Mathematics Tes...

If \(m , n\) are any two odd positive integers with \(n < m\), then the largest positive integer which divides all the numbers of the type \(m ^2- n ^2\) is ___________.

Which one of the following is correct in respect of the function f : R → R⁺ defined as f(x) = |x+1|?

If \(\mathrm{X}=\left\{8^{\mathrm{n}}-7 \mathrm{n}-1, \mathrm{n} \in \mathbf{N}\right\}\) and \(\mathrm{Y}=49(\mathrm{n}-1), \mathrm{n} \in \mathbf{N},\) then: \((\) given \(\mathrm{n}>1)\)

How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 7, 9 lying between 3000 and 5000, if repetition of digits is allowed?

The distance of the point (2,3,5) from the line \(\frac{\mathrm{x}+2}{-3}=\frac{\mathrm{y}-2}{4}=\frac{\mathrm{z}+2}{1}\) is

Area of the region bounded by the curve \(y=\cos x, x=0\) and \(x=\pi\) is:

What is the inverse of the matrix \(A=\left(\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right) ?\)

What is \(\lim _{x \rightarrow 2} \frac{x^{3}+x^{2}}{x^{2}+3 x+2}\) equal to?