Find the value of $$\lambda $$ such that the function $$f(x)$$ is a valid probability density function ________.

The solution $$\int\limits_0^{\pi /4} {{{\cos }^4}3\theta {{\sin }^3}\,6\theta d\theta \,\,} $$ is :

What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ rows and $$2$$ columns, matrix $$Q$$ has $$2$$ rows and $$4$$ columns and matrix $$R$$ has $$4$$ rows and $$1$$ column ______.

In its natural condition, a soil sample has a mass of 1.980 kg and a volume of 0.001 m³. After being completely dried in an oven, the mass of the sample is 1.800 kg. Specific gravity G is 2.7. Unit weight of water is 10 kN/m³. The degree of saturation of soil is