The value of determinant `|1 1 1^m C_1^(m+1)C_1^(m+2)C_1^m C_2^(m+1)C_2^(m+2)C_2|` is equal to `1` b. `-1` c. `0` d. none of these

The value of the determinant |(1,1,1),(.^(m)C_(1),.^(m +1)C_(1),.^(m+2)C_(1)),(.^(m)C_(2),.^(m +1)C_(2),.^(m+2)C_(2))| is equal to

If m in N and m>=2 prove that: |111^(m)C_(1)^(m+1)C_(1)^(m+2)C_(1)^(m)C_(2)^(m+1)C_(2)^(m+2)C_(2)|=1

If |[1,1,1],[^mC_1,^(m+3)C_1,^(m+6)C_1],[^mC_2,^(m+3)C_2,^(m+6)C_2]|=2^alpha3^beta5^gamma then alpha+beta+gamma is equal to

If y=sin(m sin^(-1)x), then (1-x^(2))y_(2)-xy_(1) is equal to m^(2)y(b)my(c)-m^(2)y(d) none of these

^(n)C_(m)+^(n-1)C_(m)+^(n-2)C_(m)+............+^(m)C_(m)

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

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 for which S = .^(20)C_(r.).^(10)C_(0)+.^(20)C_(r-1).^(10)C_(1)+"........".^(20)C_(0).^(10)C_(r) is maximum can not be