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Let tanx /2 = tany /3 = tanz /5 = k

so tan²x +tan² y+ tan² z = 4k² + 9k² +25k²

or, tan²x +tan² y+ tan² z = 38k² -------(1)

now tan z = tan[180 - (x+y)] = -tan(x+y)

or tanz = (- tanx - tany) / (1 - tanx.tany)

or 5k = (-5k) / (1-6k² )

or, 1-6k² = -1

or, k² = 2/6 = 1/3 ----(2)

From (1) and (2)

tan²x +tan² y+ tan² z = 38*1/3 = 38/3

The question is incomplete for the reason that it doesn't mention the no. of boys or girls among 24 persons. The question demands more conditons to be given so that it is meaningful.

In the mathematical fields of multilinear algebra and differential geometry, a tensor is a multilinear function. In physics and engineering, the same term usually means what a mathematician would call a tensor field: an association of a different (mathematical) tensor with each point of a geometric space, varying continuously with position.

For example, the Euclidean inner product (dot product) ? a real-valued function of two vectors that is linear in each - is a mathematical tensor. Similarly, on a smooth curved surface such as a torus, the metric tensor (field) essentially defines a different inner product of tangent vectors at each point of the surface. Just as a linear transformation can be

Scalar and vector quantities are also tensors of rank 0 and 1 respectively.

The rank of a particular tensor is the number of array indices required to describe such a quantity. For example, mass, temperature, and other scalar quantities are tensors of rank 0;

but force, momentum and other vector-like quantities are tensors of rank 1. The novel aspects of tensor theory are seen from rank 2 onwards.

No, there is no concept like threshhold intensity for photoelectric effect to occur. The only criteria is threshold frequency of photons with non-zero intensity

For light to be polarized due to reflection use the relation

tan

_p=

= refractive index of water

No, what you infer as the cause of Magnetic field Reversal is not true. Ofcourse your conclusion & approach is very scientific. But is not the case exactly.

Magnetic field reversal or geomagnetic reversal

Based upon the study of lava flows of basalt throughout the world, it has been proposed that the Earth's magnetic field reverses at intervals, ranging from tens of thousands to many millions of years, with an average interval of approximately 250,000 years. The last such event is theorized to have occurred some 780,000 years ago.

There is no clear theory as to how the geomagnetic reversals might have occurred. But some of the proposed ones are:

1) Some scientists have produced models for the core of the Earth wherein the magnetic field is only quasi-stable and the poles can spontaneously migrate from one orientation to the other over the course of a few hundred to a few thousand years.

2) Other scientists propose that the geodynamo first turns itself off, either spontaneously or through some external action like a comet impact, and then restarts itself with the magnetic "North" pole pointing either North or South. Regardless of the cause, when magnetic "North" reappears in the opposite direction this is a reversal, whereas turning off and returning in the same direction is called a geomagnetic excursion.

3) One theory does contend that the core of the Earth is not iron but much denser atoms. Nuclear reactions as replicated in a fast breeder reactor are suggested to take place and this accounts for the change in the Earth's magnetic field.

The Compton scattering equation is:

$lambda_2 = rac{h}{m_e c}(1-cos{ heta}) + lambda_1$

where

1

is the wavelength of the photon before scattering,

2

is the wavelength of the photon after scattering,

m_e is the mass of the electron,

h/(m_ec) is known as the Compton wavelength,

is the angle by which the photon's heading changes,

h is Planck's constant, and

c is the speed of light.

Here

is 180 degrees.

Take m_eor m as mass of electron. Substitute the values and get results.

The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess queen's moves.

Constructing a solution

There is a simple algorithm yielding a solution to the n queens puzzle for n = 1 or any n ? 4:

Divide n by 12. Remember the remainder (it's 8 for the eight queens puzzle).
Write a list of the even numbers from 2 to n in order.
If the remainder is 3 or 9, move 2 to the end of the list.
Write the odd numbers from 1 to n in order, but, if the remainder is 8, switch pairs (i.e. 3, 1, 7, 5, 11, 9, ?).
If the remainder is 2, switch the places of 1 and 3, then move 5 to the end of the list.
If the remainder is 3 or 9, move 1 and 3 to the end of the list.
Place the first-column queen in the row with the first number in the list, place the second-column queen in the row with the second number in the list, etc.

For n = 8 this results in the solution shown above. A few more examples follow.

14 queens (remainder 2): 2, 4, 6, 8, 10, 12, 14, 3, 1, 7, 9, 11, 13, 5.
15 queens (remainder 3): 4, 6, 8, 10, 12, 14, 2, 5, 7, 9, 11, 13, 15, 1, 3.
20 queens (remainder 8): 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 3, 1, 7, 5, 11, 9, 15, 13, 19, 17.

Solutions to the eight queens puzzle

The eight queens puzzle has 92 distinct solutions. If solutions that differ only by symmetry operations (rotations and reflections) of the board are counted as one, the puzzle has 12 unique solutions.

Dear ayush,

You raised a very genuine doubt. Thanks for appriciating the solution however. Here the '=' sign in the equation throughout means the set at LHS is equal to (remember its not ''equivalent to'') the set at RHS.

I suppose you agree on this point and the doubt is eliminated.

Here since we are only interested in digits at units place, so to find the digit at units place for a given series we need to carry sum of digits at units place only and will retain the digit at units place eventually.

Further keep in mind that

Digit at units place for 1! = 1

Digit at units place for 2! = 2

Digit at units place for 3! = 6

Digit at units place for 4! = 4

Digit at units place for 5! = 0

Digit at units place for 6! = 0

Digit at units place for 7! = 0,

and will be zero for n!, where n >4

So, a₈= digit at units place of the number (1+2+6+4) = 3

Similarly a₉= 3, .... a₁₆= 3

or a₈ + a₉ + a₁₀ +...+a₁₆= 3 + 3 + ....(nine times) = 27

The total no. of combinations of 2n different things taken any one or more at a time is given by

²ⁿC_1⁺²ⁿC_{2 ⁺}²ⁿC_3⁺²ⁿC_{4 ^{+... +}}²ⁿC_{2n ⁼}2²ⁿ- 1 .......(1)

Similarly, the total no. of combinations of n different things taken any one or more at a time is given by

ⁿC_1⁺ⁿC_{2 ⁺}ⁿC_3⁺ⁿC_{4 ^{+... +}}ⁿC_{n ⁼}2ⁿ- 1 .......(1)

Further it is Given that

(2²ⁿ- 1)/(2ⁿ- 1) = 65/1

let x = 2ⁿ

therefore, (x²- 1)/(x- 1) = 65/1

or x + 1 = 65

or x = 64

or 2ⁿ= 64

or n = 6

I guess the problem is clear and understandable now

HYDRAULIC PRESSURE

pressure applied to any part of a confined fluid transmits to every other part with

no loss. The pressure acts with equal force on all equal areas of the confining walls

and perpendicular to the walls. This is Hydraulic pressure.

GUAGE PRESSURE

Gauge pressure is referenced against ambient air pressure, so it is equal to absolute

pressure minus atmospheric pressure.

In general both are two different things.

ELECTRIC potential energy is due to the presence of charge or electric field in which the sphere is placed.

Whereas total energy of the sphere includes electric potential energy as well as kinetic energy (if any) of the sphere.

Further the difference may arise in context to a particular question.

An electrical generator is a device that converts mechanical energy to electrical energy, generally using electromagnetic induction.

There is a difference of commutator in ac and dc generator.

AC generator is without commutator.

DC generator is with commutator.

Please click on the following link to view animation of ac and dc generator

http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/generatorengl.htm

The frictional force always opposes the motion of the body.

Keeping this in mind take direction of frictional force to be opposite to the directionof motion of the body. No matter whether it is translational motion or rotational the direction of resistive/frictional force will always be in the opposite direction.