In a village, there are three mohallas A, B and C. 60\% farmers in mohalla A believe in new technology of agriculture, while in B it is 70\% and in C is 80\%.
The total probability that a farmer believes in new technology of agriculture is:

Match List - I with List - II.

List - I	List - II
(A) If A and B are mutually exclusive events, then \(P ( A \cup B )=\)	(I) \(\frac{ P ( A \cap B )}{ P ( B )}, P ( B ) \neq 0\)
(B) If A and B are independent events, then \(P ( A \cap B )=\)	(II) \(\frac{ P ( A \cap B )}{ P ( A )}, P ( A ) \neq 0\)
(C) If A and B are two events of a sample space of an experiment, then \(P ( A / B )=\)	(III) \(P ( A ) \cdot P ( B )\)
(D) If A and B are two events of a sample space of an experiment, then \(P ( B / A )=\)	(IV) \(P ( A )+ P ( B )\)

Choose the correct answer from the options given below :

\(\int_0^{\frac{\pi}{2}} \sqrt{1-\sin 2 x} d x\) is equal to :

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:

The domain of the function f(x) = \(\frac{x^2+1}{x^2-3 x+2}\) is

Mr. X wishes to purchase a flat for Rs. 44, 60, 800 with a down payment of Rs. 10,00,000 and the balance in equal monthly instalments (EMI) for 20 years. If the bank charges 7.5% per annum compounded monthly, then the EMI is :
[Given that \((1.00625)^{240}=4.4608\) ]

A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the winning post on the tracks so that A and B reach there at the same time?

Consider the curves, \(x^2+y^2=1\) and \((x-1)^2+y^2=1\).
Area enclosed by the two curves is :

A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the x-axis. The magnitude of the magnetic field, due to the element, on the y-axis at a distance \( r = 0.5 \, m \) from it, would be

Choose the correct option, which explains the term alleles.

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. 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 (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained a protein called _______ which was nutritionally a more balanced product for human babies than natural cow-milk.

The spin-only magnetic moment of the Hexacyanomanganate(II) ion is __________ BM.

ABO blood groups are controlled by: