Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

The variance of the number of heads in two tosses of a coin is :

The constraints of the given shaded feasible region below of an L.P.P., for non-negative variable constraints \(x\) and \(y\) are

The solution of the differential equation \(\log _e\left(\frac{d y}{d x}\right)=5 x+2 y\) is given by

The interval in which the function given by \(f(x) = \sin^4 x + \cos^4 x\), x \(\in\) [0, \(\frac{\pi}{2}\)] is decreasing is:

The angle between the vectors \(\hat{i}-2 \hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) is:

Three varieties A, B and C of rice are mixed together in the ratio 1:1:3 respectively. The price of rice A is Rs 127 per kg and that of rice B is Rs 135 per kg. If the price of the mixture is Rs. 152 per kg, then the price per kg of rice of type C is :

Read the following paragraph and answer the given questions.
Bio-fertilisers are organisms that enrich the nutrient quality of the soil like cyanobacteria, while there are organisms that help to control plant diseases and pests. The very familiar beetle, the ladybird and dragonflies are useful to get rid of aphids and mosquitoes, respectively. An example of microbial biocontrol agents that can be introduced to control butterfly caterpillars is certain bacteria, which are available in sachets in the form of dry spores. These spores are mixed with water and sprayed onto vulnerable plants. Trichoderma species that are very common in the root ecosystem, are very effective biocontrol agents of several plant pathogens.Baculoviruses attack insects and other arthropods. Usage of these viruses is desirable when an ecological sensitive area is being treated..
A farmer wants to get rid of aphids, but does not want to use insecticide, Choose the best option for him?

The area bounded by the curve \(y=x|x|, x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:

Medical termination of pregnancy (MTPs) are considered safe during the -

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 -

Read the following passage given below and answer the question.
Production of electricity by thermal plants is not very efficient method. It is now possible to make cells in which reactants are fed continuously to the electrodes and products are also removed continuously. One of the most successful fuel cells is hydrogen fuel cell.
Which is not true for the fuel cell?

The minimum value of the function f(x) = 3sinx - 4cosx, x ∈ [- 4π, 4π] is equal to