Mathematics Tes...

Find the value of\(\left|\begin{array}{ccc}1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3}\end{array}\right|\).

What is the probability of solving a given problem if three students \((A, B\) and \(C)\), try it independently, with respective probabilities \(\frac{4}{7}, \frac{3}{8}\) and \(\frac{1}{2}\)?

If \(A=\left[\begin{array}{ccc}1 & 2 & x \\ 3 & -1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{l}y \\ x \\ 1\end{array}\right]\) be such that \(A B=\left[\begin{array}{l}6 \\ 8\end{array}\right]\),then:

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), then for what value of \(\alpha, A\) is an identity matrix?

The differential equation of the family of curves \(y=c_1 e^x+c_2 e^{-x}\) is:

Find the value of \(k\) if \(\underset{{{x \rightarrow 7}}}{\lim} g(x)=k\) where \(g(x)=\sqrt{8 x-7}\)

Find the multiplicative inverse of 4 - 3i ?

The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in set A?

Find the mode of the following data

Find the angle between the line \(\frac{x-1}{3}=\frac{y+1}{-1}=\frac{z-3}{2}\) and the plane \(3 x+4 y+z+5=0\).