The probability distribution of a random variable \(X\) is given by
\(\begin{array}{lcllll}x & 0 & 1 & 2 & 3 & 4 \\ p(x) & 0.1 & k & 2 k & 2 k & k \end{array} \)
The value of \(k\) is:

The differential equation \(\frac{d y}{d x}+\frac{x}{y}=0\), represents the family of curves:

Which of the following differential equation represents the family of circles touching the \(x\)-axis at the origin?

Three bad eggs are mixed with 7 good ones
If two eggs are drawn one by one without replacement
then the probability distribution of the number X of bad eggs drawn is

Which of the following is a factor of the determinant \(\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|\)?

The solution of \(y^{\prime}-y^{\prime \prime}=2 x\) is:
A. \(y=x^2+2 x+2\)
B. \(y=x^2+2 x+1\)
C. \(y=x+2\)
D. \(y=x^2-2 x+1\)
Choose the correct answer from the options given below :

Corner points of the feasible region for an LPP are: \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\). Let \(z=4 x+6 y\) be the objective function. Then, Max \(z\) - Min \(z\) is equal to:

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermusaquaticus}), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichiacoli} RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

In the isolation process of genetic material, the purified DNA can be precipitated out after the addition of:

Identify the incorrect statement
A. Bakelite and urea-formaldehyde resins are elastomers
B. Polyamides like nylon 6, nylon 6, 6 are the examples of fibers.
C. Polystyrene, polyvinylchloride and polythene are thermoplastic polymers.
D. Thermoplastic polymers have intermolecular force between elastomers and fibers.
Choose the most appropriate answer from the options given below:

\(\int \sin x \sin 2 x \sin 3 x d x\) is equal to:

Which of the following statements are correct?
A. \(\text{CuI}_2\) is not known.
B. \(\text{Cu}_2\text{I}_2\) is known.
C. \(\text{Cu}^{2+}\) ion oxidises \(\text{I}^-\text{}\) to \(\text{I}_2\).
D. \(\text{Cu}^{2+}\) ion does not oxidise \(\text{I}^-\text{}\) to \(\text{I}_2\).

A semiconductor device is connected in series circuit with a battery and resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops at almost zero. The device may be

Molecules are the constituent particles of molecular solids. Identify the molecular solid amongst the following: