The general solution of the differential equation \(x\left(1+y^2\right) d x+y\left(1+x^2\right) d y=0\) is

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are:

If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below:

If \(A\) is a square matrix of order 3 and \(|A|=-2\), then the value of \(\left|-A^{-1}\right|\) is :

If \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{c}2 x \\ -2 \\ z-3\end{array}\right]=\left[\begin{array}{l}6 \\ 4 \\ 1\end{array}\right]\) then x + y + z is

If A and B are symmetric matrices of the same order, then which of the following are true?
(A) AB - BA is a skew symmetric matrix
(B) AB is a symmetric matrix
(C) AB is a scalar matrix
(D) AB + BA is a symmetric matrix
Choose the correct answer from the options given below:

The angle between the line \(\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}\) and the plane \(10 x+2 y-11 z=3\) is :

Answer the question on the basis of passage given below:
Proteins are the polymers of about twenty different a-amino acids which are linked by peptide bonds. Proteins perform various structural and dynamic functions in the organisms. Proteins which contain only a-amino acids are called simple proteins. The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions. This is called denaturation of proteins. Enzymes are biocatalysts which speed up the reactions in biosystems. Vitamins are accessory food factors required in the diet. They are classified as fat soluble (A, D, E and K) and water soluble (B group and C). Deficiency of vitamins leads to many diseases. Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety. Nucleic acids are responsible for the transfer of characters from parents to offsprings. There are two types of nucleic acids DNA and RNA. DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose.
Which of the following vitamin cannot be stored in our body?

The value of p so that the lines \(\frac{x-1}{-3}=\frac{2 y-2}{2 p}=\frac{z-3}{2}\) and \(\frac{x-1}{-3 p}=\frac{y-1}{4}=\frac{6-z}{5}\) are at right angles is

Read the following passage carefully and answer the given questions.
Restriction endonuclease on finding its specific recognition sequence, bind to the DNA and cut each of the two strands of the double helix at specific points in their sugar -phosphate backbones. Each restriction endonuclease recognises a specific palindromic nucleotide sequences in the DNA. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. This can be achieved by treating the bacterial cells/plant or animal tissue with enzymes such as lysozyme (bacteria), cellulase (plant cells), chitinase (fungus). Now a days the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel. The first restriction endonuclease-Hind II, whose functioning depended on a specific DNA nucleotide sequence was isolated and characterised five years later. It was found that Hind II always cut DNA molecules at a particular point by recognising a specific sequence of six base pairs. In addition to 'ori', the vector requires a selectable marker, which helps in identifying and eliminating non-transformants and selectively permitting the growth of the transformants. Transformation is a procedure through which a piece of DNA is introduced in a host bacterium. Normally, the genes encoding resistance to antibiotics such as ampicillin, chloramphenicol, tetracycline or kanamycin, etc., are considered useful selectable markers for E. coli
Hind II always cut DNA molecules at a particular point by identifying a specific sequence of six base pairs. This specific base sequence is called _______ for Hind II.

Which one of the following is a sequence of mRNA?

A network of five capacitors is shown in the figure. The total charge stored in the network connected between A and B is :

During forward bias in a p-n junction :