Consider the relation R in the set Z of integers which is given by \(R=\{(a, b): 2\) divides \(a-b\}\).
Choose the correct option for the relation \(R\) :

Which of the following functions \(f(x)\) are differentiable at \(x=0\) ?
(A) \(|x|\)
(B) \(|x-1|\)
(C) \(|\sin x|\)
(D) \(|\cos x|\)
(E) \(x^2\)
Choose the correct answer from the options given below :

As per the graph given below:

Match List - I with List - II

LIst - I (Function/Area/point)	List - II (Representation)
(A) Consumers Surplus	(I) y = g(x)
(B) Supply function	(II) v
(C) Demand function	(III) s
(D) Equilibrium point	(IV) y = f(x)

Choose the correct answer from the options given below:

If three year moving averages for five data items given by \(16,18,20,10,21\) are \(x, y\) and \(z\) respectively, then :

The objective function of an LPP is \(z=a x+\beta y,(a, \beta>0)\) that has to be maximized/minimized subject to the constraints \(x+y \leq 2, x \geq 0, y \geq 0\).
Then \(\max (z)-\min (z)\) is equal to :

The interval on which the function \(f(x)=x^3+2 x^2-1\) is decreasing, is

The intervals for which \(f(x)=x^4-2 x^2\) is increasing are:

Match List I with List II

List I	List ll
(A) Down's syndrome	(I) 44 + XX/XY
(B) Klinefelter's syndrome	(II) 44 + XO
(C) Turner's syndrome	(III) 44 + XXY
(D) Normal human	(IV) 45 + XX/XY

Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Which one of the following is not used for detection of cancer?

The value of the definite integral \(I=\int_0^2 x \sqrt{2-x} d x\) is :

\(\int e^x \sec x(1+\tan x) d x\) equals:

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.
mRNA silencing through RNA interference (RNAi) refers to the:

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is: