If the matrix \(\left[\begin{array}{ccc}1 & 3 & 9 \\ 1 & x & x^2 \\ 4 & 6 & 9\end{array}\right]\) is a singular matrix, where \(x \in N\) (the set of natural numbers), then \(x\) is equal to

The normal distribution curve is symmetrical about[ \(\mu=\) mean, \(\sigma=\) standard deviation]

The value of \(\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)\) is

If \(\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}3 & 0 \\ 4 & -8\end{array}\right|\), then value(s) of \(x\) is/are

If \(y=5 \cos x-3 \sin x\), then \(\frac{d^2 y}{d x^2}\) is equal to :

Match List-l with List-ll

List-l	List-II
(A) \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x}\)	(I) \(\frac{5}{2}\)
(B) \(\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}\)	(II) 5
(C) \(\lim _{x \rightarrow 1} \frac{x^5-1}{x^2-1}\)	(III) 2
(D) \(\lim _{x \rightarrow 0} \frac{(x+1)^5-1}{x}\)	(IV) 0

Choose the correct answer from the options given below:

Integrating factor of \(\frac{dy}{dx} + y \cot x = 2x + x^2 \cot x\) (\(x \neq 0\)) is:

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
The conversion of molecules \(X\) to \(Y\) follows second order kinetics. If the concentration of \(X\) is increased to four times, how does it affect the rate of formation of \(Y\) ?

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|+\cos |x|) d x\), is equal to:

C and Z in the species-area relationship log S = log C + Z log A represents:

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on 10 cm length of wire B:

Read the following paragraph and answer the given questions.
Bio-fertilisers are organisms that enrich the nutrient quality of the soil like cyanobacteria, while there are organisms that help to control plant diseases and pests. The very familiar beetle, the ladybird and dragonflies are useful to get rid of aphids and mosquitoes, respectively. An example of microbial biocontrol agents that can be introduced to control butterfly caterpillars is certain bacteria, which are available in sachets in the form of dry spores. These spores are mixed with water and sprayed onto vulnerable plants. Trichoderma species that are very common in the root ecosystem, are very effective biocontrol agents of several plant pathogens.Baculoviruses attack insects and other arthropods. Usage of these viruses is desirable when an ecological sensitive area is being treated.
Which one of the following is not an advantage of Nucleopolyhedrovirus as biocontrol agents?

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?