A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream.
If the speed of the boat in still water is 10 km/hr, then the speed of the stream is :

Which of the following functions satisfies Rolle's theorem?

Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at:

The area of the smaller portion enclosed by the circle \(x^2+y^2=4\) and the straight line \(x+y=2\) is:

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\)and \(B=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]\) ,then the matrix AB is equal to

The value of \(\int_0^1 x e^x d x\) is :

In p-type semiconductors, the conductivity is due to:

Match List - I with List - II.

LIST I	LIST II
A. Law of independent assortment	I. 9:3:3:1
B. Incomplete dominance	II. 3:1
C. Law of dominance	III. AB blood group
D. Co-dominance	IV. Flower colour in Snapdragon

Choose the correct answer from the options given below:

The mass of \(\text{NaOH}\) required to make a 500 mL solution of 0.5 molarity is

Which one of the following contributes the maximum percentage to the biodiversity of a vertebrate group?

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Esterification of carboxylic acid with alcohols or phenols is which type of reaction?

To avoid the unfavourable conditions, the zooplanktons enter into :