\(\int_0^{\frac{\pi}{2}} \frac{\cos x}{(1+\sin x)(2+\sin x)} d x=\)

The particular solution of the differential equation \(\frac{d y}{d x}+\frac{3 y}{x}=0, y(1)=1\) is

If A is a square matrix of order 3 and \(|A| = -2\) then, \(|-2A^{-1}|\) is:

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4}, \\ 2 K+1, & x=\frac{\pi}{4},\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is equal to

Which of the following inequalities holds true?
(A) \(\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}\).
(B) If \(a>b\) and \(c<0\), then \(\frac{a}{c}<\frac{b}{c}\).
(C) \(\frac{1}{x^2}>\frac{1}{x}>1\), if \(0<x<1\).
(D) If \(a\) and \(b\) are positive integers and \(\frac{a-b}{6.25}=\frac{4}{2.5}\), then \(b>a\).
Choose the correct answer from the options given below:

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

The corner points of the feasible region with the constraints \(x+y \leq 30, x+y \geq 15, y \leq 20, x \leq 15\), and \(x, y \geq 0\) are

If |\(\vec{a}\)| = 8, |\(\vec{b}\)| = 3, and |\(\vec{a} \times \vec{b}\)| = 12, then the value of \(\vec{a} \cdot \vec{b}\) is:

A cell is written as
\(Mg\left|Mg^{2+}(0.0001 M) \| Ag^{+}(0.01 M)\right| Ag\)
Calculate its \(E_{\text {cell }}\) if \(E_{\text {cell }}^{\ominus}=1.25 V\) at 298 K

Which of the following is a barrier method of contraception?

Read the passage carefully and answer the questions based on the passage:
Pest Resistance Plants
Various nematodes parasitize a wide variety of plants and animals, including human beings. A nematode, Meloidogyne incognitia, infects the roots of tobacco plants and causes a great reduction in yield. A noval strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). RNAi takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses (cold, drought, salt, heat). (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food, e.g., golden rice, i.e., Vitamin 'A' enriched rice. Genetic modification of organisms can have unpredicatable results when such organisms are introduced into the ecosystem. Therefore, the Indian Government has set up organisations such as GEAC (Genetic Engineering Approval Committee), which will make decisions regarding the validity of GM research and the safety of introducing GM-organisms for public services. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes).
RNA interference involves:

The points on the curve \(\frac{x^2}{16}+\frac{y^2}{25}=1\) at which tangents are parallel to \(x\)-axis are:

Primary Endosperm Nucleus is the product of :