A current of 15 A in the primary coil of a circuit is reduced to zero at a uniform rate in \( 10^{-6} \, \text{s} \). If the coefficient of the Mutual Inductance is 4 H, what is the Induced emf in secondary coil?

The flux of the electric field \( \vec{E} = 2 \times 10^3 \hat{i} \text{ N/C} \) through a square of 10 cm, on a side whose plane is parallel to the \( xy \) plane is:

The maximum distance between the transmitting and receiving antenna for a satisfactory communication in LOS mode is 48 Km . If the height of the receiving antenna is 8 (Given radius of earth \(R_e=6400 km\) )

Two capacitors of capacitance of \( 6 \, \mu\text{F} \) and \( 12 \, \mu\text{F} \) are connected in series with a battery. The voltage across \( 6 \, \mu\text{F} \) capacitor is 2 V. The total voltage across the combination is

What is the force between two small charged spheres having charges of \( 4 \times 10^{-7} \text{ C} \) and \( 6 \times 10^{-7} \text{ C} \) placed 60 cm apart in air ?

Arrange the following electromagnetic waves in the increasing order of their energy.
(A) Ultraviolet rays
(B) Infrared rays
(C) Microwaves
(D) X-rays
(E) Gamma rays
Choose the correct answer from the options given below:

In the given circuit, the resistance of the galvanometer is \( G = 100 \text{ } \Omega \). Resistance box R contributes \( 4900 \text{ } \Omega \). When key K is closed. The needle of the galvanometer deflects to the 20th division. The figure of merit of the galvanometer is:

Order of the differential equation \(\frac{d}{d x}\left(\frac{d y}{d x}\right)^5=0\) is:

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues Water-soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreated in urine and cannot be stored in our body.
Deficiency of Scurvy disease leads to

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Which of the following microbe is harmful?

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. 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.
During anaerobic sludge digestion, bacteria produce the biogas. The composition of this biogas is -

Observe the figures and answer the question.

The spent slurry in bio-gas plant is used.

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is: