Mathematics Tes...

\({I}=\int {e}^{{x}} \cdot \frac{1+\sin {x}}{1+\cos {x}} {d} {x}\) is equal to:

The sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th and the 9th term is 56. Find the sum of the 4th and the 8th terms of the same series.

If \(\mathrm{f}(\mathrm{x}), \mathrm{g}(\mathrm{x})\) be twice differential functions on \([0,~2]\) satisfying \(\mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{g}^{\prime \prime}(\mathrm{x}), \mathrm{f}^{\prime}(1)\) \(=2 g^{\prime}(1)=4\) and \(f(2)=3 g(2)=9,\) then:

If \(A=\left[\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right]\), then find the value of \((A+B)\).

The image of the point \((-1,3,4)\) in the plane \(x-2 y=0\) is:

Find the value of \(\left|\begin{array}{lll}0 & c & b \\ c & 0 & a \\ b & a & 0\end{array}\right|^{2}\)

What is the principal argument of \((-1-i \sqrt{3})\)? where \(i=\sqrt{ -1}\)

Find the middle terms in the expansion of \(\left(2 x +\frac{1}{ x }\right)^{5}\).

In figure, \(O\) is the centre of the circle. If \(\angle \mathrm{APB}=50^{\circ}\), find \(\angle \mathrm{AOB}\) and \(\angle \mathrm{OAB}\).

Find the equation of the circle whose end points of the diameter are (- 3, 5) and (5, 3).