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Integration of sin⁴x.

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Boyle's law.

Answer:- The law states that at constant temperature the volume of a given mass of gas is inversely proportional to its pressure.(i.e V ∝1/p)

First focal point.

Answer:- The first focal point is a point on the principal axis of the lens such that a beam of light passing through it is rendered parallel to the principal axis after refraction through the lens.

Why Sun 🌞 looks reddish during sunset & sunrise ?

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Answer:- During sunset & sunrise, light comes from sun have to travel more distance to reach us than the afternoon.Therefore more scattering of light occur during sunset and sunrise & the scattering phenomenon is more for that part of light which has less wavelength.Therefore during sunset & sunrise sun looks like red or orange (which has longer wavelength).

Integration of xln(1+x).

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Diffusion of gases.

Answer:- The property of the gases by virtue of which they intermix with one another irrespective of the law of gravitation is called diffusion.

Stoke's treatment.

Answer:- This law states that a light wave when gets reflected from a denser medium suffers a phase change of π or path change  λ/2.

Nodal points.

Answer:- Nodal points are points on the principal axis of the optical system where light rays, without refraction, intersect the optic axis.

Integration of tan^-¹x.

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Charle's law.

Statement:- It states that the volume of the given mass of gas increases or decreases by 1/273 of its volume at 0⁰C for every 1⁰C rise or fall of temperature at constant pressure.

Wave velocity.

Answer:- Velocity with which a wave propagates in a medium is called wave velocity.Wave velocity is also known as phase velocity because velocity of phase is same as that of velocity of wave.

Integration of ln[x+√(x²+a²)].

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What is orbital ?

Answer:- An orbital may be defined as a three dimensional space around the nucleus where the probability of finding the electron is maximum.

Refractive index.

Answer:- The refractive index of a medium is defined as the ratio of velocity of light in a vacuum to the velocity of light in the medium.Refractive index defined as above is called as absolute refractive index (n). (I.e n=c/v)

Solve, (2xy+e^y)dx+(x²+xe^y)dy.

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Le-Chatelier's principle.

Answer:- It states that if a system in equilibrium is subjected to a stress (i.e change of temperature, pressure or concentration), the equilibrium shifts in such a way so as to undo the effect of the stress imposed.

Mutual induction.

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Answer:- Mutual induction of two circuits is the property by virtue of which a current changing in the first results in the induction of an e.m.f in the second.

Coherence length.

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Answer:- The length of the wave train over which it may be assumed to have a fairly sinusoidal character and predictable phase is known as coherence length(l).

What is wedge ?

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Answer:- A thin film having zero thickness at one end and progressively increasing to a particular thickness at the other end is called a wedge.

Integration of sin³xcos³x.

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Intensive properties.

Answer:- The properties which depend only upon the nature of the substance and are independent of the amount of the substance  present in the system are called intensive properties.Examples of intensive properties are pressure, temperature, density, viscosity, surface tension, refractive index, electromagnetic force, chemical potential etc.

Young's double slit experiment.

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Answer:- It is an optical experiment which was performed by Thomas young, to demonstrate the interference phenomenon of light wave.Young passed the monochromatic light through a single slit and then directed the emerging light into two slits.Finally the light was received on a screen, where alternate dark and bright fringes are appear due to interference of light.

Integration of (sin6x+sin4x)/(cos6x+cos4x).

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Extensive properties.

Answer:- The properties which depend upon the amount of the substance or substances present in the system are called extensive properties. Examples of such  properties are mass, volume,heat capacity, internal energy, enthalpy, entropy, Gibbs free energy etc.

What is dimensional formula ?

Answer:- Dimensional formula of a physical quantity is the formula which tells us how and which of the fundamental units have been used for the measurement of that quantity. An equation written in the following manner is called dimensional equation. [M⁰L²T⁰].

Limiting reactant.

Answer:- The reactant which is completely used and determines the amount of product formed is called limiting reactant.

Empirical formula.

Answer:- It is defined as the collection of the symbols which represents the simplest whole number ratio of the atoms of same or different elements present in one molecule of the compound.

Equivalent mass.

Answer:- Equivalent mass of a substance is the number of parts by mass of a substance which combines with or displaces directly or indirectly 1.008 parts by weight of hydrogen, 8 parts by weight of oxygen or 35.5 parts by weight of chlorine.

Molecular mass.

Answer:- Molecular mass is the average relative mass of a molecule of an element or a chemical compound as compared to the mass of a carbon atom (¹²C) taken as 12 on the atomic mass unit scale.

Integration of tan⁶∅.

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Integration of cos³x/sin⁴x.

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Integration of (lnx)³.

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Solve, xdy/dx +2y =x²logx.

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Angle of repose.

Answer:- Angle of repose is the angle which an inclined plane makes with the horizontal so that a body placed over it just begins to slide of its own accord.

Friction.

Answer:- Whenever a body tends to slide over another's surface, an opposing force, called force of friction comes in to play.This force acts tangentially to the interface of two bodies.

Laws of refraction.

Answer:- ★ FIRST lAW:- The incident ray, the refracted ray & the normal to the interface at the point of incidence all lie in one plane & that plane is perpendicular to the interface separating the two media. ★ SECOND LAW:- The sine of the angle of incidence bears a constant ratio with the sine of the angle of refraction. (I.e sini/sinr = constant)

Laws of reflection.

Answer:- ★ FIRST LAW:- The incident ray, the reflected ray & the normal to the reflecting surface at the point of incidence, all lie in one plane & that plane is perpendicular to the reflecting surface. ★ SECOND LAW:- The angle of incidence is equal to the angle of reflection(i.e i=r).

Law of reciprocal or equivalent proportions.

Answer:- The law states that the ratio between the masses of two elements A and B which combine with the fixed mass of third element C, will be the same or a simple multiple of the ratio in which the elements A and B combine together.

The sources of light.

Answer:- The sun, the stars, lamps give off light.They are called luminous bodies.Other objects moon, mountains, trees etc. are non-luminous. They are visible only when they receive light from some luminous source and they send the light to our eyes.

Integration of ln(x²+1).

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Integration of x⁷lnx.

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Dalton's law of partial pressure.

Answer:- According to the kinetic theory of gases (which do not combine chemically) contains molecules of both gases which hit the walls of the vessel.The pressure of the gas is due to the bombardment of the molecules on the walls per unit area.Since the molecules do not exert any force of attraction on one another,the pressure exerted will be due to the hits of the molecules of each gas per unit area and total pressure will be the sum of these partial pressures.This is Dalton's law of partial pressure.

superposition of waves.

Answer:- When two or more waves overlap, the resultant displacement at any point and at any instant may be found by adding the instantaneous displacements that would be produced at the point by the individual waves if each were present alone.

Solve, (D⁴-3D²-4)y=5sin2x-e^-2x.

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Gibb's energy of a system.

Answer:- The maximum amount of energy available to a system that can be converted into useful work.In simple words, the Gibb's energy is the capacity of a system to do the useful work.It is denoted by the symbol G.

Aberrations.

Answer:- The departures of real images from the ideal images, in respect of the actual size, shape,and position, are called aberrations.

Solve, (D-1)³y=16e³^x.

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Optical active compounds.

Answer:- When plane polarized light is passed through a substance, it may or may not rotate the plane of the plane polarized light.The substance which does not rotate the plane of the plane polarized light is known as optically inactive compound, while a substance which rotates the plane of the plane polarized light is known as optically active compound.

Diffraction.

Answer:- It is a phenomenon of light in which light is bends round the edges of the obstacles on which it is encounter and it is occur when the dimension of obstacles are comparable with wavelength of light.

Solve, (ax+hy+g)dx+(hx+by+f)dy=0.

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Structure of H2O.

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Answer:- In H2O, the central atom is O. It can make two bonds with two hydrogen atoms due to the presence of two unpaired electrons in it.In the formation of H2O each of these electrons is shared by two hydrogen atoms. As a result the oxygen atom is surrounded by two shared pairs of electrons.Two lone pairs of electrons still remain in the valence shell.

Plane parallel film.

Answer:- A transparent thin film of uniform thickness bounded by two parallel surfaces is known as a plane parallel thin film.

Solve, (D²+1)y=2cosxcos3x.

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Electromeric effect.

Answer:- In case of compounds having a double or triple bond, the pair of π-electrons gets completely transferred to the more electronegative element under the influence of an attacking reagent.I.e complete transfer of a shared pair of electrons of a multiple bond to one of the bonded atoms under the influence  of the attacking reagent is known as the electromeric effect.

Spatial coherence.

Answer:- Spatial coherence refers to the continuity and uniformity of a wave in a direction of propagation.If the phase difference for any two fixed points in a plane normal to the wave is said to exhibit spatial coherence.

Solve,(D³-2D²-5D+6)y=e³^x.

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Steric hindrance.

Answer:- This effect was thought to be spatial effect brought into play by mechanistic interference between groups and is known as steric hindrance.Steric hindrance arises due to the geometry of the reactant molecule.

Fresnel's Biprism.

Answer:- Fresnel used a Biprism to show interference phenomenon.The Biprism consists of two prisms of very small refracting angles joined base to base.And it is also used for the determination of wavelength of monochromatic source.

Solve, (D³+D²+4D+4)y=0.

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Kapustinskii equation.

Answer:- The kapustinskii equation calculates the lattice energy for an ionic crystal, which is experimentally difficult to determine.It is named after Anatoli Fedorovich Kapustinskii.

Mechanical wave motion.

Answer:- It is possible only in material media (solids, liquids and gases) which possese inertia as well as elasticity.e.g water waves & Sound waves.

photo.

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Solve, (D³-7D²+10D)y=e²^x sinx.

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What is atrpoisomerism ?

Answer:- It has been found that some organic compounds are also optically active even though they do not contain any chiral carbon atom, are called atrpoisomerism.

Coherent waves.

Answer:- If two or more waves are in same phase or having a constant phase difference over a long distance and time then they are said to be coherent waves.

Madelung constant.

Answer:- The coefficient of coulombic force of attraction and repulsion in the Born equations is called Madelung constant.

Walden inversion.

Answer:- If an atom or a group is replaced by another atom or group in an optically active compound, then the product formed has different configuration as compared to the original one.In fact, the configuration gets inverted.It is called Walden inversion.

Solve,(D²+3D+2)y=4cos²x.

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Single refracting surface.

Answer:- A spherical surface which separates two media of different refractive indices is called single refracting surface.

Central atom.

Answer:- A central atom in a molecule, cation or anion is that atom which has maximum number of unpaired electrons, either in its ground state or excited state.

Aufbau principle.

Answer:- According to this principle“electrons are filled in various molecular orbitals in the increasing order of their energies”(,i.e molecular orbital with less energy is filled first.

Solve, (D³+3D²+3D+1)y=0.

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Solve,(D²-D-6)y=e^xcosh2x.

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Solve, (D²-6D+9)y=log2.

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Self induction.

Answer:- Self induction of a circuit is defined as the property of the circuit, by virtue of which it tends to oppose a change in the strength of current, through it, by inducing an e.m.f. in itself.

Magnetic field.

Answer:- Magnetic field, of any magnetic pole, is the region(space) around it in which its magnetic influence can be realised.

Microscope 🔬.

Answer:- These are used to see very small objects in magnified form which otherwise cannot be seen distinctly when placed close to the naked eye.

Longitudinal magnification.

Answer:- Longitudinal magnification, of a mirror, is defined as the size of the image to the size of object both measured along the direction of principal axis.

Tangent law.

Answer:- It is a relation which states the condition of equilibrium of a magnet subjected to two uniform magnetic fields at right angles to each other.

Solve, ylogydx+(x-logy)dy=0.

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Principle of Reversibility.

Answer:- It states that if a ray of light, after suffering a number of reflections and/or refractions has its path reversed, at any stage, it will retrace itself back to the source along the same path.

Meso compounds.

Answer:- These are defined as the compounds which contain two or more chiral carbon atoms and are optically inactive due to the presence of the plane of symmetry.The optical inactivity in meso compounds is due to internal compensation.In such compounds, the rotation due to one half of the molecule is cancelled by the rotation due to other half of the molecule in the opposite direction.The net rotation in meso compounds is zero.

Solve, (D²+1)y=sin3xcos2x.

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Rectilinear propagation of light.

Answer:- It is the tendency of light (or electromagn -etic waves) to propagate in a straight line without doing any deviation through a homogeneous medium which has the same refractive index throughout .

Merits of Bent's rule ?

Answer:- It is a useful tool in the inorganic and organic chemistry.For example it supplements the VSEPR interpretation of a large number of structures of non- metal fluorides. Hence, it should be used to answer wide range of questions on structure of molecules.

Solve, tanydy/dx+tanx=cosycos²x.

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Solve, (2x-y)dx=(x-y)dy.

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Wavefront.

Answer:- “Wavefront of a wave is defined as the locus of all the particles of the medium which vibrate in same phase and were disturbed at the same instant of time.”

Stereogenic centre.

Answer:- The carbon atom to which all the four atoms or groups attached are different is called asymmetric or chiral carbon atom.It is also called stereogenic centre.

What is aromaticity ?

Answer:- Aromaticity means aromatic character .Benzene and all other compounds which resemble benzene in their properties are called aromatic compounds.The property to exhibit aromatic character is called aromaticity.

Eyepiece.

Answer:- An eyepiece is the lens or combination of lenses used in an optical instrument through which eye views the image formed by the objective lens.

Solve, (D²+2D+5)y=sin2x.

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