Mathematics Tes...

The function \(f(x)=\int_{0}^{\pi} \log \left(t+\sqrt{1+t^{2}}\right) d t\) is:

The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis, is

If \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\) then a value of \(x\) is:

If \(\sin 5 x+\sin 3 x+\sin x=0,\) then the value of \(x\) other than zero, lying between \(0 \leq x \leq \pi / 2\) is...

Sum of the series
1 + 3 + 6 + 10 + 15 + ……………………….n terms is,

In an experiment with 15 observations on X, the following results where available:\(\sum X^{2}=2830, \Sigma \mathrm{x}=170\). One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is

There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is,

The number of ways in which a mixed double game can be arranged from amongst 9 married couples if no husband and wife play in the same game is,