Mathematics Tes...

If \(x+2 y=\left[\begin{array}{cc}2 & -3 \\ 1 & 5\end{array}\right]\) and \(2 x+5 y=\left[\begin{array}{ll}7 & 5 \\ 2 & 3\end{array}\right]\), then \(y\) is equal to:

If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\) are vectors of magnitude \(\alpha\) then the magnitude of the vector \(|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|\) is?

Let \(\alpha, \beta \in N\) be roots of equation \(x^2-70 x+\lambda=0\), where \(\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathrm{N}\). If \(\lambda\) assumes the minimum possible value, then \(\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}\) is equal to :

What is the value of the determinant \(\left|\begin{array}{ccc}\mathrm{i} & \mathrm{i}^{2} & \mathrm{i}^{3} \\ \mathrm{i}^{4} & \mathrm{i}^{6} & \mathrm{i}^{8} \\ \mathrm{i}^{9} & \mathrm{i}^{12} & \mathrm{i}^{15}\end{array}\right|\) where \(\mathrm{i}=\sqrt{-1} ?\)

If \(-2<2 x-1<2\) then the value of \(x\) lies in the interval:

If \(\mathrm{P}\) and \(\mathrm{Q}\) be two sets such that \(\mathrm{P} \cup \mathrm{Q}=\mathrm{P},\) then \(\mathrm{P} \cap \mathrm{Q}\) will be:

If the mean of 10 observations \(x_{1}, x_{2}, x_{3} \ldots x_{10}\) is 20 , then mean of \(x_{1}+2, x_{2}+4, x_{3}+\) \(6, \ldots x_{10}+20\) is:

If \(x,y,z\) are all different and not equal to zero and \(\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0\) then the value of \(x^{-1}+y^{-1}+z^{-1}\) is equal to:

If \(\underset{{{{x} \rightarrow \infty}}}{\lim}\left(\frac{{x}^{2}+{x}+1}{{x}+1}-{px}-{q}\right)=-3\), then \({p}\) and \({q}\) is:

The nth term of the following sequence 25, -125, 625, -3125, …….. is: