Mathematics Tes...

If \(P(A)=\frac{1}{5}, P(B)=\frac{1}{3}\) and \(P(B \mid A)=\frac{1}{3}\), then \(P(A \cap B)\) is ?

What is the number of ways that a cricket team of \(11\) players can be made out of \(15\) players?

If \(y=x^{x}\), what is \(\frac{d y}{d x}\) at \(x=1\) equal to?

The graph of the inequations \(x \leq 0, y \leq 0\), and \(2 x+y+6 \geq 0\) is:

The vector \(2 \hat{j}-\hat{k}\) lies:

Let \(\mathrm{T}(\mathrm{k})\) be the statement, \(1+3+5+\ldots \ldots . .+(2 \mathrm{k}-1)=\mathrm{k}^{2}+10\), then:

Find the distance of the point (4, 1) from the line 3x - 4y + 12 = 0?

If ‘a’ is inversely proportional to ‘b’ and ‘b’ is inversely proportional to c. then:

Under which one of the following conditions are the lines \(x = ay + b; z = cy + d\) and \(x = ey + f; z = gy + h\) perpendicular?

For what value of \(\alpha \in R\) the system of equation: \(x+2 y+z=3,2 x+4 y+2 z=6\) and \(\alpha x+ \alpha y+ \alpha z=3\alpha\) has infinitely many solutions.