Mathematics Tes...

If \(\mathrm{x}=(7+4 \sqrt{3})^{2 \mathrm{n}}=[\mathrm{x}]+\mathrm{f}\), then \(\mathrm{x}(1-\mathrm{f})\) is equal to:

How many different words can be formed by using all the letters of the word, ALLAHABAD if both L's do not come together? 

A box contains \(4\) tennis balls, 6 season balls and \(8\) dues balls. \(3\) balls are randomly drawn from the box. What is the probability that the balls are different?

The second degree equation \(2 x^{2}+2 y^{2}-5 x-7 y-3=0\) represents:

The straight lines \(1_1\) and \(1_2\) pass through the origin and trisect the line segment of the line \(L: 9 x+5 y=45\) between the axes. If \(\mathrm{m}_1\) and \(\mathrm{m}_2\) are the slopes of the lines \(1_1\) and \(1_{2^{\prime}}\) then the point of intersection of the line \(\mathrm{y}=\left(\mathrm{m}_1+\mathrm{m}_2\right) \mathrm{x}\) with L lies on.

Let \(\alpha\) and \(\beta\) be two roots of the equation \(x^2+2 x+2=0\), then \(\alpha^{15}+\beta^{15}\) is equal to:

If \({A}=\left[\begin{array}{ll}{x} & 2 \\ 4 & {x}\end{array}\right]\) and det \(\left(A^{2}\right)=64\), then \({x}\) is equal to:

The smallest positive integer \(n\) for which

\(\left(\frac{1-i}{1+i}\right)^{n^{2}}=1\)

where \(i=\sqrt{-1}\), is

A room contains \(3\) red, \(5\) green and \(4\) blue chairs. Two chairs are picked and are put in the lawn. What is the probability that none of the chairs picked is blue?

Solve: 2x + 1 > 3