For which of the following ordered pairs ($$\mu $$, $$\delta $$), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = $$\mu $$
4x + 4y + 4z = $$\delta $$
is inconsistent ?

The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the sum of the diagonal elements of AA^T is 3, is

Let A and B be two independent events such that
P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$.
Then, which of the following is TRUE?

If $$\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$$

where c is a constant of integration, then $$\lambda f\left( {{\pi \over 3}} \right)$$ is equal to