The value of \(\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|\) is:

A die is thrown twice and the sum of the numbers appearing is observed to be 6 .
The probability that the number 4 has appeared at least once is:

The inverse of the matrix \(A=\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8}\end{array}\right]\) is

If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then

If \(A\) is a square matrix of order 3 and \(|A|=4\), then the value of \(\left|2 A^T\right|\) is

Which of the following is not correct about the Central Limit Theorem?

\(\int \frac{d x}{2 \sin ^2 x+5 \cos ^2 x}\) is equal to

If \(\left|\begin{array}{lll}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then the values of \(x\) are:

If \(A\) and \(B\) are square matrices of the same order, then \(A B^T-B A^T\) is a

Arrange the following compounds in the increasing order of their boiling points:
(A) Pentan-1-ol
(B) n-Butane
(C) Pentan-1-al
(D) Ethoxyethane
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?

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.
What is the purpose of using a gene promoter in recombinant DNA technology?

If the interval in which the function \(f(x)=4 x^3-6 x^2-72 x+30\) is strictly decreasing, is \(( a , b )\) then \(a + b\) is equal to