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The value of .^(20)C(0)+.^(20)C(1)+.^(20...

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

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The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

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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) .

If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is

If a= ^(20)C_(0) + ^(20)C_(3) + ^(20)C_(6) + ^(20)C_(9) + "…..", b = ^(20)C_(1) + ^(20)C_(4) + ^(20)C_(7) + "… and c = ^(20)C_(2) + ^(20)C_(5) + ^(20)C_(8) + "…..", then Value of (a-b)^(2) + (b-c)^(2) + (c-a)^(2) is

Find the value of .^20 C_0-(.^20C_1)/2+(.^20C_2)/3-(.^20C_3)/4+...

Evaluate the following : (i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20) (ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9) (iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25) (iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)

The value of r for which .^(20)C_(r ), .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

The value of r for which .^(20)C_(r ), .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

If m, n, r, in N then .^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0) = coefficient of x^(r) in (1+x)^(m)(1+x)^(n) = coefficient of x^(f) in (1+x)^(m+n) The value of r(0 le r le 30) for which S = .^(20)C_(r).^(10)C_(0) + .^(20)C_(r-1).^(10)C_(1) + ........ + .^(20)C_(0).^(10)C_(r) is minimum can not be