The value of \(\int_{-\pi / 6}^{\pi / 6}\left(4 x^5+x \sin ^2 x+\tan ^3 x+2\right) d x\) is :

\(\int \frac{dx}{x^2 - 9} =\)

If A is a singular matrix, then A(adj A) is equal to

A vector \(\vec{a}\) of magnitude \(3 \sqrt{2}\) making an angle of \(\frac{\pi}{3}\) with \(\hat{i}, \frac{\pi}{4}\) with \(\hat{j}\) and an acute angle \(\theta\) with \(\hat{k}\), is :

The probability that a plant \(A\) survives is \(\frac{3}{4}\) and the probability that another plant \(B\) survives is \(\frac{1}{3}\).
The probability that only one of them survives is :

The vector in the direction of the vector \(2 \hat{i}-\hat{j}-2 \hat{k}\) that has magnitude 9 units is :

The area of the region bounded by the parabola \(y^2=4 a x\) and its latus rectum is:

Consider the following statements:
(A) An emf can be induced by moving a conductor in a magnetic field.
(B) An emf can be induced by changing the magnetic field
(C) An emf can be induced by changing the electric field
(D) An emf can be induced by moving a conductor in an electric field
Choose the correct answer from the options given below:

Read the Passage carefully and answer the the questions
Insulin consists of two short polypeptide chains : chain A and chain B, that are linked together by disulphide bridges. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis of diseases. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (α-1-antitrypsin) used to treat emphysema. Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment.
Insulin has 2 polypeptide chains linked together by _______ bridges.

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following is not used as a vector in recombinant DNA technology?

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001, the probability that out of 2000 individuals, more than two individuals suffer from bad reaction.
[Given that \(e^{-2}=0.13534\) ]

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.
Which one of the following enzymes works as molecular glue?

Answer the question on the basis of passage given below :
Adsorption is the phenomenon of attracting and retaining the molecules of a substance on the surface of a solid resulting into a higher concentration on the surface than in the bulk. The substance adsorbed is known as adsorbate and the substance on which adsorption takes place is called adsorbent. In physisorption adsorbate is held to the adsorbent by weak van der Waals forces and in chemisorption by strong chemical bond.
Out of Milk, butter, ice cream, fruit juice and lemonade. Identify the one which is not a colloid.