Mathematics Tes...

For what value of \(x\), the matrix \(A\) is singular?

\(A=\left[\begin{array}{ccc}3-x & 2 & 2 \\2 & 4-x & 1 \\-2 & -4 & -1-x\end{array}\right]\)

Evaluate: \(\lim _{x \rightarrow \frac{\pi}{2}}(\sec x-\tan x)\)

In a G.P., the 3rd term is 24 and the 6th term is 192. Find the 12th term.

While solving a linear programming model, if a redundant constraint is added, then what will be its effect on existing solution?

The interval in which the function \(f(x)=x^{3}-6 x^{2}+9 x+10\) is increasing in:

If \(\underset{{x \rightarrow 1}}{\lim} \frac{x^{4}-1}{x-1}=\underset{{x \rightarrow k}}{\lim} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}\), where \(k \neq 0\), then what is the value of \(k\)?

Given the magnitude of vector \(A\) to be 6 units. Find the component of \(A\) alongthe \(x\) -axis:

The average of 35 raw scores is 18. The average of the first seventeen of them is 14 and that of the last seventeen is 20. Find the eighteenth raw score.

Find the area of the region bounded by the curves y = x³, the line x = 2, x = 5 and the x - axis?

The number of 4-digit numbers strictly greater than 4321 that can be formed from the digits \(0,1,2,3,4,5\) allowing for repetition of digits is: