If the matrix \(\left(\begin{array}{ccc}2 & 4 & 5 \\ 4 & 2 & 3 \\ K & 3 & 2\end{array}\right)\) is a symmetric matrix, then the value of \(K\) is :

The function \(y=f(x)\) has extreme values at the points where ___________ .

The projection of \(\hat{i}-\hat{j}\) on the vector \(\hat{i}+\hat{j}\) is :

A machine costing ₹1,00,000 has a useful life of 5 years. The estimated scrap value is ₹20,000.
Using straight line method, the annual depreciation is:

The value of \(3^{18}(\bmod 4)\) is equal to

If matrices \(A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\), then \(B A\) is equal to:

Solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=3 x+4 y\) given that y = 0 when x = 0 :

Consider the relation R in the set Z of integers which is given by \(R=\{(a, b): 2\) divides \(a-b\}\).
Choose the correct option for the relation \(R\) :

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
Restriction enzymes are also known as

Identify the free living nitrogen fixing bacteria
A. Rhizobium
B. Mycorrhiza
C. Azospirillum
D. Azotobacter
Choose the correct answer from the options given below:

There are two kinds of nucleases - exonucleases and endonucleases. Exonucleases remove nucleotides from the ends of the DNA whereas, endonucleases make cuts at specific positions within the DNA. The cutting of DNA by restriction endonucleases results in the fragments of DNA. These fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. Small volume cultures cannot yield appreciable quantities of products. To produce in large quantities, the development of bioreactors, where large volumes (100 - 1000 litres) of culture can be processed, was required. Thus, bioreactors can be thought of as vessels in which raw materials are biologically converted into specific products, individual enzymes, etc., using microbial plant, animal or human cells. PCR stands for Polymerase Chain Reaction. In this reaction, multiple copies of the gene (or DNA) of interest are synthesised in vitro using two sets of primers (small chemically synthesised oligonucleotides that are complementary to the regions of DNA) and the enzyme DNA polymerase.
Bioreacters are generally used to process large volumes of culture toobtain yield of desire protein. Identify the correct volume of given culture processed by a bio-reactor?

A moving charge produces :

In Young's double slit experiment using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\), is 'T' units. What is the intensity of light at a point where path difference is \(\frac{\lambda}{4}\) ?