Mathematics Tes...

If \(A B^{T}\) is defined as a square matrix then what is the order of the matrix \(B\), where matrix \(A\) has order \(2 \times 3\)?

The relation between, AM, GM and HM is:

A fair die with faces \(\{1,2,3,4,5,6\}\) is thrown repeatedly till \(3\) is observed for the first time. Let \(X\) denote the number of times the die is thrown. The expected value of \(X\) is:

Find the interval in which the function \(f(x)=\log (1+x)-\frac{x}{(1+x)}\) is decreasing?

If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A A^T=9 I\), where I is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to:

If \(\mathrm{P}(\mathrm{n})\) be the statement that \(\mathrm{n}^{2}-\mathrm{n}+41\) is prime, then which of the following is not true?

The interval in which the function \(f(x)=2 x^{3}-15 x^{2}+36 x+12\) is increasing in:

If three distinct numbers \(a, b, c\) are in G.P. and the equations \(\mathrm{ax}^2+2 \mathrm{bx}+\mathrm{c}=0\) and \(\mathrm{dx}^2+2 \mathrm{ex}+\mathrm{f}=0\) have a common root, then which one of the following statements is correct?

The feasible region of an LPP is shown in the figure. If \(z=3 x+9 y\), then the minimum value of \({z}\) occurs at: