If the lines \(\frac{1-x}{3}=\frac{2 y-4}{4 K}=\frac{z-3}{2}\) and \(\frac{x-1}{3 K}=\frac{1-y}{-1}=\frac{6-z}{5}\) are perpendicular, then the value of \(K\) is :

The interval on which the function \(f(x)=x^4-\frac{x^3}{3}\) is strictly decreasing, is :

The function \(f: R \rightarrow R , f(x)=x^2\) is

If the points \(A, B, C\) with position vectors \(20 \hat{i}+\lambda \hat{j}, 5 \hat{i}-\hat{j}\) and \(10 \hat{i}-13 \hat{j}\) respectively are collinear, then the value of \(\lambda\) is:

The remainder, when \(5^{60}\) is divided by 7 , is :

If \(\vec{a}\) and \(\vec{b}\) are two non-zero orthogonal vectors, then \(|\vec{a}+\vec{b}|\) is equal to:

The slope of the normal to the curve \(y=2 x^2\) at \(x=1\) is:

Match List I with List II.

LIST I	LIST II
A. Lungs of the planet	I. Bali tiger
B. Invasive species	II. Taxol
C. Anti cancer drug	III. Amazon rain forests
D. Extinct species	IV. Parthenium

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Read the passage carefully and answer the Questions
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 products formed when 2,2-Dimethylpropan-1-al is heated with concentrated KOH are :

An a.c. source of 200 V is connected through a diode 'D' to a capacitor as shown in figure. Find the maximum potential difference across the capacitor :

Match List I with List II

LIST I	LIST II
A. \(\lim_{x \to 0} \frac{(1 - \cos 2x) \sin 5x}{x^2 \sin 3x}\)	I. 18
B. \(\lim_{x \to \infty} \frac{(3x-5)(2x-7)}{(4x-9)(5x-3)}\)	II. \(\frac{10}{3}\)
C. \(\lim_{x \to 0} \frac{2 \sin^2 3x}{x^2}\)	III. \(\frac{3}{4}\)
D. \(\lim_{x \to \frac{\pi}{4}} \frac{1 - \cos^3 x}{2 \cot x - \cot^3 x}\)	IV. \(\frac{3}{10}\)

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Arrange the following in the increasing order of rate of the second order reaction Reactants → products
(A) Reaction at 298 K
(B) Reaction at 298 K with catalyst
(C) Reaction at 500 K with catalyst and double the initial concentration of reactant
(D) Reaction at 500 K with double the initial concentration of reactant
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Which of the following is used as a biological control agent for insects and other arthropods ?