Mathematics Tes...

If f(x) = | x |, then f′(2) =

\(\int_{0}^{\pi / 2} \sin ^{2} x d x=\)

The area of the region bounded by y = | x - 1 | and y = 1 is

In how many ways can 8 students be arranged in a row?

India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting atleast 7 points is

Find shortest distance between lines \(\overrightarrow{\mathrm{r}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+4 \hat{\mathbf{k}})\) and \(\overrightarrow{\mathrm{r}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}+\mu(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\)

A man of 2 m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increases is

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices will be equilateral is