1. If y=ln(lnx) y=\ln (\ln x) y=ln(lnx), then dydx= \frac{d y}{d x}= dxdy= What?
1x \frac{1}{x} x1
1ln(x) \frac{1}{\ln (x)} ln(x)1
ln(x)x \frac{\ln (x)}{x} xln(x)
1xln(x) \frac{1}{x \ln (x)} xln(x)1
2. M=[130−1] M=\left[\begin{array}{cc}1 & 3 \\ 0 & -1\end{array}\right] M=[103−1]
Which one is the M−1 \mathbf{M}^{-1} M−1 ?
[103−1] \left[\begin{array}{cc}1 & 0 \\ 3 & -1\end{array}\right] [130−1]
[−10−31] \left[\begin{array}{ll}-1 & 0 \\ -3 & 1\end{array}\right] [−1−301]
[−1301] \left[\begin{array}{cc}-1 & 3 \\ 0 & 1\end{array}\right] [−1031]
[130−1] \left[\begin{array}{cc}1 & 3 \\ 0 & -1\end{array}\right] [103−1]
3. M=[130−1] M=\left[\begin{array}{cc}1 & 3 \\ 0 & -1\end{array}\right] M=[103−1]
The matrix M M M is-
symmetric
nilpotent
idempotent
involutory
4. What is the value of x x x if xlnx \frac{x}{\ln x} lnxx is minimum?
1e \frac{1}{\mathrm{e}} e1
e
−1e -\frac{1}{\mathrm{e}} −e1
-e
5. Which one is correct for increasing function?
dydx≥0 \frac{d y}{d x} \geq 0 dxdy≥0
dydx>0 \frac{d y}{d x}>0 dxdy>0
dydx< \frac{d y}{d x}< dxdy<
dydx≤0 \frac{d y}{d x} \leq 0 dxdy≤0