Which of the following are correct about t-test statistics?
(A) The mean of t-test distribution is 0.
(B) It depends on the degrees of freedom.
(C) It depends on population standard deviation
(D) With more degrees of freedom, it closely resembles standard normal distribution.
Choose the correct answer from the options given below :

The area of the region bounded by the parabola \(y^2=4 a x\) and its latus rectum is:

For the objective function \(Z = 3x + 5y\) subject to constraints \(x + 3y ≥ 3, x + y ≥ 2, x ≥ 0, y ≥ 0\):

If a sample has \(n\) observations \(x_1, x_2, \ldots, x_n\) with \(m\) constraints on these values, then the degree of freedom of the sample statistic is:

The interval in which the function \(f(x)=2 x^3+3 x^2-12 x+1\) is strictly increasing, is

Let \(f(x)\) satisfies the requirements of Lagrange's mean value theorem in \([0,2]\).
If \(f(0)=0\) and \(f^{\prime}(x) \leq \frac{1}{2}\) for all \(x \in[0,2]\), then :

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are:

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Which one of the followings is not true about insulin?

If the optimal value of the objective function \(z=p x+y\) of an L.P.P occurs at two corner points \((2,11)\) and \((4,5)\) of its bounded feasible region, then its optimal value is

The rate of biomass production is called productivity and it is expressed in terms of:

To demonstrate the phenomenon of interference, required two sources of light must have

Which of the following is not correct?

Two coils of self inductances \( L_1 \) and \( L_2 \) are kept close to each other so that the effective flux in one is completely linked with the other. What is the mutual inductance M between them ?