An a.c. voltage source of fixed amplitude \( E_0 \) and variable angular frequency \( \omega \) is connected with an electric bulb of resistance R (inductance zero) and a capacitor of capacitance C in series. On increasing the angular frequency of the source, the total impedance of the circuit

A transmitting antenna at the top of a tower has a height 18 m and the height of the receiving antenna is 32 m. What is the maximum distance between them for satisfactory communication in line-of-sight mode? Given radius of earth is \( 6.4 \times 10^6 \text{ m} \)

The light of wavelength 600 mm is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 2.54 m ?

In a coil, a current of 0.2 A increases at the rate of \( 0.4 \text{ A s}^{-1} \). If the power flow in the coil is \( 0.6 \text{ J s}^{-1} \) the inductance of the coil is:

If 'n' identical resistors, each of value 'R' are first connected in series to a battery of emf 'E' and internal resistance 'R', the current drawn is 'I'. Now if they are connected in parallel, then the current drawn is '5 I'. The value of n is

Which of the following statements are correct related to electric potential energy?
(A) The electric potential energy is a vector quantity.
(B) The potential energy of two like charges is positive and for two unlike charges, it is negative.
(C) The work done by an electrostatic field in moving a charge from one point to another is independent of the path taken.
(D) The potential energy of an electric dipole in a uniform electric field is maximum, when the dipole moment is opposite to the electric field.
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Which of the following statements are correct?
A. In a photon-particle collision number of photons are conserved.
B. The photoelectric current is directly proportional to the intensity of incident light.
C. The photoelectric emission is an instantaneous process.
D. Maximum kinetic energy of photoelectrons depend on the intensity of incident radiation.
E. The threshold frequency is different for different metals.
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A thick long straight wire of radius 'a' is carrying steady current I. The current I is uniformly distributed across the cross-section. The ratio of magnetic fields at a distance a/2 and 3a/2 from the central axis of the wire is

Which of the following amine forms a stable diazonium salt?

The following statements are given related to Wheatstone Bridge:
1. when Wheatstone Bridge is balanced, no current flows through the galvanometer arm.
2. Wheatstone Bridge works on the principle of Kirchhoff's law.
3. Being a null method based experiment, the result is free from the effect of extra resistances (cell resistance) of the circuit
4. Wheatstone Bridge is most sensitive when all the four resistances are nearly of the same magnitude.
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A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement.
The probability that first is blue and second is green is

Microbes in human welfare Microbes are a very important component of life on earth. we use microbes and microbially derived products almost every day, like LAB to make curd, yeast to make bread, adding flavor and texture to cheese, producing antibiotics etc. The addition of LAB, improves the milk quality by increasing vit. B12. Cheese is one of the oldest food items in which microbes are used. For example, large holes in Swiss cheese are due to CO2 produced by the bacterium Propionibacterium sharmanii. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water. The greater the BOD of waste water, the more is its polluting potential. In anaerobic sludge digesters, bacteria produce a mixture of gases like methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as a source of energy. Biofertilisers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilisers are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as a nutrient. Other bacteria can fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter).
The large holes in Swiss cheese are generated by-

Select the correct sequence for transport of sperm in the male reproductive
system.
(A) Urethra
(B) Urethra meatus
(C) Ejaculatory duct
(D) Vas deferens
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