The value of \(\tan ^{-1} \frac{2}{11}+\tan ^{-1} \frac{7}{24}\) is :

The integral \(I=\int \frac{e^{5 \log _0 x}-e^{4 \log _0 x}}{e^{3 \log _0 x}-e^{2 \log _0 x}} d x\) is equal to:

The binomial distribution for which the mean is 5 and variance 4, is

For what value of k, the following system have a unique solution? (where R is set of real numbers)
x + y + z = 1
2x + 3y + 4z = 3
x - y + kz = 5

In what ratio must pulses at ₹72 per kg be mixed with pulses ₹90 per kg so that the mixture be worth ₹80 per kg?

The region represented by the system of inequalities \(x \geq 0 ; y \geq 0\),
\(2 x+y \geq 8\) and \(x+2 y \geq 10\) is :

\(\tan ^{-1} \frac{1}{\sqrt{3}}-\sin ^{-1} \frac{1}{2}\) is equal to :

What is the name of the reaction when acetamide is converted to methylamine?

A series AC circuit has a resistance \( 8 \, \Omega \) and a reactance of \( 6 \, \Omega \). The impedance of the circuit is :

On dissolving sugar in water at room temperature it feels cool to the touch. Under which of the following cases, dissolution of sugar will be most rapid?

Match List I with List ||

List-I	List-II
Complex species	Isomerism
A. \([\text{Co(NH}_3\text{)}_4\text{Cl}_2\text{]}^{+}\)	I. Optical
B. \(\text{cis-[Co(en)}_2\text{Cl}_2\text{]}\)	II. Ionisation
C. \([\text{Co(NH}_3\text{)}_5\text{SO}_4\text{]Br}\)	III. Coordination
D. \([\text{Co(NH}_3\text{)}_6\text{]}[\text{Cr(CN)}_6\text{]}\)	IV. Geometrical

Choose the correct answer from the options given below:

Identify the INCORRECT statement(s) in the context of phenomenon of interference.
1. All bright and dark fringes have equal width.
2. All bright fringes have the same intensity.
3. Fringe width depends on the distance of screen from the slits.
4. All dark and bright fringes are not equally spaced.
Choose the correct answer from the options given below:

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.
Which one of the following is not correct statements about cloning sites of vectors?