Let us suppose that two independent random samples of sizes \(n_1\) and \(n_2\) have been drawn from the same normal population.
Then the degree of freedom of the statistic \(t\)-distribution is

The greatest integer function \(f(x)=\lfloor x\rfloor\) is differentiable for all values of

The maximum value of \(Z=2 x+3 y\) subject to the constraints \(x \geq 0, y \geq 0, x+y \leq 10,3 x+4 y \leq 36\) is:

If \(x y+\frac{x^2}{y}=x^3 y+y\), then \(\frac{d y}{d x}\) is equal to

The value of \(c\) for which \(f(x)=x(x-3)^2, 0 \leq x \leq 3\), satisfies Rolle's theorem is:

The area (in sq. units) of the region bounded by the parabola \(y^2=8 x\) and the line \(x=2\) is

If \(A=\left[a_{i j}\right]\) is a skew-symmetric matrix of order \(n\), then

If the matrix \(\left[\begin{array}{ccc}2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4\end{array}\right]\) is not invertible, then the value of \(\lambda\) is :

Which of the following features are required to facilitate cloning?
(A) Presence of origin of replication (Ori) in the cloning vector
(B) Presence of a selectable marker in the cloning vector
(C) Presence of a single recognition site (preferably) for restriction enzyme in the cloning vector
(D) Presence of more than two promoter regions in the cloning vector
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus-

Half life of the zero order reaction is:

For the following data :

	Size	Mean	Standard Deviation
Sample 1	4	40	8
Sample 2	5	50	10

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to :

The transfer of pollen grains from one plant to the stigma of a different plant is known as: