Match List-1 with List-2

List-1	List-2
(A) A fire in a factory causing production delay for some time is	(I) Secular trend
(B) Technological progress is	(II) Seasonal trend
(C) The rise in prices before big festival is example of	(III) Irregular trend
(D) Rise and fall of share market is	(IV) Cyclic trend

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The function \(f(x)=\tan x-x\) for \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\) is :

If \(y=5 e^{2 x}+4 e^{3 x}\), then \(\frac{d^2 y}{d x^2}\) equals:

If \(x=2 a t, y=a t^2\), where ' a ' is a constant, then \(\frac{d^2 y}{d x^2}\) at \(x=2\) is :

The shortest distance between the lines \(\vec{r}_1=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(\vec{r}_2=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\) is :

The general solution of the differential equation \(\left(x^2-y x^2\right) d y+\left(y^2+x^2 y^2\right) d x=0\) is :

Consider a random sample of 10 students having 116 cm as mean height and standard deviation as 9.798 cm .
If the suggested mean height of the students population is 110 cm , then the \(t\)-test statistic of the sample is :
Given: \(\frac{\sqrt{10}}{9.798}=0.3227\)

The area (in sq.units) of the region bounded by the curves \(y = x\) and y = \(x^3\) is:

Match List I with List II

List I	List ll
(A) Dodo	(I) Africa
(B) Quagga	(II) Russia
(C) Thylacine	(III) Mauritius
(D) Steller Sea Cow	(IV) Australia

Choose the correct answer from the options given below:

Given that the function \(f(x)\) is continuous on \(R\). Match \(List - I\) with \(List - II\) .

\(List - I\)	\(List - II\)
(A) \(f(x)=\left\{\begin{array}{ll}k x^2, & x<3 \\ 3, & x \geq 3\end{array}\right.\)	(I) \(k=\frac{5}{4}\)
(B) \(f(x)=\left\{\begin{array}{ll}k x+1, & x \geq 4 \\ x+2, & x<4\end{array}\right.\)	(II) \(k=-1\)
(C) \(f(x)=\left\{\begin{array}{ll}\frac{5+x}{2}, & x \neq 0 \\ 3 k, & x=0\end{array}\right.\)	(III) \(k=\frac{1}{3}\)
(D) \(f(x)=\left\{\begin{array}{ll}x+k, & x>-2 \\ -3, & x \leq-2\end{array}\right.\)	(III) \(k=\frac{5}{8}\)

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'Bt toxin gene has been cloned from Bacillus thuringiensis and has been expressed in plants.' This in effect created which of the following?

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Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^x[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
If the temperature is raised by \(10^{\circ} C\), then the rate of the reaction increases approximately by

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Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature
adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C- OH bond and the O_H bond along with the reactions involving the complete -COOH group.
The IUPAC name of following compound is
OHC - C₆H₄ - CHO - p