\(\int \mathrm{e}^{x}\left(\frac{1-x}{1+x^{2}}\right)^{2} \mathrm{~d} x=\)

Which of the following equation has no solution?

Let \(\mathrm{A}=\lim _{\mathrm{x} \rightarrow 0^{+}}\left(1+\tan ^2 \sqrt{x}\right)^{\frac{1}{2 x}}\), then \(\log _{\mathrm{e}} \mathrm{A}=\)

If the lines \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}\) intersect, then \(k=\)

The general solution of the differential equation \(\cos (x+y) \frac{d y}{d x}=1\) is

The length of the altitude through the point D of tetrahedron where the vertices of the tetrahedron are \(\mathrm{A}(2,3,1), \mathrm{B}(4,1,-2), \mathrm{C}(6,3,7)\), \(D(-5,-4,8)\), is

If \(\mathrm{p}\) and \(\mathrm{q}\) are true statements and \(\mathrm{r}\) and \(s\) are false statements, then the truth values of the statement patterns \((p \wedge q) \vee r\) and \((\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r})\) are respectively

If \(\bar{x}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \bar{y}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) and \(\overline{\mathrm{z}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) where \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors, then value of \(\bar{x} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})+\bar{y} \cdot(\overline{\mathrm{~b}}+\overline{\mathrm{c}})+\overline{\mathrm{z}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})\) is

What volume of ammonia is formed when \(10 \mathrm{dm}^3\) dinitrogen reacts with \(30 \mathrm{dm}^3\) dihydrogen at same temperature and pressure?

If \(f(x)=x^{2}-3 x+4\) and \(f(x)=f(2 x+1)\), then \(x=\)

The statement pattern $\left(p\wedge q\right)\wedge \left[~r\vee \left(p\wedge q\right)\right]\vee \left(~p\wedge q\right)$ is equivalent to ________

Two stones of masses \(\mathrm{m}\) and \(3 \mathrm{~m}\) are whirled in horizontal circles, the heavier one in radius \(\left(\frac{\mathrm{r}}{3}\right)\) and lighter one in radius ' \(\mathrm{r}^{\prime}\). The tangential speed of lighter stone is 'n' times that of the value of heavier stone, when they experience same centripetal force. The value of \(\mathrm{n}\) is

If \(|z-2+i| \leq 2\), then the difference between the greatest and least value of \(|z|\) is \((\mathrm{i}=\sqrt{-1})\)