If \(A\) be a square matrix of order 3 such that \(|A|=2\), then \(|\operatorname{adj}(2 A)|\) is equal to

A tank has two outlet pipes A and B, which together take 6 hours to empty a full tank when opened simultaneously.
The tank was initially half-full and both outlets were opened.
After one hour, an inlet pipe was also opened.
If the inlet alone can fill the empty tank in 4 hours, how much time will it now take to fill the tank completely?

The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by

If the function \(f(x)=x^4-62 x^2+a x+9\) attains its local maximum value at \(x=1\), then \(a\) is equal to :

Solution of differential equation \(\frac{d y}{d x}=\cos (x+y+3)\) is:

The value of \(\int_1^2 \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}} d x\) is:

The value of the integral \(\int \frac{d x}{e^x+e^{-x}}\) is equal to:

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 IUPAC name of following compound is
OHC - C₆H₄ - CHO - p

What are the respective numbers of \( \alpha \) and \( \beta \) particles emitted respectively in the following radioactive decay?
\( {}^{200}_{90}X \rightarrow {}^{168}_{80}Y \)

Which one of the following is an incorrect statement about endosperm
production during double fertilization in plants?

The value of van't Hoff factor, i, for CH₃COOH solution in water will be

Direction ratios of the line perpendicular to the lines \(\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2}\) and \(\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1}\) are:

The magnetic field at a distance r from a long wire carrying current I is 0.4 T. The magnetic field at a distance 2r from the wire is