If x is real, the minimum value of \(x^2-8 x+17\) is:

Particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y=0\) when \(x=1\), is:

For what value of \(k\), the following system of equations has infinitely many solutions?
\(x+2 y=5\), \(3 x+k y=15\)

The solution of the differential equation \(\frac{d y}{d x}=\frac{x+y}{x-y}\) is

Let \(A =\left[a_{i j}\right]\) be a \(2 \times 2\) matrix such that \(a_{i j}=\frac{|-3 i+j|}{2}\) then \(a_{21}\) is :

Assume \(A, B\) and \(C\) are matrices of order \(m \times n, n \times 3\) and \(3 \times q\) respectively. The restrictions on \(m, n\) and \(q\) so that \(A B+B C\) is defined are

A random variable \(x\) has the following probability distribution.
\(\begin{array}{lllllll}x &1\ 2 \ \ \ 3 \ \ \ 4\ 5\ \ \ 6 \\P(x)_\alpha \ & 0.1\ 0.3 \ \beta\ 0.4\ 0.1\end{array}\)
In the above table, \(P[x=1\) or \(x=4]\) is equal to:

Paleontological evidences for evolution refers to :

When a ray of light is incident at an angle \( \theta = 60^{\circ} \) on an air-glass interface, the reflected ray is 100 percent plane polarised. The value of the refractive index of the glass with respect to air (\( ^an_g \)) is given by :

If \(f: R \rightarrow A\) given by \(f(x)=x^2-6 x+12\) is a surjective function, then the set \(A\) is :

If we take \(8\) identical slips of paper and write the number \(0\) on one of them, the number \(1\) on three of the slips, the number \(2\) on three of the slips and the number \(3\) on one of the slips. These slips are folded, put in a box and roughly mixed. One slip is drawn at random from the box. If \(X\) is the random variable denoting the number written on the drawn slip, the variance of \(X\) is:

A proton and an alpha particle accelerated through different potential differences have the same de-Broglie wavelength. The ratio of their respective accelerating potentials is

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.
Conversion of nitro group into primary amine is preferred using