The area of the region bounded by the parabola \(y^2=x\) and the straight line \(2y=x\) is

If \(A\) and \(B\) are invertible matrices of the same order, then \((AB)^{-1}\) is equal to

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 value of \(\int_{-1}^{1}|x^3-x|\,dx\) is

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

The corner points of the bounded feasible region determined by the system of linear constraints are \((15,0),(40,0),(4,18)\) and \((6,12)\). If objective function is \(Z=30x+20y\), then the sum of the maximum and the minimum values of \(Z\) is

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…

The value of \(\int \frac{x^5}{\sqrt{1+x^3}}\,dx\) 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…