A battery of emf 3 V and internal resistance \( r \) is connected in series with a resistance of \( R = 55 \text{ } \Omega \) through an ammeter of resistance \( R_A = 1 \text{ } \Omega \). The ammeter reads a current \( I = 50 \text{ mA} \). Find the internal resistance \( r \) of the battery.

In Young's Double Slit experiment, the intensities of two coherent monochromatic waves are I and 4I. The ratio of intensity at maxima to minima will be :

A convex lens of focal length 10 cm is placed in front of a convex mirror of radius of curvature 14 cm. An object is placed at a distance of 20 cm from convex lens. The distance between the lens and the mirror so that the final image formed by the combination coincides with the object itself will be:

A freshly prepared radioactive sample of half life 1 hour emits radiations that are 128 times as intense as the permissible safe limit. What is the minimum time after which the sample can be safely used?

In which of the following transitions will the wavelength of light emitted be minimum?

Out of the following, which one is not correct?

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry 0.2 A and 0.3 A currents respectively in opposite directions. The magnetic field at the center is:

When aniline is reacted with benzoyl chloride, the correct product is

An electric dipole of dipole moment \(p\) is rotated in an electric field of magnitude \(E\) from the most stable orientation to most unstable orientation. The work done in the process is:

Read the passage carefully and answer the Questions
Aldehydes and ketones are important organic compounds prepared mainly by oxidation of alcohols. Primary alcohols give aldehyde and secondary alcohols yield ketones. Aldehydes can also be formed by partial reduction of acid chlorides, reduction
of esters or by Gattermann-Koch reaction. Ketones are prepared by Friedel-Craft's acylation, hydration of alkyne and reaction of Grignard's reagent with nitriles. Chemically, aldehydes and ketones are reactive in nature due to the carbonyl group and undergo nucleophilic addition reactions. Aldehydes are more reactive than ketones and can be oxidized to carboxylic acids, while both can be reduced to alcohols or hydrocarbons and exhibit condensation reaction.
Hydration of propyne in the presence of \(H _2 SO _4\) and \(HgSO _4\) gives

In an experiment with Meter Bridge, with unknown resistance R in the left gap, the null point is obtained at \( l_1 = 40 \text{ cm} \) from the left end. Now a resistance of \( R' = 10 \Omega \) is connected in series with resistance R, the null point is obtained at \( l_2 = 70 \text{ cm} \) from the left end. The value of resistance R is

Time period of oscillation of a bar magnet in a uniform magnetic field is \( T_o \). The magnet is cut into 3 equal parts transverse to its length. The new time period of oscillation of one part will be :

Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is: