Mathematics Tes...

The cartesian equations of a line are \(5 x-3=3 y+4=2 z-3\). Direction ratios of the line are:

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale:

Find the points on the curve \(y=x^3-3 x+12\) at which the tangent is perpendicular to the straight line \(y=\frac{-x}{9}\).

Find the area between the curve \(y=\sin x\) and lines \(x=-\frac{\pi}{3}\) to \(x=\frac{\pi}{3}\).

Consider the inequations 2x + y > 3, x + 2y > 6 and x, y > 0. Which one of the following points lies in the common region?

How many different permutations can be made out of the letters of the word 'INDIANARMY'?

Find the sum of the vectors \(\vec{a}=6 \hat{i}-3 \hat{j}\) and \(\vec{b}=5 \hat{i}+4 \hat{j}\).

If \(\mathrm{V}=\frac{4}{3} \pi \mathrm{r}^3\) at what rate is \(\mathrm{V}\) increasing in cubic units when \(\mathrm{r}=10\) and \(\frac{\mathrm{dr}}{\mathrm{dt}}=0.01\)

Find the area bounded by the curve \(\mathrm{y}=\sin \mathrm{x}\) between \(\mathrm{x}=0\) and \(\mathrm{x}=2 \pi\).

A variable chord PQ of the parabola y² = 4ax subtends a right angle at the vertex, then the locus of the points of intersection of the normal at P and Q is: