The area enclosed by the ellipse \(\frac{x^2}{9^2}+\frac{y^2}{6^2}=1\) is :

If \(A\) is a square matrix and \(I\) is an identity matrix of same order such that \(A^2=A\), then \((2 I+A)^2-5 A\) is :

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then

The domain of the function \(\sin ^{-1}(4 x-1)\) is:

A boat can row at the speed of \(16 km / hr\) in still water. If the river is flowing at \(8 km / hr\), and it takes 8 hours for a round trip, then the distance between the two places is :

Let A be a square matrix of order n, then which of the following are TRUE?
(A) \(|\operatorname{adj} A|=|A|^{n-1}\)
(B) \(|A \cdot \operatorname{adj} A|=|A|^n\)
(C) A. (adj A) = |A|
(D) |KA| = K|A|
(E) \(\left|A^{-1}\right|=\frac{1}{|A|},|A| \neq 0\)
Choose the correct answert from the option given below :

Let functions \(f:\{1,3,4\} \rightarrow\{1,2,5\}\) and \(g:\{1,2,5\} \rightarrow\{1,3\}\) be defined as \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(1,3),(2,3),(5,1)\}\) respectively. Then, which one of the following is correct statement for \(g \circ f\)?

A first order reaction is found to have a rate constant, k = 5.5 × 10^-14 s^-1. The half life of the reaction will be :

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichia coli RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

Stanley Cohen and Herbert Boyer constructed the first recombinant DNA by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid of ____________ resistance. which was responsible for conferring antibiotic

Given that \(\sigma p_{0} q_{0} = 1000, \sigma p_{0} q_{0} = 1200, \sigma p_{0} q_{0} = 1350, \sigma p_{0} q_{0} = 1500\), where subscripts 0 and and 1 used for base year and current year respectively. The Paasche's Index number is :

The area (sq. units) bounded by the curve \(y=\sin x, \pi \leq x \leq 2 \pi\) and the \(x\)-axis is

If \(\left|\begin{array}{ccc}1 & \cos \theta & 0 \\ \sin \theta & 1 & \cos \theta \\ \cos \theta & 1 & -\sin \theta\end{array}\right|=A \sin \theta+B \cos \theta+C \sin \theta \cos \theta\) then :

Which of the following crosses is showing a Test cross?