Corner points of the feasible region determined by the system of linear constraints are \((0, 3), (1, 1)\) and \((3, 0)\). Let \(Z = px + qy\) where \(p, q > 0\). Condition on \(p\) and \(q\) so that minimum of \(Z\) occurs at \((3, 0)\) and \((1, 1)\) is:

Match List-l with List-ll

List-l (Mathematical Statement)	List-ll (Value)
(A) \(\hat{i} \cdot(\hat{j} \times \hat{k})\)	(I) \(-\hat{k}\)
(B) \(\hat{j} \cdot(\hat{i} \times \hat{k})\)	(II) 1
(C) \(\hat{i} \times(\hat{j} \times \hat{k})\)	(III) \(-1\)
(D) \(\hat{j} \times \hat{i}\)	(IV) \(\overrightarrow{0}\)

Choose the correct answer from the options given below :

If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then

The feasible region for the constraints \(x \geq 0, x+y \leq 1\) and \(x-y \leq 1\), is situated in:
(A) I and II Quadrant
(B) I Quadrant
(C) II and IV Quadrant
(D) IV Quadrant
(E) I, II, III and IV Quadrant
Choose the correct answer from the options given below:

The value of \(\left|\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right|\) is

\(\int_{0}^{1} (x^3 + 3x^2)e^x dx =\)

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of k/4 is

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichia coli RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

In agarose gel electrophoresis, the separated DNA fragments can be visualized with the help of compound known as:

In the course of evolution, life forms on earth tend to move from

Which of the following statements are correct?
(A) The resistivity of a semiconductor decreases with increasing temperature.
((B) The potentiometer is unaffected by the internal resistance of the source.
((C) In ionic crystals and electrolytic liquids electrons carry the electric current.
((D) Ohm's law fails if V depends on I non-linearly.
((E) Kirchhoff's rules are used for analysis of electric circuits.
(Choose the correct answer from the options given below :

The far point of a myopic person is 80 cm. The power of corrective lens will be

Particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y=0\) when \(x=1\), is:

Read the following passage carefully and answer the given questions.
Immune System in the Body
The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The primary lymphoid organs are bone marrow and thymus where immature lymphocytes differentiate into antigen-sensitive lymphocytes. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells. The bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Hence, an antibody is represented as H2L2. Different types of antibodies are produced in our body. IgA, IgM, IgE, IgG are some of them. 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.
Which one of the following technique is not useful for the detection of cancers of internal organs?