Missing letter puzzle 6

1. Which letter replaces the question mark?

2. Which letter replaces the question mark?

3. Which letter replaces the question mark?

4. Which letter replaces the question mark?

5. Which letter replaces the question mark?

Uniform circular motion

If the particle moves in the circle with a uniform speed, we call it a uniform circular motion. In this case, dv/dt = 0 and equation gives .

Thus, the acceleration of the particle is in the direction of , that is, towards the centre. The magnitude of the acceleration is α = ω²r.



Thus, if a particle moves in a circle of radius r with a constant speed v, its acceleration is v²/r directed towards the centre. This acceleration is called centripetal acceleration. Note that the speed remains constant, the direction continuously changes and hence the “velocity” changes and there is an acceleration during the motion.

The linear acceleration is .

This acceleration is directed towards the centre of the circle.

Non uniform circular motion: If the speed of the particle moving in a circle is not constant, the acceleration has both the radial and the tangential components. According to equation, the radial and the tangential acceleration are 

Thus, the component of the acceleration towards the centre is ω²r = - v²/r and the component along the tangent (along the direction of motion) is dv/dt. The magnitude of the acceleration is .

The direction of this resultant acceleration makes an angle α with the radius where .

Puzzle 6 [With Answers]

Puzzle 1: Pick the odd one out:

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

Answer: Happy

Explanation: All the words except "happy" contain three consecutive letters of the alphabet.

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

Puzzle 2: Fill in the missing pair:

BF   CH   ?   HO   LT

Answer: EK

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

Answer: FIM

Puzzle 4: Fill in the sequence:

5   6   9   15   ?   40

Answer: 25

Puzzle 5: Fill in the blanks:

3   3   5   4   4   ?   5

Answer: 3

Explanation: Number of letters in one, two, three, four, five, six, seven and so on.

Ordinary D.F equations, their order and degree

Differential equation: An equation containing an independent variable, dependent variable and differential coefficient of dependent variable with respect to independent variable is called a differential equation.

Order of a differential equation: The order of a differential Equation is the order of the highest order derivative appearing in the equation.

For example, in the equation , the order of highest order derivative is 2. So. It is a differential equation of order 2.

The equation  is of the order 32, It is a differential equation of order 2.

Degree of a differential equation: The degree of a differential equation is the degree of the highest order derivative, when differential coefficient are made free from radicals and fractions.

Example I: Consider the differential equation

In this equation the number of highest order derivative is 2. So it is a differential equation of degree 1.

Example II: Consider the differential equation

In this equation, the order of the highest order derivative is 3. And its power its power is 2. So it is a differential equation of order 3 and degree 2.

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.