The general solution of differential equation \(\frac{dy}{dx} - xy = e^{\frac{x^2}{2}}\) is:

For the system of equations \(A X=B\), which of the following is correct?

The general solution of the differential equation \(\log _e\left(\frac{d y}{d x}\right)=a x+b y\) is

Which of the following statements are correct?
(A) The method of least squares determines the position of the trend line of the given time series.
(B) The trend line is called the line of best fit.
(C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive.
(D) The normal equations of the trend line \(y=a+b x\) are \(\sum y=n a+b \sum x\) and \(\sum x y=a \sum x+b \sum x^2\), where \(n\) is the numbers of observations.
Choose the correct answer from the options given below:

If \(x=a \sec ^3 \theta, y=a \tan ^3 \theta\) then \(\frac{d^2 y}{d x^2}\) equals.

Let \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}4 & -6 \\ -2 & 4\end{array}\right]\), then
(A) \(\operatorname{det}\left(A^T\right)=1\)
(B) \(A B=I\), where \(I\) is the identity matrix of order 2
(C) \(A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]\)
(D) \(\operatorname{adj}(B)=\left[\begin{array}{ll}4 & 2 \\ 6 & 4\end{array}\right]\)
Choose the correct answer from the options given below :

If \(f(x)=\left|\begin{array}{ccc}0 & x-1 & x-2 \\ x+1 & 0 & x-3 \\ x+2 & x+3 & 0\end{array}\right|\), then the value of f(0) is equal to:

Select the correct name for the following reaction:

What is an example of globular protein?
(A) Insulin
(B) Keratin
(C) Albumin
(D) Myosin
Choose the correct answer from the options given below :

If \(A=\{1,2,3,4, \cdots, n\}\) and \(B=\{x, y\}\), then the number of surjections from \(A\) to \(B\) is

Which is an example of homology?

Answer the questions from the figure given below:

Taq polymerase is the preferred DNA polymerase in PCR because :

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base.
Four bases present in RNA molecule are: