A person can row a boat in still water at the rate of \(5 km / hr\). It takes him \(4\) times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is:

For the function \(f(x)=x^{1 / x}, x>0\), which of the following are correct?
(A) \(x=0\) is the only point where extremum may occur.
(B) The given function is maximum at \(x=e\).
(C) The function has no extreme value for \(x>0\).
(D) The maximum value of the function \(f(x)\) is \(e^{1 / e}\)
Choose the correct answer from the options given below :

The value of \(\int_{0}^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) dx\) is:

The two events E and F are independent. If \(P(E)=0.3\) and \(P(E \cup F)=0.5\), then \(P(E / F)-P(F / E)\) is :

Match List I with List II with regard to degree of the Differential Equation.

List - I	List - II
(A) \(\frac{d^3 y}{d x^3}+\sin y=0\)	(I) 4
(B) \(\left(\frac{d y}{d x}\right)^4+\cos \left(\frac{d y}{d x}\right)-1=0\)	(II) 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^4=0\)	(III) Not defined
(D) \(\left(\frac{d^2 y}{d x^2}\right)^5+2\left(\frac{d^3 y}{d x^3}\right)^4+7=0\)	(IV) 2

A metal wire under constant potential difference, when heated, shows that the drift velocity of the electron :

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is \(\theta=60^{\circ}\), is :

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
Wilkinson catalyst used for hydrogenation of alkenes is a complex of ___________.

Which of the following pairs of solutions are isotonic?

Identify the hormone from the following

If \(I=\int_0^\pi x \sin x d x\), then

Which of the following will not respond to Fehling's Test?
(A) Benzaldehyde
(B) Acetone
(C) Acetaldehyde
(D) Acetophenone
Choose the correct answer from the options given below:

Which of the following hormone is responsible for the development of secondary female characteristic and participate in control of menstrual cycle?