Mathematics Tes...

\(\frac{d}{dx}\left(\frac{x^{4}+x^{2}+1}{x^{2}-x+1}\right)=ax+\mathrm{b},\) what is the value of \(a\) and \(\mathrm{b}\) ?

Calculate the work done by a force \(F=5 i+3 j+2 k\) on a particle when the particle is displaced by \(\vec{S}=3 \hat{i}-\hat{j}+2 \hat{k}\).

How many different salads can be made from onion, cucumber, tomato, and carrot?

If the straight line \(x \cos \alpha+y \sin \alpha=p\) is tangent to the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), then:

If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\) are vectors of magnitude \(\alpha\) then the magnitude of the vector \(|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|\) is?

If \(y=\tan ^{-1}\left(\frac{3-2 \tan \sqrt{x}}{2+3 \tan \sqrt{x}}\right)\) then what is \(\frac{d y}{d x}\) equal to?

The total number of ways in which 5 toys of different colours can be distributed among 3 children, so that, each child gets at least one toy is:

Find the set of value of x for which f(x) = cos x − x is decreasing in