A Television transmitting antenna is 84m tall. How much service area can it cover, if the receiving antenna is at the ground level?

In a p-n junction under equilibrium:

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to the

Match List-I with List-II

List-I	List-II
(A) AC generator	(I) Michael Faraday
(B) Polarity of induced emf	(II) Foucault
(C) Electromagnetic Induction	(III) Nicola Tesla
(D) Eddy Current	(IV) Heinrich Friedrich Lenz

Choose the correct answer from the options given below:

The magnetic flux linked with a coil at any instant t is given by \( \Phi = (4t^3 - 3t^2 + 2t + 5) \text{ Wb} \). The emf induced in the coil at \( t = 3 \text{ s} \) is

If \( +\sigma \) and \( -\sigma \) are the uniform surface charge densities of two parallel infinite thin plane sheets then the net electric field at the mid point of the two sheets will be given by (Where \( \epsilon_0 \) is the permittivity of free space, where the sheets are kept)

The ratio of total energy to the kinetic energy of an electron in a Bohr orbit of the hydrogen atom is

The corner points of the bounded feasible region determined by the system of linear constraints are \((0,8),(4,4)\), \((12,12),(0,20)\). Let \(z=p x+q y\), where \(p, q>0\). Condition on \(p\) and \(q\) so that the maximum of \(z\) occurs at both the points \((12,12)\), \((0,20)\) is

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
Question: Formaldehyde on reaction with benzaldehyde in basic medium gets converted 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.
Select the chemical substances which are produced by some microbes and they can kill or prevent growth of other microbes :

Answer the question on basis of passage given below :
A ketone \([A]\) which undergoes haloform reaction gives compound \([B]\) on reduction. Compound \([B]\) on heating with sulphuric acid gives compound \([C]\) which forms monozonide \([D]\). The compound [D] on hydrolysis in the presence of zinc dust gives compound [E].
Compound [E] on oxidation gives \(C _2 H _4 O _2\) [F]
The boiling point of \([ A ]\) observed is exceptionally high because of :

The particular solution of the differential equation \(\cos \left(\frac{d y}{d x}\right)=a,(a \in R ) ; y=2\) at \(x=0\) is given by

Shown below is the graph of parabola \(y^2=x\), the area (in sq. units) of the shaded region is: