Which of the following is correct about the compound annual growth rate?

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

The standard deviation of a sampling distribution of a statistic is also known as:

The integral \(\int \frac{d x}{\sqrt{\frac{1}{2}-5 x-x^2}}\) is equal to:

\(\int(x-1) e^{-x} d x=\)

Match List-I with List-II

List I (Function)	List II (Derivative with respect to ' x ')
(A) \(f(x)=x^x\)	(I) \(a x^{a-1}\)
(B) \(f(x)=a^x\)	(II) 0
(C) \(f(x)=a^a\)	(III) \(a^x \log _e a\)
(D) \(f(x)=x^a\)	(IV) \(x^x\left(1+\log _e x\right)\)

Choose the correct answer from the options given below:

\(\int \frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}} d x \) is equal to :

Which of the followings is NOT a monosaccharide?

Answer the question on basis of passage given below :
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
\(X e F _4 \quad\) and \(X e F _6 \quad\) are expected to be :

If A is a square matrix of order \(3 \times 3\) and \(\left|A^T\right|=-3\), then \(\left|A A^T\right|\) is equal to

In an electromagnetic wave, the amplitude of magnetic field is \( 1.1 \times 10^{-6} \text{ T} \). What is the amplitude of electric field?

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

In a linear programming problem, the constraints on decision variables x and y are \(y-2 x \leq 0, y \geq 0,0 \leq x \leq 5\). The feasible region of the above problem :