The magnifying power of a compound microscope is high, if

A TV tower has a height of 20 m and the radius of earth is \(6.4 \times 10^6 m\). The range of the tower is:

Three parallel plates (each of area A) are separated by distances \( d_1 \) and \( d_2 \) respectively. The in-between spaces are filled with dielectrics of relative permittivity \( \epsilon_1 \) and \( \epsilon_2 \). The permittivity of free space is \( \epsilon_0 \). The capacitance of the combination is:

A substance, when placed in a magnetic field acquires feeble magnetization in a direction opposite to the applied field, is

A charged particle carrying charge \(q = 1 \mu C\) moves in a uniform magnetic field with velocity \(v_1 = 10^6 \text{ m/s}\) at an angle of \(45^\circ\) with the x-axis in the xy-plane and experiences a force \(F_1 = 0.4\sqrt{2} \text{ N}\) along the negative z-axis. When the same particle moves with velocity \(v_2 = 10^6 \text{ m/s}\) along the z-axis, it experiences a force \(F_2\) in the y-direction. Find the magnitude of the magnetic field.

A 50 W, 100 V bulb is to be used on a 200 V, 50 Hz a.c. supply. Calculate the inductance of inductor used so that the bulb glows with normal brightness.

If the angular velocity of coil in an AC generator is doubled while keeping other parameters constant, the maximum induced emf

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.
Benzoic acid in the presence of conc. \(HNO _3\) and conc. \(H _2 SO _4\) gives major product as:

Three point charges are placed at the corners of an equilateral triangle ABC as shown. The work done to put together these charges from infinity to their respective locations is

The angle between thee curves \(x y=\sqrt{2}\) and \(x^2-y^2=1\) at \((\sqrt{2}, 1)\) is:

The total charge of an electric dipole is (Where 'q' is the point charge on either side of the dipole and 'e' is the charge of an electron)

The maximum profit that a company can make if the profit function is
\(P(x)=41+24 x-18 x^2\) is :

For the LPP, Min \(z=6 x+10 y\) subject to \(x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0\), redundant constraint is: