Mathematics Tes...

The value of \(\int_{0}^{\frac{\pi}{4}} \log (1+\tan x) d x\) is equal to:

If \([\vec{a} \vec{b} \vec{c}]=1\), then the value of \(\frac{\vec{a} \cdot \vec{b} \times \vec{c}}{\vec{c} \times \vec{a} \cdot \vec{b}}+\frac{\vec{b} \cdot \vec{c} \times \vec{a}}{\vec{a} \times \vec{b} \cdot \vec{c}}+\frac{\vec{c} \cdot \vec{a} \times \vec{b}}{\vec{b} \times \vec{c} \cdot \vec{a}}\) is

Find the value of \(∫e^x cos x\) dx.

If \(\frac{\operatorname{cosec} \theta+\sin \theta}{\operatorname{cosec} \theta-\sin \theta}=\frac{21}{15}\), then the value of \(\tan \theta\) is equal to-

Find the numerical value of \(\frac{2}{1+\cot ^{2} \theta}+\frac{4}{1+\tan ^{2} \theta}+2 \sin ^{2} \theta\).

What is the degree of the differential equation \(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}+2\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)-\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0 ?\)

If \(y=(\tan x)^{\tan x^{\tan x}}\) then the value of \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\)

The second degree equation \(2 x^{2}+2 y^{2}-2 x-6 y+5=0\) represent:

If a straight line makes angles \(\alpha, \beta\) and \(\gamma\) with the co-ordinate axes, then \(\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma\) is equal to:

Minimize \(\mathrm{Z}=7 \mathrm{x}+\mathrm{y}\) subject to

\(5 x+y \geq 5, x+y \geq 3, x \geq 0, y \geq 0 \text {. }\)