A trust invites a deposit of a lump sum amount from an individual so that an annual scholarship of Rs. 5000 is paid. Rate of interest is 5% per annum.
If the scholarship is to start at the end of this year, then the amount needed to deposit to the trust is:

If \(\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0\), then value of x is

For an electric dipole in a non-uniform electric field with dipole moment parallel to the field, force F and torque t are :

If the binomial distribution \(X \sim B(n, p)\) has mean 3 and variance \(\frac{3}{2},(p+q)=1\), then which of the following is/are TRUE?
(A) \(q=\frac{1}{2}, n=6\)
(B) \(P(X \leq 5)=\frac{63}{64}, p=\frac{1}{2}\)
(C) \(q=\frac{1}{3}, p=\frac{2}{3}\)
(D) \(P(X=4)=\frac{15}{64}, n=6\)
Choose the correct answer from the options given below:

For the given values 8, 10, 12, 14, 16, the three-year moving averages are:

If A speaks truth in \(75\%\) cases and B speaks truth in \(80\%\) cases, then the probability that they contradict each other in a statement, is :

The function \(f(x)=\tan x-x\) for \(x \in\left(0, \frac{\pi}{2}\right)\) is :

Choose the correct formula for magnifying power of a simple microscope from the following

Read the paragraph given below and answer the question.
Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone.
Bonds which link 'A' and 'B' peptide chains of human insulin are

Read the following paragraph and answer the given questions:
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 site in the vector will generate several fragments, which will complicate the gene cloning. 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. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. The recombinant plasmids will lose tetracycline resistance due to insertion of foreign DNA but can still be selected out from non-recombinant ones by plating the transformants on tetracycline containing medium.
The recombinants will grow in ampicillin containing medium but not on that containing tetracycline. But, non- recombinants will grow on the medium containing both the antibiotics. In this case, one antibiotic resistance gene helps in selecting the transformants, whereas the other antibiotic resistance gene gets 'inactivated due to insertion' of alien DNA, and helps in selection of recombinants. Origin of replication (ori) is a sequence from where replication starts and any piece of DNA when linked to this sequence can be made to replicate within the host cells. This sequence is also responsible for controlling the copy number of the linked DNA. So, if one wants to recover many copies of the target DNA it should be cloned in a vector whose origin support has high copy number.
In pBR322 'rop' codes for -

The Medical Termination of Pregnancy (Amendment) Act, 2017 was enacted by the government of India with the intension of __________.

Identify " \(Y\) " in the following reaction:

The rate of a first order reaction is 0.06 mol \(L^{-1} s^{-1}\) after 20 seconds and 0.03 mol \(L^{-1} s^{-1}\) after 30 seconds from the start of the reaction. The half life period of this reaction is