Two events A and B will be independent, then

In a binomial distribution, the probability of getting a success is \(\frac{1}{3}\) and the standard deviation is 2 . Then its mean is :

If a 99% confidence interval states that the population mean is greater than 100 and less than 400, then the sample mean and margin of error respectively are:

Match List-I with List-II

List - I (Differential Equations)	List - II (Degree/Order)
(A) Degree of the differential equation \(\frac{d^3 y}{d x^3}+2 \log x \cdot y=0\)	(I) 3
(B) Order of the differential equation \(\frac{d^4 y}{d x^4}+\left(\frac{d y}{d x}\right)^4+x y=0\)	(II) 2
(C) Degree of the differential equation \(\left(\frac{d^4 y}{d x^4}\right)^2+\left(\frac{d y}{d x}\right)^3+x^2 y=0\)	(III) 1
(D) Order of the differential equation \(\frac{d^3 y}{d x^3}+y\left(\frac{d y}{d x}\right)^3=0\)	(IV) 4

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]\) and \(I\) is an identity matrix of order \(2\) , then \(A-3 I\) equals :

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

The interval in which \(f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi\) is strictly decreasing is:

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.
Biopiracy is the term used to refer:

A cylindrical wire is stretched to increase its length by 10%. The percentage increase in resistance will be

The flow of solvent from pure solvent side to solution side across a semipermeable membrane can be stopped if some extra pressure is applied on the solution. This pressure that just stops the flow of solvent is called

Match List-I with List-II
The function \(f(x)=2 x^3-15 x^2+36 x+5\) for \(x \in[2,5]\) has

List-I	List-II
(A) absolute maximum value	(I) 5
(B) absolute minimum value	(II) 60
(C) point of absolute maxima	(III) 3
(D) point of absolute minima	(IV) 32

Choose the correct answer from the options given below:

The feasible region represented by the constraints \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y \geq 0\) of an LPP is

A point charge – 5 µC is at a distance 5 cm directly above the centre of a square of side 10 cm.
The magnitude of electric flux through this square is: