The relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) on the set \(A=\{1,2,3\}\) is :

A and B are two sets such that n(A) = 5 and n(B) = 7. The number of one-one functions from A to B is

\(\int \frac{\log _e x}{\left(1+\log _e x\right)^2} d x\)2 is equal to

Two ropes are tied along the two diagonals of a cubic room. Ropes are inclined to each other at :

Which of the following statements are correct.
A. Every polynomial function is continuous.
B. Every constant function is continuous.
C. Modulus function is not continuous.
D. Identity function on real numbers is not continuous.
E. Every differentiable function is continuous.
Choose the correct answer from the options given below:

If lines \(\frac{x+5}{5 \lambda+2}=\frac{4-2 y}{10}=\frac{1-3 z}{-3}\) and \(\frac{x-2}{1}=\frac{1+2 y}{4 \lambda}=\frac{2+z}{3}\) are perpendicular, then value of ' \(\lambda\) ' is

The mean number of heads in two tosses of a coin is:

\(\text{CH}_3-\text{CH}(\text{Br}) - \text{CH}_2 - \text{CH}_3 \xrightarrow{\text{alc. KOH}} \text{A} \xrightarrow{\text{Br}_2} \text{CH}_3-\text{CH}(\text{Br}) - \text{CH}(\text{Br}) - \text{CH}_3 \text{(B)}\)
\(\text{(B)} \xrightarrow{\text{alc. KOH}} \text{CH}_3-\text{C} = \text{C} – \text{CH}_3 \text{(C)}\)
\(\text{(C)} \xrightarrow{\text{Hg}^{2+}/\text{H}^+\atop \text{H}_2\text{O}} \text{D}\)
A and D respectively are :

Keeping the voltage of the charging source constant, the separation between the plates of the capacitor is decreased by 10%. The percentage change in the energy stored in the capacitor will be:

If a match box of size \( 5 \text{ cm} \times 4 \text{ cm} \times 1 \text{ cm} \) is filled with nuclear matter, what will be its expected mass? The density of nuclear matter is approximately \( 2.3 \times 10^{17} \text{ kg/m}^3 \).

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:

Bt toxins are insect group specific proteins. Gene named crylAc and cryllAb control:

Assuming the same rate of change continues for the following data :

Year(X)	2019	2020	2021	2022	2023
Profit in Percentage (y)	38	40	65	72	69

The equation of the straight line trend using the least square method is :