Duduli

A warmhole is a theoretical concept in physics that suggests the existence of a shortcut or a tunnel through spacetime. It is a hypothetical connection between two separate regions of space or two different points in time. This idea is that a warmhole could create a shortcut, allowing  for faster travel between distant locations or even time travel.

A controlled chain reaction refers to a process in which a chain reaction, typically involving the release of energy, is managed and controlled to ensure it proceeds at a desired rate and does not lead to uncontrolled or catastrophic outcomes. Chain reactions are characterised by a self sustaining sequence of reactions in which the products of one reaction step initiate further reactions, creating a chain like effect. 

An atom can be excited to state higher than the ground state by one of the following methods (i) Due to collision with another atom during which part of kinetic energy is absorbed by the atom and can come back to the ground state in time ≈ 10-⁸ sec by the emission of a Photon. (ii) By making use of an electric field which may accelerate atomic ions till they have enough energies to excite atoms they come across during collisions.

Complex number can be written as z=x+iy , where x & y are real numbers, and i=√-1 . This form x+iy , is called the standard form of complex number. When graphing these we can represent them on a coordinate plane called the argand plane or complex plane.

Suppose p(n) is a proposition defined on the positive integer N i.e n€N Step-I (basis of induction) Show p(1) is true.(Generally)  If given  n≥a then show p(a) is true. Step-II (Induction hypothesis) Assume p(K) is true. where k≥a Step-III (Induction step) Show p(k+1) is true using p(k).

The unit step function u(t-a) is defined as follows u(t-a)={0  , when  t<a                             {1   , when t≥a I.e ★Laplace transform of unit step function is e^-as/s ★with the help of unit step functions, we can find the inverse transform of functions.

Activity of a radioactive substance may be defined as the rate at which the nuclei of its atoms disintegrate in the sample. Activity of radioactive sample at any time t is given as A=Aoe^-kt Where, K= radioactive decay constant             Ao=initial activity 

A nucleus in the excited state undergo transition to lower energy by directly transforming energy to atomic electron which is emitted. This process is called internal conversion.

Radioactive decay constant is defined as the reciprocal of time during which the no. of atoms of radioactive sample are reduce to 1/e times it's original value.

It states that a quantum state that exists for only a short time cannot have a definite energy. Mathematically,   ∆E.∆t≈h/2π Where, ∆E=uncertainty in energy            ∆t=uncertainty in time 

Not gate is a logic gate having one input and one output. It performs logical NOT operation. NOT operation is also known as negation or inversion or complementation operation. NOT gate is known as inverter because it inverts the input. The output of NOT gate is in state 1 only when the input is in state 0.

The excitation of an atom by any method from one state to another involves transfer of energy in quanta. This quanta either absorbed or emitted corresponds to some line in the spectrum of the atom. With the consideration Franck and Hertz  in 1914 performed the experiment using inelastic collision of accelerated electrons with atoms as a source of excitation. A direct demonstration of existence of discrete stationary states postulated by Bohr theory of atom was first provided by James Franck and Hertz.

When the electron in a hydrogen atom jumps from higher energy level to the lower energy level, the difference of energies of the two energy levels is emitted as a radiation of particular wavelength. It is called a spectral line.

As the name implies, “multi”, more than one, individual chips are interconnected. The active components that are contained in this kind of ics are diffused transistors or diodes. The passive components are the diffused resistors or capacitors on a single chip. These components are connected by metallised patterns. Hybrid ics are widely used for high power amplifier applications from 5W to more than 50W. Its performance is better than that of monolithic ics.

4 bit binary subtractor is a digital circuit which performs substraction of binary numbers in paralled form and produces results in parallel form. The substraction of two binary number can be done by adding the complement of the subtrahend to the minuend. The logic circuit of a 4 bit binary subtractor is shown in the figure The minuend bits at A and subtrahend bits of B are designated by subscripts from right to left with subscript 1, representing the lower bit. Ci is the input carry and C4 is the output carry. The output S generates the result bits. The entire circuit of 4 bit binary subtractor is enclosed within an IC. It has four terminals for minuend bits and four terminals for subtrahend bits and two terminals for carries input and output.

The mean (or average) life of a radioactive substance is defined as the ratio of sum of life time of all the radioactive atoms to the total number of such atoms present in it. Mean life=Total life time of all the atoms/total number of atoms 

Counters are sequential circuits that keep record of the clock pulses sent. Counter consists of a group of flip-flops. It has a characteristic internal sequence of states through which it passes if a series of clock pulses are applied to it. Ring counter is the most widely used shift register counter which is the basic ring counter as well as the twisted ring counter. MSI counters are of two types namely asynchronous counters and synchronous counters.

A wafer is a thin slice of semiconductor material, such as a crystalline silicon, used in electronics for the fabrication of integrated circuits. It is used in photovoltaics for conventional wafer-based solar cells. A wafer is also called a slice or substrate, wafer fabrication is a procedure composed of many repeated sequential processes to produce complete electrical or photonic circuits. Wafer are used in the production of radio frequency (RF) amplifiers, LEDS, Optical computer components, and CPUs for computers.

A black body is one which absorbs radiations of all wavelengths incident on it. It neither reflects nor transmit any of the incident radiation and therefore appear black whatever be the colour of incident radiation. When a black body is heated, it emits radiation, known as black body radiation.

Einstein explained photoelectric effect on the basis of planck's theory. It is the matter of common observation that electrons are emitted only when light is incident on the metal. Thus, the metal surface behaves like a potential barrier. So some energy require to cross the barrier. The minimum amount of energy required to come out from the surface of metals is called work function. Let Wo be the work function. An incident photon supplies whole of its energy hμ to the electron & the electron consumes some energy Wo against work function & comes out with the remaining energy as kinetic energy. 1/2 MV²max = hμ - hμ' This is the einsteins equation of photoelectric effect.

A moving particle is not associated with one wave but with a wave packet. A wave packet consists of a group waves. Each wave slightly different velocity and wavelength and wave packet is the result of superposition of individual waves.

If the two branches of the curve pass through the double point and the tangent to them are the point is real and coincident, then the double point is called cusp. Shown in the figure

If an algebraic curve passes through the origin, the equation of tangent or tangents at the origin is obtained by equating to zero the lowest degree terms in the equation of the curve.

Binary substraction using 2's component method is performed as follows (i) The 2's complement of the binary number to be subtracted is added to the number from which subtraction to be done. (ii) If the carry in the last position of the sum is 1 then it is dropped and the result is positive. (iii) If there is no carry in the last position of the sum then the 2's complement of the sum is the final result and it is negative. 

A nuclear reactor is a device based on controlled nuclear chain reaction wherein the nuclear energy produced is utilised for constructive purposes.

A function defined by f(x)=1/x is called the reciprocal function or rectangular hyperbola, with coordinate axis as asymptotes. The domain and range of f(x)=1/x is R-{0}. Since, f(x) is odd function, so its graph is symmetrical about opposite quadrants.

A function given by f(x)=x² is called the square function. The domain of square function is R and its range is R^+ U  {0} or [0,♾️). Clearly y=x², is a parabola. Since y=x² is an even function, so its graph is symmetrical about y-axis, shown as: