An objective function \(z=a x+b y\) is maximum at points \((15,15)\) and \((0,20)\). If \(a, b \geq 0\) and \(a b=27\), then the maximum value of the objective function is

The differential equation whose solution is \(A x^2+B y^2=1\) where \(A\) and \(B\) are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below :

The integral \(\int e^x\left(\frac{x-1}{2 x^2}\right) d x\) is equal to:

The equation of the line (in Cartesian form) which passes through the point \((-2,4,5)\) and parallel to the line given by \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is:

If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), then the value of \(A^2-5 A+6 I\) is

A matrix which is symmetric as well as skew symmetric is:

Acute angle between the lines \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\) and \(\frac{x-1}{4}=\frac{y+1}{-3}=\frac{z+10}{5}\) is :

In a college, 30 % students fail in Physics, 25 % fail in Mathematics and 10 % fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is

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.
Which one of the following statements is correct about DNA separation and isolation?

Which one of the following is not the invasive alien species?

Haloalkanes can be represented by the formula

The values of p for which the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 p}=\frac{y-5}{1}=\frac{6-z}{5}\) are at right angles is:

Kirchhoff's junction rule and loop rule are based on which of the following conservation laws respectively ?