Thursday, 10 August 2017

Important Formulas - Area


Important Formulas - Area


Important Formulas - AreaPythagorean Theorem (Pythagoras' theorem)
right-angled triangleIn a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
c2=a2+b2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Length of the longest rod that can be placed in a box
of length l, breadth b and height h

=l2+b2+h2
Pi is a mathematical constant which is the ratio of a circle's circumference to its diameter. It is denoted by ππ3.14227
Sum of Interior Angles of a polygonSum of the interior angles of a polygon =180(n2) degrees where n = number of sides

Example 1:
Number of sides of a triangle =3.
Hence, sum of the interior angles of a triangle
=180(32)=180×1=180°

Example 2:
Number of sides of a quadrilateral =4.
Hence, sum of the interior angles of any quadrilateral
=180(42)=180×2=360°
If each of side of a rectangle or any two dimensional shape is increased by x%, its area is increased by (x2100+2x)%

If radius of a circle is increased by x%, its area is increased by (x2100+2x)%

Example 1
If each side of a triangle is doubled, what is the percentage increase in its area?

Here, each side is increased by 100%   (because each side is doubled)

percentage increase in its area
=(1002100+2×100)%=300%

Example 2
If circumference of a circle is increased by 50%, what is the percentage increase in its area?

Circumference of the circle is increased by 50%. Since circumference of the circle is 2πr, radius, r is increased by 50%.

percentage increase in its area

ENGLISH NOTES (IDIOMS)


1. A hot potato -   Speak of an issue (mostly current) which many people are talking about and which is usually dispute

2. Ball is in your court -   It is up to you to make the next decision or step

3. Burn the midnight oil - To work late into the night,alluding to the time before electric lighting.

4. Can't judge a book by its cover - Cannot judge something primarily on appearance.

5. Don't put all your eggs in one basket - Do not put all your resources in one possibility.

6. keep something at bay - Keep something away.

7. Last straw - The final problem in a series of problems.

8. Not playing with a full deck - Someone who lacks intelligence.

9. Take with a grain of salt - This means not to take what someone says too seriously.

10.Wouldn't be caught dead - Would never like to do something.

ENGLISH CLASS,


ADJECTIVE
Rule-1 Adjective of quantity like much, LITTLE, ENOUGH, SUFFICIENT, WHOLE, etc. must be used with uncountable nouns only as they express quantity and not number. 
Ex.-Many (not much) boys are absent from the class today. 
Many (not much) boys failed in the examination. 
Rule-2 The use of ‘few’, ‘a few’ and ‘the few’ should be used with care they denote number. Few means ‘NOT MANY’.
Few has negative meaning 
A few means ‘SOME AT LEAST’ 
The few means ‘WHATEVER THERE IS’.

Ex. I read few books.
I Read a few books.
I Read the few books I had.
A few men are true from fault. (Incorrect)
Few men are true from fault. (Correct)
Rule-3 Use of little, a little, the little 
Little means ‘hardly any’ in quantity. 
Ex.-He had little money
There is little water in the bottle 
There is a little hope of his recovery (Incorrect)
There is little hope of his recovery (Correct)

A little means ‘Some’ in quantity if not much. 
Ex.-Little knowledge is a dangerous thing. (Incorrect)
A little knowledge is a dangerous thing.(correct) 
He had a little money. 
There is a little water in the bottle. 

The little means ‘not much in quantity but all that is’. 
Ex.-I spent the little money I had. 
 little water that is in the bottle may be used for the patient. (Incorrect)
A little water that is in …………….. (Correct)
Rule-4 Adjective of number must be used only with the countable nouns and not with uncountable as they indicate number and not quantity. 
Ex-I have taken many milk today. (Incorrect)
I have taken much milk today. (Correct)

Do not drink so many water. (Incorrect)
Do not drink so much water. (Correct)
Rule-5 Some, All, Any, No. Most etc. may be used both as adjectives of number and Adjectives of quantity as they can express number as well as quantity. 
Ex.-There are no boys in the class (Adj. of Number)
There is no milk in the pot. (Adj. of quantity)

All big machines are imported from foreign countries. (Adj. of number)
All the sugar was thrown into the sea. (Adj. of Quantity)

Give me some water. (Adj. of Quantity)
Some of these students are excellent. (Adj. of Number)
Rule-6 the comparative adjectives, ending with like superior, inferior, senior, junior,  prior, anterior, posterior, exterior etc. Take ‘to after them and not ‘than’.
Ex.-He is senior than me. (Incorrect)
He is senior to  me. (Correct)

Health is preferable than wealth. (Incorrect)
Health is preferable to wealth.  (Correct)
Rule-7 Double comparative adjectives or double superlative adjectives must not be used. 
(Incorrect) He is more senior than me. 
(Correct) He is senior to me.

Milk is more preferable than tea. (Incorrect)
Milk is preferable to tea. (Correct)

Ashoka was the most strongest  of the kings. (Incorrect)
Ashoka was the strongest of the kings. (Correct)
Rule-8 Comparative degree must be used when the comparison is between two persons of things and superlative degree when the comparison is among more than two things. 
Ex.-Who is the tallest of these two brothers ? (Incorrect)
Who is taller of these two brothers ? (Correct)

He is wise of all students in the class. (Incorrect)
He is the wisest of all students in the class. (Correct)
Rule-9 The comparative ending in ‘er’ is not used when we compare two qualities in the same person or thing. In that case we use ‘more’ before the Adjective. 
Ex.- Ram is braver than wise. (Incorrect)
Ram is more brave than wise (Correct)
Rule-10 Use of (Later, Latter; latest, last)
Later and Latest – shows time
Latter and last – shows position

Ex.-He latter refused to come (Incorrect)
He later refused to come. (Correct)

The later part of the novel is not clearly written (Incorrect)
The latter part of the novel is not clearly written . (Correct)
Rule-11 Use of (farther, further; farthest, furthest) 
Farther, Farthest - denote distance 
Further, Furthest - next, also (position)

Ex.-After this he made no farther statement. (Incorrect)
After this he made no further statement. (Correct)

Delhi is farther from Haridwar than Roorkee. 
Don’t make further delay. 
Rule-12 Before superlative adjectives articles ‘THE’ must (always) placed. 
Ex.-He is the best boy of the class. 
She is the most intelligent girl. 
Rule-13 Use of (Nearest, next)
Nearest denotes distance. 
Next denotes position. 

Ex.-He was sitting next to me. 
Patna junction is the nearest to my house. 

This is the next post-office to my house. (Incorrect)
This is the nearest post-office to my house. (Correct)
Rule-14 Use of (Elder, older; Eldest, oldest)
Elder and eldest – are used of members of the same family.
Older and oldest are used for persons or things. 

Elder takes ‘To’ after it while older takes ‘than’ 
Ex.-I have an older brother (Incorrect)
I have an elder brother (Correct)

Mohan is the eldest boy in the town. (Incorrect)
Mohan is the oldest boy in the town. (Correct)

Rule-15 Use of less and fewer 
Less - Quantity 
Fewer - Number 
Ex.-There is fewer sugar in your tea than in mine. (Incorrect)
There is less sugar in your tea than in mine. (Correct)
He has less money than I.

Rule-16 Some adjectives like (Perfect, Ideal, Full, Chief, Unique, Complete, Infinite, Extreme, Entire, Universal, Empty, Impossible, Unanimous, square, sound etc. are not compared as they express meaning which do not admit of any variation of degrees. 
Ex.-This achievement was most unique. (Incorrect)
His achievement was unique. (Correct) 

Your knowledge is most perfect. (Incorrect)
Your knowledge is perfect (Incorrect)

Rule-17 When a comparison is introduced and has ‘ANY’ after it, the things compared must always be excluded from the class of things with which it is compared, by using ‘OTHER’
Ex.-London is larger than any city in England. (Incorrect)
London is larger than any other city in England (Correct)

Ram is cleverer than any student in his class (Incorrect)
Ram is cleverer than any other student in his class. (Correct)

The tiger is as swift as any animal.
The tiger is as swift as any other animal. 

Rule-18 ‘Each’ is used to indicate a limited number and ‘EVERY’ to denote an unlimited number  in selection or choice. 
Ex.-Everyone of the two boys was given a prize. (Incorrect)
Each one of the two boys was given a prize (Correct)

He came to see us Each day. (Incorrect)
He came to see us Every day. (Correct)

Rule-19 "Some" is used in the affirmative sentence "any" is used in negative and interrogative  sentence. 
I don’t want some chocolates. (Incorrect)
I don’t want any chocolates (Correct)

I will have any tea. (Incorrect)
I will have some tea. (Correct)

Did you go somewhere last night ?
Did you go anywhere last night ? 
Rule-20 What’s the Correct Order for Multiple Adjectives in a sentence?
When you list several adjectives in a row, there’s a specific order they need to be written or spoken. Native speakers of English tend to put them in the correct order naturally, but if you’re learning English, you’ll have to memorize the order. It goes like this:
Before the adjectives you will normally have the Determiner.

1.Determiner: The determiner tells us if the noun is singular or plural, definite or indefinite
a, an, the, my, your, four, those, some etc

2.Quantity or number: 

3.Quality or opinion: Explains what we think about something. This is usually our opinion, attitude or observations. These adjectives almost always come before all other adjectives.
beautiful, boring, stupid, delicious, useful, lovely, comfortable

4.Size: Tells us how big or small something is.
big, small, tall, huge, tiny

5.Shape / Weight / Length: Tells about the shape of something or how long or short it is. It can also refer to the weight of someone or something.
round, square, circular, skinny, fat, heavy, straight, long, short,

6.Condition: Tells us the general condition or state of something
broken, cold, hot, wet, hungry, rich, easy, difficult, dirty

7.Age: Tells us how old someone or something is.
old, young, new, ancient, antique

8. Colour: The colour or approximate colour of something.
green, white, blue, reddish, purple

9.Pattern: The pattern or design of something.
striped, spotted, checked, flowery

10.Origin: Tells us where something is from.
American, British, Italian, eastern, Australian, Chilean

11.Material: What is the thing made of or constructed of?
gold, wooden, silk, paper, synthetic, cotton, woolen

12.Purpose/Qualifier/Use: What is it for? These adjectives often end in –ing.
sleeping (bag), gardening (gloves), shopping (bag), wedding (dress)
If you look at the examples above, you can ask… what are the gloves used for? (gardening) What is the bag used for? (shopping)

And after these  adjectives we have the…
13.Noun: The person or thing that is being described

This is the correct order for adjectives that come directly before a noun, and they are separated by commas.

Ex- My beautiful, big, circular, antique, brown, English, wooden coffee table was broken in the move.

If the adjectives come after the verb “be” as the complement, then the qualifier will stick with the noun at the beginning of the sentence. The adjectives in the complement are separated by commas with the final two being separated by “and.”
For example-
My coffee table is beautiful, big, circular, antique, brown, English and wooden.

Ex- I love that really big old green antique car that always parked at the end of the street. 
Ex- a wonderful old Italian Car.(opinion-age- origin) 
A big square blue box. (size -shape- color) 
A disgusting pink plastic ornament. (opinion- color- material)
I bought a pair of black leather.  (color-material)