Question

Find the equation of tangent to the curve $y={\frac{x-7}{x^{2}-5x+6}}$ at the point, where it cuts the x-axis.

A speaks truth in 60% of the cases, while B in 90% of cases. In what percent of cases are they likely to contradict each other in stating the same fact ? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A ?

The amount of pollution content added in air in a city due to x-diesel vehicles is given by p(x) = 0·005x³ + 0·02x² + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added.

If A = $\left(\begin{array}{l l l }2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right)$ , find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = 0.

Solve the differential equation given as : $\left(\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}}\right)\frac{d x}{d y}\;=1,x\neq0$

If A = $\left(\begin{array}{l l l }1 & -2 & 3 \\ 0 & -1 & 4 \\ -2 & 2 & 1\end{array}\right)$, find $\left(A^{\prime}\right)^{-1}.$

Find the equations of the tangent and normal to the curve x = a sin³θ, y = b cos³θ at $\mathbf{\theta}={\frac{\pi}{4}}\,.$