Mathematics Tes...

If \(p, q, r\) and \(s\) are positive real numbers such that \(p+q+r+s=2\), then \(M=(p+q)(r+s)\) satisfies the relation:

The graph of the inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0 is:

Find the vector equation of the line passing through the point with position vector \(\hat{i}-2 \hat{j}+5 \hat{k}\) and perpendicular to the plane \(\vec{r} \cdot(2 \hat{i}-3 \hat{j}-\hat{k})=0\).

Find out the value of \(x\) for which the function \(f(x)=\frac{x^2-5 x-6}{x^2+5 x-6}\) is not continuous.

Consider an objective function Z(x, y) = 5x + 10y and the constraints:

x + 2y ≤ 120

x + y ≥ 60

x - 2y ≥ 0

x ≥ 0, y ≥ 0

The minimum value of the objective function is:

Solve \((2 y+x) \frac{d y}{d x}=1\):

If \(A=\left[\begin{array}{ll}0 & 5 \\ 0 & 0\end{array}\right]\) and \(f(X)=1+x+x^2+\ldots .+x^{16}\), then \(f(A)=?\)

If \(a_{1}, a_{2}, a_{3},=t_{9}, a_{9}\) are in GP, then what is the value of the following determinant?

\(\left|\begin{array}{lll}\ln a_{1} & \ln a_{2} & \ln a_{3} \\ \ln a_{4} & \ln a_{5} & \ln a_{6} \\ \ln a_{7} & \ln a_{8} & \ln a_{9}\end{array}\right|\)

If the sum of three numbers in A.P is 24 and their product is 440, find the numbers.

\(\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\) holds, when: