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Friday, May 26, 2017

Puzzles 6


Puzzle 1: Pick the odd one out:

Crabcake, Laughing, Calmness, Canopy, Stupid, Hijack, First, Deft, Happy

Puzzle 2: Fill in the missing pair:

BF   CH   ?   HO   LT

Puzzle 3: If BDG is equal to CFJ, then find the value of EGJ

Puzzle 4: Fill in the sequence:

5   6   9   15   ?   40

Puzzle 5: Fill in the blanks:

3   3   5   4   4   ?   5

Nucleic Acids

Definition:
The particles in nucleus of a cell, responsible for heredity, are called chromosomes which are made up of proteins and nucleic acids.
Nucleic acids are long chain polymers of nucleotides, so they are also called polynucleotides.
Examples: Deoxyribonucleic acid (DNA) & Ribonucleic acid (RNA).

Chemical Composition of Nucleic Acids:
Each nucleotide has three components: a 5 - carbon sugar, a phosphate group, and a nitrogenous base.
In DNA molecules, the sugar moiety is β - D - 2 - deoxyribose where as in RNA molecule, it is β -  D - ribose.
DNA contains four bases viz. adenine (A), guanine (G), cytosine (C) and thymine (T).
RNA also contains four bases, the first three bases are same as in DNA but the fourth one is uracil (U).

Structure of Nucleic Acids:
A unit formed by the attachment of base to 1’ position of sugar is known as nucleoside, the sugar carbons are numbered as 1’, 2’, 3’, etc. in order to distinguish these from bases. When nucleoside is linked to phosphoric acid at 5’ - position of sugar moiety we get a nucleotide.
Nucleotides are joined together by phosphodiester linkage between 5’ and 3’ carbon atoms of pentose sugar.
A simplified version of nucleic acid chain is as shown below.
Information regarding the sequence of nucleotides in the chain of nucleic acid is called primary structure. Nucleic acids have a secondary structure also.
James Watson and Francis Crick gave a double strand helix structure for DNA. Two nucleic acid chains are wound about each other and held together by hydrogen bond between pairs of bases.
These are complementary to each other because the hydrogen bonds are formed between specific pairs of bases.

DNA Fingerprinting:
Every individual has unique fingerprints.
A sequence of bases on DNA is also unique for a person and information regarding this is called DNA fingerprinting.
It is same for every cell and cannot be altered by any known treatment.

Uses of DNA finger printing:
i) In forensic laboratories for identification of criminals.
ii) To determine paternity of individual
iii) To identify racial groups to rewrite biological evolution.

Biological functions of Nucleic acids:
DNA is the chemical basis of heredity and may be regarded as the reserve of genetic information.
DNA is responsible for maintaining the identity of different species of organisms over millions of years.
A DNA is capable of self-duplications during cell division and identical DNA strands are transferred to daughter cells.
Nucleic acids are responsible for protein synthesis in the cell.

Thursday, May 25, 2017

Logic Puzzles 5 [With Answers]

Puzzle-1:
You work at a fruit factory. 
There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges. 
And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges".
But the labeling machine has gone crazy and is now labeling all boxes incorrectly.
If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?

Answer: Take a piece of fruit from the "apples and oranges" crate. If it's an apple then you know that is the "apples" crate since ALL THE CRATES ARE LABELED INCORRECTLY. This means the crate marked "apples" must be "oranges" and the crate marked "oranges" must be "apples and oranges".

Puzzle-2:
A man is caught on the King's property. He is brought before the King to be punished.
The King says, "You must give me a statement. If it is true, you will killed by lions. If it is false, you will be killed by trampling of wild buffalo."
But in the end, the King has to let the man go.
What was the man's statement?

Answer: "I will be killed by trampling of wild buffalo."
If you think about it carefully: the King can't say it is true, because if so the man should be killed by the lions. But if he is killed by the lions, then his statement would be false, and so should have been trampled by buffalo.
So the King can't tell if it is a lie or truth, so decides to just let him go.

Puzzle-3:
A man works on the 10th floor and always takes the elevator down to ground level at the end of the day.
Yet every morning, he only takes the elevator to the 7th floor and then walks up the stairs to the 10th floor, even when in a hurry.
But he will go all the way to the 10th floor when others are in the elevator with him or on a rainy day.
Why?

Answer: He is too short to reach the "10" button.
But when others are with him, he can ask them to push the button for the 10th floor. 
And on a rainy day he has an umbrella, so he can push the button using that.

Puzzle-4:
There are five gears connected in a row, the first one is connected to the second one, the second one is connected to the third one, and so on.
How much faster would the last gear be if the second gear was twice the size of the first gear, and all the other gears were the same size as the first gear?
Answer: The last gear would be the same speed.

Puzzle-5:
There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy.
The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.
Alex says: "Cody is a knave."
Brook says: "Alex is a knight."
Cody says: "I am the spy."
Who is the knight, who the knave, and who the spy?

Answer:
Alex is a Knight
Brook is a Spy
Cody is a Knave
Brook is not the knight, since if he is, then Alex would also be the knight.
Cody is not the knight, since his statement would then be a lie. 
Therefore Alex is the knight. Hence Cody is the knave, and Brook is the spy.

Total Internal Reflection

When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back in to the same medium and partly refracted to the second medium. This reflection is called the internal reflection.

When a ray of light enters from a denser medium to a rarer medium. It bends away from the normal, for example, the ray AO₁B in figure. The incident ray AO₁ is partially reflected (O₁C) and partially transmitted (O₁B) or reflected, the angle of refraction (r) being larger than the angle of incidence (i) As the angle of incidence increases, so does the angle of refraction, till for the ray AO₃. The angle of refraction is π/2. The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media. This is shown by the ray AO₃D in figure. If the angle of incidence is increased still further (e.g., the ray AO₄), refraction is not possible, and the incident ray is totally reflected.
This is called total internal reflection, when light gets reflected by a surface, normally some fraction of it gets transmitted. The reflected ray, therefore, is always less intense than the incident ray, howsoever smooth the reflecting surface may be. In total internal reflection, on the other hand, no transmission of light takes place.

The angle of incidence corresponding to an angle of refraction 90⁰ say AO₃N is called the critical angle (ic) for the given pair of media. We see from Snell’s law  that if the relative refractive index is less than one then, since the maximum value of  is unity, there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that sin ic = n21.

Wednesday, May 24, 2017

Logic Puzzles 5

Puzzle-1:
You work at a fruit factory. 
There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges. 
And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges".
But the labeling machine has gone crazy and is now labeling all boxes incorrectly.
If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?

Puzzle-2:
A man is caught on the King's property. He is brought before the King to be punished.
The King says, "You must give me a statement. If it is true, you will killed by lions. If it is false, you will be killed by trampling of wild buffalo."
But in the end, the King has to let the man go.
What was the man's statement?

Puzzle-3:
A man works on the 10th floor and always takes the elevator down to ground level at the end of the day.
Yet every morning, he only takes the elevator to the 7th floor and then walks up the stairs to the 10th floor, even when in a hurry.
But he will go all the way to the 10th floor when others are in the elevator with him or on a rainy day.
Why?

Puzzle-4:
There are five gears connected in a row, the first one is connected to the second one, the second one is connected to the third one, and so on.
How much faster would the last gear be if the second gear was twice the size of the first gear, and all the other gears were the same size as the first gear?

Puzzle-5:
There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy.
The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.
Alex says: "Cody is a knave."
Brook says: "Alex is a knight."
Cody says: "I am the spy."
Who is the knight, who the knave, and who the spy?

Integral Function and its Properties

Let f(x) be a continuous function defined on [a, b], then a function φ(x) defined by  for all x ϵ [a, b] is called the integral function of the function f(x).


Property I: The integral function of an integrable function is always continuous.

Property II:  if φ(x) is differentiable on (a, b) and φ’(x) = f(x) for all x ϵ (a, b).

Property III: The integral function of an odd function is an even function.

If f(x) is an odd function, then  is an function.

Example: Find the greatest value of  in the interval [5π/3, 7π/4]

Solution:  We have,


F’(x) = 6 cosx - 2sinx

For all x ϵ [5π/3, 7π/4], we have

cos x > 0 and sin x < 0

F(x) = 6 cosx - 2sinx > 0

F(x) is an increasing function on [5π/3, 7π/4]

F(x) attains greatest value at x = 7π/4.

Hence,

Greatest value = F (7π/4)


= 3√3 - 2√2 - 1.