The value of \(\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)\) at \(x=\frac{1}{5}\) is

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is : [Given \(e^{-2}=0.135\)]

The greatest integer function \(f(x)=\lfloor x\rfloor\) is differentiable for all values of

If the function \(f(x)=2 x^3+9 x^2+12 x-1\) is given, then \(f(x)\) has

The value of \(k\) for which the system of equations
\(\begin{array}{l}x+y+z=1 \\x-k y+z=1\end{array}\)
\(x-y+z=1\)
has more than one solution is :

The function \(f: R \rightarrow R, f(x)=|x|\) (\(R\) is the set of real numbers) is

The number of arbitrary constants in the general solution of a differential equation of order 4 and degree 1 is

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:

The energy required to excite an electron in hydrogen atom to its first excited state is

Which of the following is a type of 'in-situ' conservation approach?

A resistor connected to a battery is heated due to the current. The quantity which does not change is

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. 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.
pBR322, which is used in recombinant DNA technology, is a -

Which of the following gives the correct order of stability constant in solution?