Let $$A$$ be an $$n \times n$$ matrix with rank $$r\left( {0 < r < n} \right).$$ Then $$AX=0$$ has $$p$$ independent solutions, where $$p$$ is

The double integral $$\,\,\int_0^a {\int_0^y {f\left( {x,y} \right)\,dx\,dy\,\,\,} } $$ is equivalent to

The magnitude of the directional derivative of the function $$f\left( {x,y} \right) = {x^2} + 3{y^2}$$ in a direction normal to the circle $$\,{x^2} + {y^2} = 2,$$ at the point $$(1,1),$$ is

The probability that a thermistor randomly picked up from a production unit is defective is $$0.1.$$ The probability that out of $$10$$ thermistors randomly picked up, $$3$$ are defective is