Mathematics Tes...

If \(\lambda \in \mathbf{R}\) is such that the sum of the cubes of the roots of the equation, \(x^{2}+(2-\lambda) x+(10-\lambda)=0\) is minimum, then the magnitude of the difference of the roots of this equation is:

In a group of 70 persons, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like coffee but NOT tea?

The domain of the function \(f: R \rightarrow R\) defined by \(\sqrt{x^{2}-x-110}\) is:

The focus of a parabolic mirror as shown in Figure is at a distance of \(5~cm\) from its vertex. If the mirror is \(45~cm\) deep, findthe distance of \(AB\).

The objective function \(z=x_{1}+x_{2}\), subject to \(x_{1}+x_{2} \leq 10,-2 x_{1}+3 x_{2} \leq 15, x_{1} \leq 6, x_{1}, x_{2} \geq 0\) has maximum value __________ of the feasible region.

If \(A=\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\), then \(A B\) is:

For what values of \(k\), the equations:

\(x+y+z=1\)

\(2 x+y+4 z=k\)

\(4 x+y+10 z=k^{2}\)

have a solution?

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always \(10~m\) and the distance between the flag posts is \(8~m\). Find the equation of the posts traced by the man.

Consider the following statements:

1. The cross product of two unit vectors is always a unit vector.

2. The dot product of two unit vectors is always unity.

3. The magnitude of sum of two unit vectors is always greater than the magnitude of their difference.

Which of the above statements are not correct?

Find the acute angle between the lines 7x - 4y = 0 and 3x - 11y + 5 = 0.