The solution of the differential equation \(2 x \frac{d y}{d x}-y=3\) represents:

If \(A=\left[\begin{array}{ccc}0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} A|\) is equal to:

If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identity matrix of same order as \(A\), then the matrix \((2 I+A)^3-19 A-3 I\) is equal to

If \(A=\left[\begin{array}{lll}2 & -3 & 4\end{array}\right], B=\left[\begin{array}{l}3 \\ 2 \\ 2\end{array}\right]\)
\(X=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right], Y=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]\)
then \(A B+X Y=\)

Ram can row a boat in still water at the rate of 6 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river is

For \(x \in\left(0, \frac{\pi}{2}\right), \int \frac{\sin x+\cos x}{\sqrt{\sin 2 x}} d x\) is equal to

If \(A\) and \(B\) are square matrices of the same order 3 , such that \(\operatorname{det}(A)=3\) and \(A B=3 I\), where \(I\) is an identity matrix of order 3. Then the value of \(\operatorname{det}(B)\) is :

The mutual inductance \( M_{12} \) of coil 1 with respect to coil 2:

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

What is the power factor of an ac circuit having resistance R and inductance L connected in series? (\( \omega \) is the angular frequency )

The differential equation representing the family of curves \(y=A \cos (x+B)\), where \(A\) and \(B\) are arbitrary constants is :

The matrix \(X\) in the equation \(A X=B\), such that \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) is given by

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
The final product of the following reaction is:
\(C _6 H _5 NH _2 \xrightarrow[\text { (iii) } NaNO _2 / Cu , \Delta]{\text { (i) } HNO _2}\) (ii) \(HBF _4\) ?