The foot of the perpendicular drawn from the point \((1,6,3)\) to the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is :

If the radius of the spherical ball is increasing at the rate of 1 m/sec and the radius of the ball is 3 meter then the volume of the ball is increasing at the rate of

Area of the region bounded by the curve \(|x|+|y|=1\) and \(x\)-axis is :

Difference between the maximum and minimum value of the objective function \(Z=5 x+3 y\), subject to the constraints: \(3 x+5 y \leq 15 ; 5 x+2 y \leq 10 ; x, y \geq 0\) is:

If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0\), and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{6}\), then

The number of all possible matrices of order \(2 \times 3\) with each entry 0 or 1 is:

If \(A\) and \(B\) are events such that \(P\left(A^{\prime} \cup B^{\prime}\right)=\frac{1}{3}\) and \(P(A \cup B)=\frac{4}{9}\), then the value of \(P\left(A^{\prime}\right)+P\left(B^{\prime}\right)\) is:

Which one of the following is not true for a molecule that can act as a genetic material?

The barnacles growing on the back of whale are example of:

Which cell is used in automobiles and inverters?

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.
Multiple recognition sites in vector generate several fragments, which will complicate the-

The radius of the arc BD representing a wire is 60 cm. The magnitude of the magnetic field produced at centre C, if a current of 3.0 A flows in the wire, will be:

(A) \(\frac{d}{d x} a^x=\frac{a^x}{\log _e a}\)
(B)\(\frac{d}{d x} e^{a x}=a e^{a x}\)
(C) \(\frac{d}{d x} x^x=x \cdot x^{x-1}\)
(D) \(\frac{d}{d x} x^a=a x^{a-1}\)
(E) \(\frac{d}{d x} a^a=0\)
Choose the correct answer from the options given below: