Cosine of the acute angle between the lines \(\frac{x-3}{2}=\frac{y-2}{1}=\frac{z-5}{2}\) and \(\frac{x-1}{6}=\frac{y-3}{-3}=\frac{z+6}{2}\) is

Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A box is selected at random and then a ball is randomly drawn from the selected box. If the color of the ball is black then the probability that th…

If…

If A and B are independent events, then which of the following is/are true? (A) \(\overline{A}\) and B are independent events (B) \(P(A\cap B)=0\) (C) \(\overline{A}\) and \(\overline{B}\) are independent events (D) \(P(A\cap B)=P(A)+P(B)\) Choose the correct answer from the opti…

\(\int \frac{dx}{e^x+e^{-x}}\) is equal to

Which one of the following equations is a homogeneous differential equation?

If \(P(A)=\frac{3}{5}\), \(P(B)=\frac{1}{2}\) and \(P(A\cap B)=\frac{1}{4}\), then \(P(\overline{A}\,|\,\overline{B})\) is

The feasible region represented by the constraints: \(x+2y\ge100,\ 2x-y\le0,\ 2x+y\le200,\ x\ge0,\ y\ge0\) of an LPP is: [Figure: graph with x and y axes (ticks at 50, 100, 150, 200) showing the lines x + 2y = 100, 2x - y = 0 and 2x + y = 200, with four shaded regions labelled A,…

The area (in sq.units) of the region enclosed by the curve \(y=\cos x,\ \frac{-\pi}{2}\le x\le\frac{\pi}{2}\) and the \(x\)-axis is: