Mathematics Tes...

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the threeapply for the same house is:

A person walking along a straight road observes that at two points 1 km apart, the angle of elevation of a pole in front of the person is 30° and 75°. The height of the pole is:

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability they are both yellow?

If f(x) = |cos x – sin x|, then f'$\left(\frac{\mathrm{\pi }}{4}\right)$ is equal to-

The integrating factor of the differential equation \(2y\frac{{d} x}{{d} y}+ x = 5y^{2}\) is: (y≠0)

If \(\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k},\) then find the value of \(|\vec{a} \times \vec{b}|\).

If \(A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\) then what is the value of \(\mathrm{A}^{100}\)?

\(\lim _{x \rightarrow-1^{+}} \frac{\sqrt{\pi}-\sqrt{\cos ^{-1} x}}{\sqrt{x+1}}=\)