Riddle 11 [With Answers]

Puzzle 1: What kind of room has no doors or windows?

Answer: Mushroom

Puzzle 2: What kind of tree can you carry in your hand?

Answer: A Palm

Puzzle 3: Which word in the dictionary is spelled incorrectly?

Answer: Incorrectly

Puzzle 4: If you have me, you want to share me. If you share me, you haven't got me. What am I?

Answer: Secret

Puzzle 5: What gets broken without being held?

Answer: A promise

Voltage Source across Resistor

 

V(t) = V_m sin ωt

i(t) = I_m sin ωt

And P(t) = v(t) i(t)

P(t) = V_m sin ωt I_m sin ωt

Hence, average power is

It is clear that if current or voltage waveform has a frequency of 50 Hz then power waveform has a frequency of 100Hz.

Riddles 11

Riddle 1: What kind of room has no doors or windows?

Riddle 2: What kind of tree can you carry in your hand?

Riddle 3: Which word in the dictionary is spelled incorrectly?

Riddle 4: If you have me, you want to share me. If you share me, you haven't got me. What am I?

Riddle 5: What gets broken without being held?

First order and first degree differential equations and their geometrical interpretations

A first order and first degree differential equation involves the independent variable x (say), dependent variable y (say) so, it can be put in any one of the following forms:

dy/ dx = f(x, y) or f (x, y) = 0, or f(x, y) dx + g(x, y)dy = 0

Where f(x, y) and g(x, y) are functions of x and y.

Geometrical interpretation

The general from of a first order and first degree differential equation is f(x, y, dy/dx) = 0 … (i)

We know that the tangent of the direction of a curve in Cartesian rectangular coordinates at any point is given by dy/dx, so the equation in (i) can be known as an equation which establishes the relationship between the coordinates of a point and the slope of the tangent i.e., dy/dx to the integral curve at that point. Solving the differential equation given by (i) means finding those curves for which the direction of tangent at each point coincides with the direction of the field. All the curves represented by the general solution when taken together will give the locus of the differential equation. Since there is one arbitrary constant in the general solution of the equation of first order, the locus of the equation can be said to be made up of single infinity of curves.

Riddles 10 [With Answers]

Puzzle - 1:

A car has to carry an important person across the desert.

There is no petrol station in the desert and the car has space only for enough petrol to get it half way across the desert.

There are also other identical cars that can transfer their petrol into one another.

How can we get this important person across the desert?

Answer: We need 4 cars (including the car with the important person).

All 4 cars start full.

At 1/6th of the way, all cars are 2/3rds full. One car sacrifices itself and fills up two of the other cars. Two cars are now full, one is 2/3rds full. (An empty car is left behind.)

At 2/6th of the way, two cars are 2/3rds full. One car is one third full, and sacrifices itself to fill up one of the other cars. One car is now full, one is 2/3rds full. (An empty car is left behind.)

At half way, one car is 2/3rds full. One car is one third full, and sacrifices itself to fill the other car, which is now full and can make the other half of the journey.

Puzzle - 2:

Joey leaves his house in the morning to go to day camp.

Just as he is leaving his house he looks at an analog clock reflected in the mirror.

There are no numbers on the clock, so Joey makes an error in reading the time since it is a mirror image. Joey assumes there is something wrong with the clock and rides his bike to day camp.

He gets there in 20 minutes and finds that just as he gets there the day camp clock has a time that is 2 1/2 hours (2 hours and 30 minutes) later than the time that he saw in the mirror image of his clock at home.

What time was it when he got to day camp?

(The clock at camp and the clock at home were both set to the correct time.)

Answer: First subtract 20 minutes from 2 1/2 hours to compensate for his 20 minute bike ride to give a difference of 2 hours and 10 minutes.

To be a "Mirror Effect" it must be mirrored around 12 o'clock (when the hands are straight up), or around 6 o'clock (when the hands are pointing up and down), as we know he left in the morning, it must be 6 o'clock.

So, divide that 2 hours and 10 minutes by 2 and this will give you the center-point (65 minutes) for compensating for the mirror.

By adding that 65 minutes to 6 o'clock you get the time he left home (7:05), and the time he saw in the mirror (4:55).

Furthermore, by re-adding the 20 minutes from when he left (7:05), you get what time he got to camp (7:25).

Puzzle - 3:

In front of you are several long fuses.

You know they burn for exactly one hour after you light them at one end.

But the entire fuse does not burn at a constant speed. For example, it might take five minutes to burn through half the fuse and fifty-five minutes to burn the other half.

With your lighter and using these fuses, how can you measure exactly three-quarters of an hour of time?

Answer: Light both ends of one fuse.

At the same time light one end of a second fuse.

The first fuse will finish in half an hour.

At that point the second fuse will be half done (in time, not necessarily in distance) and you immediately light its other end. The second half hour will now take only quarter of an hour.

Total time: half an hour plus quarter of an hour equals three-quarters of an hour.

Puzzle - 4:

You have two straight lengths of wood.

How can you cut one of them so that one of the three pieces is the average length of the other two?

Answer: Put the two pieces end to end in a straight line

Then the average length of the three cut pieces has to be one third of this total length.

So we simply cut one third of the way along the longer piece.

Puzzle - 5:

A girl, a boy, and a dog start walking down a road.

They start at the same time, from the same point, in the same direction.

The boy walks at 5 km/h, the girl at 6 km/h.

The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn.

How far does the dog travel in 1 hour?

Answer: 10km. Because the dog's speed is 10 km/h.

Diazonium Salts - Methods of Preparation

The diazonium salts have the general formula RN⁺₂X⁻ where R stands for an aryl group and X^- ion may be Cl⁻, Br⁻, HSO⁻₄, BF⁻₄ etc.

Primary aliphatic amines form highly unstable alkyldiazonium salts.

Primary aromatic amines form arenediazonium salts which are stable for a short time in solution at low temperatures (273 - 278 K).

Preparation: Benzenediazonium chloride is prepared by the reaction of aniline with nitrous acid at 273-278K.

Nitrous acid is produced in the reaction mixture by the reaction of sodium nitrite with hydrochloric acid. The conversion of primary aromatic amines into diazonium salts is known as diazotisation.

Due to its instability, the diazonium salt is not generally stored and is used immediately after its preparation.