Mathematics Tes...

What is the area bounded by \(y=\tan x, y=0\) and \(x=\frac{\pi}{4}?\)

A set containing \(n\) elements, has exactly ___________ subsets.

The line passing through the points (1, 2, -1) and (3, -1, 2) meets the yz-plane at which one of the following points?

If the sum of first n terms of a series is (n + 12) , then what is its third term?

For \(\mathrm{t} \in(0,2 \pi)\), if \(\mathrm{ABC}\) is an equilateral triangle with vertices \(\mathrm{A}(\sin \mathrm{t},-\cos \mathrm{t}), \mathrm{B}(\cos t, \sin \mathrm{t})\) and \(\mathrm{C}(\mathrm{a}, \mathrm{b})\) such that its orthocentre lies on a circle with centre \(\left(1, \frac{1}{3}\right)\), then \(\left(a^2-b^2\right)\) is equal to:

The imaginary part of \((3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}\) can be:

The slope of the line perpendicular to the line passing through the points \((3,2)\) and \((1,-1)\) is:

What is \(\lim _{x \rightarrow 0} \frac{\sin x \log (1-x)}{x^{2}}\) equal to?

If the points (k, 4, 2), (6, 2, - 1) and (8, - 2, - 7) are collinear, then find the value of k.

Let \(\mathrm{S}=\{1,2,3,4,5,6,9\}\). Then, the number of elements in the set \(\mathrm{T}=\{\mathrm{A} \subset \mathrm{eqS}: \mathrm{A} \neq \varphi\) and the sum of all the elements of \(\mathrm{A}\) is not a multiple of \(3 \backslash\}\) is