Which of the following is NOT correct about the Central Limit Theorem?

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is:

The maximum value of the function \(f(x)=-x^2+2 x-1\) is:

A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random (without replacement), then the probability that both the balls are white is:

Which of the following terms are associated with a linear programming problem?
(A) Constraints
(B) Independent events
(C) Feasible region
(D) Objective function
Choose the correct answer from the options given below :

The integral \(\int e^x(\tan x+\log \sec x) d x\) is equal to :

For the function \(f(x)=x^{1 / x}, x>0\), which of the following are correct?
(A) \(x=0\) is the only point where extremum may occur.
(B) The given function is maximum at \(x=e\).
(C) The function has no extreme value for \(x>0\).
(D) The maximum value of the function \(f(x)\) is \(e^{1 / e}\)
Choose the correct answer from the options given below :

What is the relative permittivity of a medium of relative permeability \( \mu_r = 1.0 \) in which an electromagnetic wave travels at a speed of \( v = 2 \times 10^8 \, \text{m s}^{-1} \)?

The probability of a man hitting a target is \(\frac{1}{2}\).
How many times must he fire so that the probability of hitting the target at least once is more than \(90 \%\) ?

Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\). If \(A^T+A=I\), then:

The type of pollination which brings genetically different types of pollen grains to the stigma is -

Arrange the given organisms involved in an ecosystem in correct sequence from lower to higher order.
(A) Fish
(B) Phytoplankton
(C) Man
(D) Zooplankton
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. 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. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Statins, used as blood-cholesterol lowering agents are produced by -