Which of the following statements are correct?
(A) If \(f: R \rightarrow R\) then \(f(x)=|x|\) is continuous everywhere.
(B) If \(f: R \rightarrow R\) then \(f(x)=|x|\) is continuous everywhere but not differentiable at \(x=0\).
(C) Let \(f: R -\{0\} \rightarrow R\) then \(f(x)=1(\) or \(1 / x)\) is continuous everywhere.
(D) Let \(f: R \rightarrow R\) then \(f(x)=|x-1|+|x-2|\) is continuous everywhere but not differentiable at exactly 2 points.
(E) If \(f: R \rightarrow R\) then \(f(x)=\cot (x)\) is continuous everywhere.
Choose the correct answer from the options given below :

If \(x, y\) and \(z\) are non zero real numbers, the inverse of matrix \(A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) is:

The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

Let \(a \leq \tan ^{-1} x+\cot ^{-1} x+\sin ^{-1} x \leq b\). If \(\alpha\) and \(\beta\) denote the minimum and maximum possible values of \(a\) and \(b\) respectively, then :

In an influenza epidemic, the number of cases diagnosed in a week were as follows:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Number of Cases	10	12	8	16	9	14	4

The 3-day moving averages are :

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

If the normal to the curve \(y=f(x)\) at the point \((3,4)\) makes an angle \(\frac{3 \pi}{4}\) with the positive \(x\)-axis, then \(f^{\prime}(3)=\) ________ .

The interval in which \(f(x)=2 x^3-9 x^2+12 x+1\) is decreasing is:

Complete hydrolysis of DNA does not yield

For the principal value branch, the value of \(\sin \left(\frac{\pi}{2}-\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is

The degree of the differential equation \(\left(2+\left(\frac{d y}{d x}\right)^2\right)^{\frac{3}{2}}=a^2 \frac{d^2 y}{d x^2}\) is :

If \(I=\int_0^\pi x \sin x d x\), then

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).
Which one infects the roots of tobacco plants and causes a great reduction in yield?