Let \(\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\). Then \(y\) is :

Consider the LPP, optimize \(Z=x+5 y\) subject to \(x+y \geq 5 ; 2 x-5 y \geq 10, x \leq 2 ; x \geq 0, y \geq 0\), then which of the following is correct?

A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

400 g of apple vinegar has \(40 \%\) apple juice in it. The amount of apple juice, which should be added to make it \(60 \%\) in apple vinegar, is :

A tank has two outlet pipes A and B, which together take 6 hours to empty a full tank when opened simultaneously.
The tank was initially half-full and both outlets were opened.
After one hour, an inlet pipe was also opened.
If the inlet alone can fill the empty tank in 4 hours, how much time will it now take to fill the tank completely?

The following data are from a simple random sample: 6, 8, 11, 9, 15, 17,
then the point estimate of the population mean is:

The mean of the numbers obtained on throwing a die having 1 on three faces, 2 on two faces and 5 on one face is:

A plane meets the coordinates axes at A, B and C such that centroid of \(\triangle A B C\) is at the point (2, 3, 1). If the equation of the plane is 3x + 2y + 6z = k, then k is:

The force between the plates of a parallel plate capacitor of capacitance C, distance between plates d and potential difference V is:

Let functions \(f:\{1,3,4\} \rightarrow\{1,2,5\}\) and \(g:\{1,2,5\} \rightarrow\{1,3\}\) be defined as \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(1,3),(2,3),(5,1)\}\) respectively. Then, which one of the following is correct statement for \(g \circ f\)?

Arrange the following nuclei in the increasing order of their binding energy per nucleon: \( ^4\text{He}, ^6_3\text{Li}, ^{56}_{26}\text{Fe}, ^{238}_{92}\text{U} \)

Which of the following compounds will not give azo coupling reaction with benzene diazonium chloride?

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\(^{2+}\)
In photography undecomposed AgBr is removed as ___________