If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\) and \(B=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\) then the matrix \(A B\) is equal to:

Match List-I with List-II

List-I (Differential Equations)	List-II (Order and degree)
(A) \(\frac{d y}{d x}+e^y=0\)	(I) order 2, degree not defined
(B) \(\frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2]}\)	(II) order 2, degree 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+e^{\left(\frac{\text { 临 })}{}\right.}=0\)	(III) order 1, degree 1
(D) \(\frac{d^2 y}{d x^2}+x \frac{d y}{d x}-2 y=\log x ; x>0\)	(IV) order 2, degree 2

Choose the correct answer from the options given below:

Let \(f(x)=\left\{\begin{array}{ll}2 x-1, & x<1 \\ 1, & x=1 \\ x^2, & x>1\end{array}\right.\) then at \(x=1\)

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is:

For any two non zero vectors \(\vec{a}\) and \(\vec{b}\)
A. If \(|\vec{a}| = |\vec{b}|\) then \(\vec{a} = \vec{b}\)
B. If \(\vec{a} = \vec{b}\) then \(|\vec{a}| = |\vec{b}|\)
C. \(\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}\)
D. \(\vec{a} \times \vec{b} = \vec{b} \times \vec{a}\)
E. area of the parallelogram = \(\frac{1}{2}|\vec{a} \times \vec{b}|\), where \(\vec{a}\) and \(\vec{b}\) represent the diagonals of the parallelogram.
Choose the correct answer from the options given below:

The order and degree of the differential equation \(x\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2-3 \frac{d y}{d x}+y=0\) respectively, are:

\(\int \frac{\sqrt{\tan x}}{\sin x \cos x} d x\) equals :

Identify the product C in the following sequence of reactions.
\(\text{CH}_3 - \text{CH} = \text{CH} - \text{CH}_3 \xrightarrow{\text{O}_3} \text{A} \xrightarrow{\text{Zn/H}_2\text{O}} \text{B} \xrightarrow{\text{LiAlH}_4} \text{C}\)

Read the given paragraph carefully and answer the following questions:
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). There are some basic steps in genetically modifying an organism (i) identification of DNA with desirable genes; (ii) introduction of the identified DNA into the host; (iii) maintenance of introduced DNA in the host and transfer of the DNA to its progeny. Agrobacterium tumifaciens, a pathogen of several dicot plants is able to deliver a piece of DNA known as 'T-DNA' to transform normal plant cells into a tumor and direct these tumor cells to produce the chemicals required by the pathogen. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure because it requires simultaneous plating on two plates having different antibiotics. Therefore, alternative selectable markers have been developed which differentiate recombinants from non-recombinants on the basis of their ability to produce colour in the presence of a chromogenic substrate. In this, a recombinant DNA is inserted within the coding sequence of an enzyme, ß-galactosidase. This results into inactivation of the gene for synthesis of this enzyme, which is referred to as insertional inactivation.
Which enzyme is not used to lyse the cells for extraction of DNA?

If \(\int_0^1 \frac{e^x}{1+x} d x=m\), then the value of \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is :

Meiotic division taking place during oogenesis is an unequal division resulting in the formation of a:

Which of the following is not a female contraceptive?

Rolle's theorem holds for the function \(x^3+b x^2+c x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), the respective values of \(b\) and \(c\) are :