The area bounded by \(y^2=4 x\) and its latus rectum and \(x\)-axis in the first quadrant is:

If \(A=\left[\begin{array}{ccc}0 & x^2-6 & -3 \\ -x & 0 & -8 \\ x^2-2 x & 8 & 0\end{array}\right]\) is a skew symmetric matrix, then the value(s) of \(x\) is/ are -
(A) 3
(B) -3
(C) -2
(D) -1
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The maximum value of \(Z\) for the linear Programming problem maximum \(Z=2 x+y\) subject to the constraints \(x+y \leq 2, \quad x \geq 0, \quad y \geq 0\) is :

The system of equations \(2 x+\lambda y=8, \lambda x+8 y=3\) has a unique solution if the value of \(\lambda\) is (are):

Which of the following matrices is not invertible?

Let \(\vec{a}, \vec{b}\) be two vectors such that \(|\vec{a}|=2,|\vec{b}|=3, \vec{a} \cdot \vec{b}=4\). Then \(|\vec{a}-\vec{b}|\) is equal to :

Two numbers are selected without replacement at random, one at a time from the first six positive integers. Let x denotes the larger of the two numbers. Match List-I with List-II

List-I	List-II
(A) \(P(x=2)\)	(I) \(\frac{4}{15}\)
(B) \(P(x=3)\)	(II) \(\frac{1}{15}\)
(C) \(P(x=4)\)	(III) \(\frac{2}{15}\)
(D) \(P(x=5)\)	(IV) \(\frac{1}{5}\)

Choose the correct answer from the options given below:

The vapour pressure of a solution is 2985 \(\text{Nm}^{-2}\) when 5 g of a non-electrolyte is added to 100 g of water at a particular temperature.
The vapour pressure of pure water at this temperature is 3000 \(\text{Nm}^{-2}\).
The molecular mass of the solute is

Which of the following statements are true about phosphorous cycle?
A. There is no respiratory release of phosphorus in the atmosphere
B. The reservoir of phosphorus is rock
C. There are large atmospheric inputs of phosphorus through rainfall
D. The gaseous exchange of phosphorus between organisms and environment is negligible
Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions.
RNAi takes place in all eukaryotic organisms as a method of cellular defense. The source of this complementary RNA could be from an infection by viruses having RNA genomes or mobile genetic elements (transposons) that replicate via an RNA intermediate. Insulin from an animal source, though caused some patients to develop allergy or other types of reactions to the foreign protein. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked together by disulphide bridges. Transgenic mice are being developed for use in testing the safety of vaccines before they are used on humans. Transgenic mice are being used to test the safety of the polio vaccine. If successful and found to be reliable, they could replace the use of monkeys to test the safety of batches of the vaccine. Specific Bt toxin genes were isolated from Bacillus thuringiensis and incorporated into the several crop plants such as cotton. The choice of genes depends upon the crop and the targeted pest, as most Bt toxins are insect-group specific. The toxin is coded by a gene cryIAc named cry. There are a number of them, for example, the proteins encoded by the genes cryIAc and cryIIAb control the cotton bollworms, that of cryIAb controls corn borer.

The Bt toxin gene cryIAb controls the:

Which of the following statements are correct?
A. Number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation
B. Cut off potential is the minimum negative potential given to the plate for which photocurrent becomes maximum
C. For a given frequency of the incident radiation, the stopping potential is independent of its intensity
D. Even for the exceedingly dim incident radiation apparent time lag is \( \sim 10^{-9} \) s or less
E. Photons are electrically neutral and are not deflected by electric and magnetic fields
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Silicon can be doped to get an n-type semiconductor by using :
(A) Arsenic (As)
(B) Phosphorus (P)
(C) Boron (B)
(D) Antimony (Sb)

Match List-I with List-II

List-I (Characteristics)	List-II (Examples)
(A) Symbiotic association with roots of leguminous plants	(I) Glomus
(B) Fixes atmospheric nitrogen while free living in the soil	(II) Rhizobium
(C) Symbiotic association of fungi and plants	(III) Anabaena
(D) Cyanobacteria which can fix atmospheric nitrogen	(IV) Azotobacte

Choose the correct answer from the options given below: