(30) (c) .^(60)C_(29) (d) .^(70)C_(30)

The value of sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r) is (a) 40.^(69)C_(29) (b) 40.^(70)C_(30) (c) .^(60)C_(29) (d) .^(70)C_(30)

Jdot If^(n)C_(30)=^(n)C_(4), find n