If \(\left[\begin{array}{lll}1 & 2 & 3\end{array}\right] A=\left[\begin{array}{ll}4 & 5\end{array}\right]\), then the order of matrix \(A\) is:

A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :

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

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

\(\int \sin^3 x dx\) is equal to:

If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]\) is symmetric, then the value of \((a+b)\) is :

For Z = 3x + 4y, subject to the constraints \(x+y \leq 5, x \geq 0, y \geq 0\), the shaded region shown in the figure as OAB is bounded and the coordinates of the corner points O, A, B are (0, 0), (5, 0) and (0, 5) respectively. The maximum value of Z is:

If \(y=e^{a \cos ^{-1} x},-1< x< 1\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}\) is equal to

If \(f: R \rightarrow R\) be given by \(f(x)=\left(3-x^3\right)^{\frac{1}{3}}\), then \((f \circ f)(x)\) is:

If \(\left(t_1, y_1\right),\left(t_2, y_2\right)\),...,\(\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variables \(y\), then

A cell of emf 3 V and internal resistance 0.1 \(\Omega\) is connected to a 3.9 \(\Omega\) external resistance. What will be the potential difference across the terminals of the cell ?

In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. 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. 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.
Which one of the following statements is correct with reference to biolistics?

Formic acid does not respond to