सिद्ध कीजिए : `C(2,1)+C(3,1)+C(4,1)=C(3,2)+C(4,2)`

यदि triangleABC में (If इन triangleABC), a = (1)/(sqrt(6)-sqrt(2)), b = (1)/(sqrt(6)+sqrt(2)), C = 60^(@) तो सिद्ध कीजिए कि (Prove that) c = (sqrt(4))/(2) .

Prove that : ""^(2)C_(1)+ ""^(3)C_(1)+""^(4)C_(1)=""^(3)C_(2)+""^(4)C_(2) .

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

The value of the expression C(n+1,2)+2[C(2,2)+C(3,2)+C(4,2)+......+C(n,2) is:

If C_(0),C_(1), C_(2),...,C_(N) denote the binomial coefficients in the expansion of (1 + x)^(n) , then 1^(3). C_(1)-2^(3). C_(3) - 4^(3) . C_(4) + ...+ (-1)^(n-1)n^(3) C_(n)=

If C_(0),C_(1), C_(2),...,C_(N) denote the binomial coefficients in the expansion of (1 + x)^(n) , then 1^(3). C_(1)-2^(3). C_(3) - 4^(3) . C_(4) + ...+ (-1)^(n-1)n^(3) C_(n)=

If A = [(5,3),(4,2)], B = [(1,1),(-1,2)], C = [(-3,2),(-7,5)] find 2 A + 3 B - 4 C

On using elementary operation C_(2) to C_(2) - 2C_(1) in the following matrix equation : [ (1,-3),(2,4)] = [ (1,1),(0,1)] [ (3,1),(2,4)] we have :