If the minimum value of \(a\) is \(-\frac{k}{2}\), such that the function \(f(x)=x^2+a x+5\) is increasing in \([1,2]\). Then value of \(k\) is

A dishonest delivery man purchases 20 liters of pure milk and dilutes it by adding 4 liters of water. If he sells the diluted milk at \(Rs .50 / L\), then what is the cost price of pure

If A and B are symmetric matrices of the same order, then

Given equation of the plane is \(5x + 2y - 3z = 17\). Then,
A. A point \((2, 2, -1)\) lies on the plane
B. The direction cosines of normal to plane are \((2, 2, -1)\)
C. Coordinates of foot of perpendicular from origin are \((5, 2, -3)\)
D. The plane does not pass through the origin
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For \(x<\frac{1}{2}\), derivative of \(\tan ^{-1}\left(\frac{1+2 x}{1-2 x}\right)\) with respect to \(\sqrt{1+4 x^2}\) is:

For \(x>e\),\(\int \frac{d x}{x-\sqrt{x}}\) is equal to

If \(A\) and \(B\) are square matrices of order 3 such that \(|A|=-1\) and \(|B|=5\), then the value of \(|3 A B|\) is

An inverted pyramid of biomass can be found in:

An electron of mass \( 9.1 \times 10^{-31} \text{ kg} \) carrying charge \( 1.6 \times 10^{-19} \text{ C} \), is moving horizontally with a speed of \( 4 \times 10^6 \text{ m/s} \) in a uniform magnetic field of magnitude \( 8 \times 10^{-4} \text{ T} \) acting vertically upward. The radius of its circular path is,

Identify the order of reaction if its rate constant is \(k = 2 \times 1 0 ^{- 2 } s ^{- 1 }\) :

Following are the wavelength of some constituents of the electromagnetic spectrum. The wavelength range that are used in Radar system for Aircraft navigation is :
(A) 1 mm to 700 nm
(B) 0.1 m to 1 mm
(C) 400 nm to 1 nm
(D) < \(10^{-3} nm\)
(E) > 1 m
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What is the product formed when benzyl ethyl ether reacts with HI?

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.
Arrange the following in the increasing order of their pK_a values:
(A) CF₃-COOH
(B) O₂N-CH₂-COOH
(C) NC-CH₂-COOH
(D) H-COOH
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