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

If…

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

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

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:

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…

Match List-I with List-II List-I | List-II (A) If vector \(\vec a\) and \(\vec b\) are such that \(\vec a=\lambda\vec b\) and \(|\vec a|=|\vec b|\), then | (I) \(\vec a\) and \(\vec b\) are orthogonal (B) Projection vector of \(\vec a\) on \(\vec b\) | (II) [0,12] (C) \(\vec a\)…

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…

Match List-I with List-II List-I | List-II (A) The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2+\left(\frac{dy}{dx}\right)^2=x\sin\left(\frac{dy}{dx}\right)\) | (I) 4 (B) The degree of the differential equation…