Mathematics Tes...

Find the nature of roots of \(x^{2}+7 x-10=0\).

Solve the following Linear Programming Problems graphically:

Minimise \(\mathrm{Z}=-3 \mathrm{x}+4 \mathrm{y}\), subject to

\(x+2 y \leq 8,3 x+2 y \leq 12, x \geq 0, y \geq 0\)

The angle of intersection of the curves \(y=4-x^{2}\) and \(y=x^{2}\) is:

Lines \(x=a y+b, z=c y+d\) and \(x=a^{\prime} y+b^{\prime}, z=c^{\prime} y+d^{\prime}\) are perpendicular, if:

If \(\tan 20^{\circ}={p}\), then \(\frac{\tan 160^{\circ}-\tan 110^{\circ}}{1+\tan 160^{\circ} \tan 110^{\circ}}\) is equal to:

Modulus of vector \(\vec{c}=4 \hat{i}-5 \hat{j}+11 \hat{k}\) is:

The value of \(\int \sqrt{\mathrm{x}} \mathrm{e}^{\sqrt{\mathrm{x}}} \mathrm{dx}\) is equal to:

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:

What is \(\cot A+\operatorname{cosec} A\) equal to?