The point which does not lie in the half plane \(2 x+3 y-12 \leq 0\) is:

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

The term of the perpetuity is:

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth \(6\%\) per annum compounded monthly?

If \(\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|\), then x is equal to :

Match List - I with List - II

List - I	List - II
(A) Line: x = 2y + 1 = z - 1	(I) Crosses xz-plane at (1,0,1)
(B) Line: x + 1 = 2y + 1 = z	(II) Crosses xz-plane at (0,0,1)
(C) Line: x - 1 = 2y = z + 1	(III) Crosses xz-plane at (1,0,-1)
(D) Line: x - 1 = 2y = z - 1	(IV) Crosses xz-plane at (1,0,2)

Choose the correct answer from the options given below:

The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:

Match List I with List II.

LIST I	LIST II
A. Trichoderma polysporum	I. Statins
B. Monascus purpureus	II. Butyric acid
C. Aspergillus niger	III. Cyclosporin A
D. Clostridium butylicum	IV. Citric acid

Choose the correct answer from the options given below:

The area (in sq. units) bounded by the parabola \(y^2=16 x\) and its latus rectum is

\(2 N_2 O _5 \rightarrow 4 NO _2+ O _2\)
At a given instant of time, the rate and rate constant are 1.02 \(\times\) 10\(^-\)\(\mathrm{4}\) mol L\(^-\)\(\mathrm{1}\) s\(^-\)\(\mathrm{1}\) and 3.4 \(\times\) 10\(^-\)\(\mathrm{5}\) s\(^-\)\(\mathrm{1}\), respectively.
The concentration of N\(_2\)\(\mathrm{O}\)_5 at that time will be:

The probability distribution of a random variable X is given below:
\(\begin{array}{lllll} X & 0 & 1 & 2 & 3 \\ P ( X ) & k & & \\ & & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}\end{array}\)
then the value of \(P(X \leq 2)+P(X>2)\) is :

RNA interference:
(A) Involves silencing of specific mRNA
(B) Involves silencing of specific DNA
(C) is used to produce pest-resistant plants
(D) is used to produce recombinant insulin
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.
The bottled juices are clarified by the combination of -