Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution :
(A) The number of trials is indefinitely large.
(B) The probability of success for each trial is indefinitely small.
(C) The product of the number of trials and the probability of success for each trial is finite.
(D) The probability of success for each trial is indefinitely large.
Choose the correct answer from the options given below :

Shyam invested ₹ 2, 00, 000 in 2019 for 5 years.
If the compound annual growth rate (CAGR) for his investment is \(10 \%\), then the end balance of his investment is :

\(\int \frac{d x}{9 x^2-16}\) is equal to:

The differentiation of \(\frac{x^3}{1-x^3}\) w.r.t. \(x^3\) is:

The solution set of the inequality \(3 x+5 y<15\) is :

If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\), then the value of (x + y) is :

consider the linear programming problem: Maximise \(z=3 x+y\) subject to the constraints \(x+y \leq 6, x \geq 0, y \geq 0\). Which of the following statements are true?
(A) \(x \geq 0, y \geq 0\) are non-negative restrictions.
(B) The point \((1,1)\) does not lie in the half plane \(x+y \leq 6\).
(C) There are 2 corner points of the feasible region of given LPP.
(D) Maximum value of \(z\) is 18.
Choose the correct answer from the options given below:

Two wires A and B of the same material and same mass have radii 2r and r, respectively. If the resistance of wire A is \( 4 \, \Omega \), then resistance of B will be

Arrange the stages in the life cycle of Plasmodium after the bite of mosquito.
(A) gametocytes in human RBCs
(B) sporozoites in mosquito's salivary glands
(C) sporozoites in human liver
(D) Fertilization in gut of mosquito host
Choose the correct answer from the options given below:

The general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is :

A magnetic needle has magnetic moment of \( 5 \times 10^{-2} \, \text{Am}^2 \) and Moment of inertia \( 12 \times 10^{-6} \, \text{Kg m}^2 \). It performs 60 oscillations in 1 minute when suspended in a magnetic field. What is the magnitude of the magnetic field ?

Which of the following is the primary female sex organ?

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.
ELISA is based on the principle of: