Solution of \(\frac{d y}{d x}+y=2\) is:

A machine costing Rs. \(25000\) has a useful life of \(4\) years. The estimated scrap value is Rs. \(5000\) . The annual depreciation by linear method is:

Which of the following functions has a local minima at \(x=0\) ?
(A) \(f(x)=x^3\)
(B) \(f(x)=|x|\)
(C) \(f(x)=x^2\)
(D) \(f(x)=x^{-2}\)
Choose the correct answer from the options given below :

The principal value of \(\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)\) is:

\(\int_{-\pi}^\pi \frac{e^{\sin x}}{e^{\sin x}+e^{-\sin x}} d x\) is equal to:

For the L.P.P. Maximize \(z=10 x+6 y\) subjected to
\(3 x+y \leq 12\)
\(2 x+5 y \leq 34\)
\(x, y \geq 0\)
Then the feasible region represented by system of inequalities is

The region represented by the constraints \(x \geq 0, y \geq 0\) of an LPP is

Consider a permanent dipole of dipole moment P in a non-uniform electric field E. Which of the following option is correct?

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\(^{2+}\)
Impure nickel is converted to which of its complex to be decomposed to yield pure nickel?

What are the two types of isomerism that exist in \(\text{[Pt(Cl)}_2\text{(NO}_2)_2]\) ?

A thin lens L1 of focal length 20 cm placed in combination with another thin lens L2 acts as a lens of focal length 12.5 cm. The power of L2 is

The correct sequence A, B, C, D, E with reference to atomic spectral series is :
(A) Lyman series \(\frac{1}{\lambda}=R\left(\frac{1}{A^2}-\frac{1}{n^2}\right)\)
(B) Balmer series \(\frac{1}{\lambda}=R\left(\frac{1}{B^2}-\frac{1}{n^2}\right)\)
(C) Pfund series \(\frac{1}{\lambda}=R\left(\frac{1}{C^2}-\frac{1}{n^2}\right)\)
(D) Brackett series \(\frac{1}{\lambda}=R\left(\frac{1}{D^2}-\frac{1}{n^2}\right)\)
(E) Paschen series \(\frac{1}{\lambda}=R\left(\frac{1}{E^2}-\frac{1}{n^2}\right)\)
Choose the correct answer from the options given below :

If the random variable X has the following probability distribution :

X	0	1	2	Otherwise
P(X)	K	3K	5K	0

then \(K\) is equal to