Number | Cube |
2 | 8 |
3 | 27 |
4 | 64 |
5 | 125 |
6 | 216 |
7 | 343 |
8 | 512 |
9 | 729 |
Cat Preparation
Sunday, 29 April 2012
Squares
n
|
n^2
|
13
|
169
|
14
|
196
|
15
|
225
|
16
|
256
|
17
|
289
|
18
|
324
|
19
|
361
|
20
|
400
|
21
|
441
|
22
|
484
|
23
|
529
|
24
|
576
|
25
|
625
|
26
|
676
|
27
|
729
|
28
|
784
|
29
|
841
|
Learning common formulae - fractions/reciprocals
1/n
|
1/n as %
|
1/1
|
100
|
1/2
|
50
|
1/3
|
33.33
|
1/4
|
25
|
1/5
|
20
|
1/6
|
16.66
|
1/7
|
14.28
|
1/8
|
12.5
|
1/9
|
11.11
|
1/10
|
10
|
1/11
|
9.09
|
1/12
|
8.33
|
1/13
|
7.69
|
1/14
|
7.14
|
1/15
|
6.66
|
1/16
|
6.25
|
1/17
|
5.88
|
1/18
|
5.55
|
1/19
|
5.26
|
Monday, 30 May 2011
Divisibility Tests for 7,13,17 & 19
Divisibility test of 7
1).Double the last digit (digit at the rightmost place) and subtract it from the number left (excluding the last digit). If this number is divisible with 7 then the original number is divisible by 7.
This procedure can be followed as many times as required (until the number is reduced to 2 digit number). Then the number so obtained can be checked whether it is divisible by 7 or not. If the number so obtained is divisible by 7 then the original number is divisible by 7 and if not then original number is not divisible by 7.
E.g.-
Consider the number 1057.
Now the last digit is 7. On doubling it we get 14.
On subtracting it from 105 we get 91.
Now it can be seen that 91 is divisible by 7 so the original number is divisible by 7.
(It can further be simplified by doubling 1 and subtracting it from 9 and thus we get 7 which is divisible by7.)
——————XXXXXXXX———-
Divisibility test of 13
To check whether a number is divisible by 13 we follow the procedure as follows:
1). Multiply the last digit with 4 and add it to the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 13 or not.
If the 2-digit number so obtained is divisible by 13 then the original number is divisible by 13 otherwise not.
E.g.-
Let us consider the number 195.
Now the last digit is 5 and on multiplying it with 4 we get 20.
Now on adding this with the remaining number (i.e. 19) we get 39. Now as 39 is divisible by 13 therefore the original
number id divisible by 13.
———————XXXXXXXXXXX————
Divisibility test of 17
To check whether a number is divisible by 17 we follow the procedure as follows:
1). Multiply the last digit with 5 and subtract it from the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 17 or not.
If the 2-digit number so obtained is divisible by 17 then the original number is divisible by 17 otherwise not.
E.g.-
Let us consider the number 221.
Now the last digit is 1 and on multiplying it with 5 we get 5.
Now on subtracting 5 from the remaining number (i.e. 22) we get 17. Now as 17 is divisible by 17 therefore the original number id divisible by 17.
——————XXXXXXXXXX——————–
Divisibility test of 19
To check whether a number is divisible by 19 we follow the procedure as follows:
1). Multiply the last digit with 2 and add it to the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 19 or not.
If the 2-digit number so obtained is divisible by 19 then the original number is divisible by 19 otherwise not.
E.g.-
Let us consider the number 209.
Now the last digit is 9 and on multiplying it with 2 we get 18.
Now on adding th18 with the remaining number(i.e. 20) we get 38. Now as 38 is divisible by 19 therefore the original number id divisible by 19.
Number Multiply last digit -/+
7 2 -
13 4 +
17 5 -
19 2 +
1).Double the last digit (digit at the rightmost place) and subtract it from the number left (excluding the last digit). If this number is divisible with 7 then the original number is divisible by 7.
This procedure can be followed as many times as required (until the number is reduced to 2 digit number). Then the number so obtained can be checked whether it is divisible by 7 or not. If the number so obtained is divisible by 7 then the original number is divisible by 7 and if not then original number is not divisible by 7.
E.g.-
Consider the number 1057.
Now the last digit is 7. On doubling it we get 14.
On subtracting it from 105 we get 91.
Now it can be seen that 91 is divisible by 7 so the original number is divisible by 7.
(It can further be simplified by doubling 1 and subtracting it from 9 and thus we get 7 which is divisible by7.)
——————XXXXXXXX———-
Divisibility test of 13
To check whether a number is divisible by 13 we follow the procedure as follows:
1). Multiply the last digit with 4 and add it to the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 13 or not.
If the 2-digit number so obtained is divisible by 13 then the original number is divisible by 13 otherwise not.
E.g.-
Let us consider the number 195.
Now the last digit is 5 and on multiplying it with 4 we get 20.
Now on adding this with the remaining number (i.e. 19) we get 39. Now as 39 is divisible by 13 therefore the original
number id divisible by 13.
———————XXXXXXXXXXX————
Divisibility test of 17
To check whether a number is divisible by 17 we follow the procedure as follows:
1). Multiply the last digit with 5 and subtract it from the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 17 or not.
If the 2-digit number so obtained is divisible by 17 then the original number is divisible by 17 otherwise not.
E.g.-
Let us consider the number 221.
Now the last digit is 1 and on multiplying it with 5 we get 5.
Now on subtracting 5 from the remaining number (i.e. 22) we get 17. Now as 17 is divisible by 17 therefore the original number id divisible by 17.
——————XXXXXXXXXX——————–
Divisibility test of 19
To check whether a number is divisible by 19 we follow the procedure as follows:
1). Multiply the last digit with 2 and add it to the number left (after removing the last digit).
2). Follow this method again and again and reduce the number to 2-digit number form.
3). Now check whether the number is divisible by 19 or not.
If the 2-digit number so obtained is divisible by 19 then the original number is divisible by 19 otherwise not.
E.g.-
Let us consider the number 209.
Now the last digit is 9 and on multiplying it with 2 we get 18.
Now on adding th18 with the remaining number(i.e. 20) we get 38. Now as 38 is divisible by 19 therefore the original number id divisible by 19.
Number Multiply last digit -/+
7 2 -
13 4 +
17 5 -
19 2 +
Quant… Basic Formulae
Consolidated some of the basic formula.
ALGEBRA :
1. Sum of first n natural numbers = n(n+1)/2
2. Sum of the squares of first n natural numbers = n(n+1)(2n+1)/6
3. Sum of the cubes of first n natural numbers = [n(n+1)/2]2
4. Sum of first n natural odd numbers = n2
5. Average = (Sum of items)/Number of items
Arithmetic Progression (A.P.):
An A.P. is of the form a, a+d, a+2d, a+3d, …
where a is called the ‘first term’ and d is called the ‘common difference’
1. nth term of an A.P. tn = a + (n-1)d
2. Sum of the first n terms of an A.P. Sn = n/2[2a+(n-1)d] or Sn = n/2(first term + last term)
Geometrical Progression (G.P.):
A G.P. is of the form a, ar, ar2, ar3, …
where a is called the ‘first term’ and r is called the ‘common ratio’.
1. nth term of a G.P. tn = arn-1
2. Sum of the first n terms in a G.P. Sn = a|1-rn|/|1-r|
Permutations and Combinations :
1. nPr = n!/(n-r)!
2. nPn = n!
3. nP1 = n
1. nCr = n!/(r! (n-r)!)
2. nC1 = n
3. nC0 = 1 = nCn
4. nCr = nCn-r
5. nCr = nPr/r!
Number of diagonals in a geometric figure of n sides = nC2-n
Tests of Divisibility :
1. A number is divisible by 2 if it is an even number.
2. A number is divisible by 3 if the sum of the digits is divisible by 3.
3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
4. A number is divisible by 5 if the units digit is either 5 or 0.
5. A number is divisible by 6 if the number is divisible by both 2 and 3.
6. A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
7. A number is divisible by 9 if the sum of the digits is divisible by 9.
8. A number is divisible by 10 if the units digit is 0.
9. A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places, is divisible by 11.
H.C.F and L.C.M :
H.C.F stands for Highest Common Factor. The other names for H.C.F are Greatest Common Divisor (G.C.D) and Greatest Common Measure (G.C.M).
The H.C.F. of two or more numbers is the greatest number that divides each one of them exactly.
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
Two numbers are said to be co-prime if their H.C.F. is 1.
H.C.F. of fractions = H.C.F. of numerators/L.C.M of denominators
L.C.M. of fractions = G.C.D. of numerators/H.C.F of denominators
Product of two numbers = Product of their H.C.F. and L.C.M.
PERCENTAGES :
1. If A is R% more than B, then B is less than A by R / (100+R) * 100
2. If A is R% less than B, then B is more than A by R / (100-R) * 100
3. If the price of a commodity increases by R%, then reduction in consumption, not to increase the expenditure is : R/(100+R)*100
4. If the price of a commodity decreases by R%, then the increase in consumption, not to decrease the expenditure is : R/(100-R)*100
PROFIT & LOSS :
1. Gain = Selling Price(S.P.) – Cost Price(C.P)
2. Loss = C.P. – S.P.
3. Gain % = Gain * 100 / C.P.
4. Loss % = Loss * 100 / C.P.
5. S.P. = (100+Gain%)/100*C.P.
6. S.P. = (100-Loss%)/100*C.P.
Short cut Methods:
1. By selling an article for Rs. X, a man loses l%. At what price should he sell it to gain y%? (or)
A man lost l% by selling an article for Rs. X. What percent shall he gain or lose by selling it for Rs. Y?
(100 – loss%) : 1st S.P. = (100 + gain%) : 2nd S.P.
2. A man sold two articles for Rs. X each. On one he gains y% while on the other he loses y%. How much does he gain or lose in the whole transaction?
In such a question, there is always a lose. The selling price is immaterial.
Formula: Loss % =
3. A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms. For a kg weight. Find his gain percent.
Formula: Gain % =
RATIO & PROPORTIONS:
1. The ratio a : b represents a fraction a/b. a is called antecedent and b is called consequent.
2. The equality of two different ratios is called proportion.
3. If a : b = c : d then a, b, c, d are in proportion. This is represented by a : b :: c : d.
4. In a : b = c : d, then we have a* d = b * c.
5. If a/b = c/d then ( a + b ) / ( a – b ) = ( d + c ) / ( d – c ).
TIME & WORK :
1. If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
2. If A and B work together for n days, then (A+B)’s 1 days’s work = 1/n
3. If A is twice as good workman as B, then ratio of work done by A and B = 2:1
PIPES & CISTERNS :
1. If a pipe can fill a tank in x hours, then part of tank filled in one hour = 1/x
2. If a pipe can empty a full tank in y hours, then part emptied in one hour = 1/y
3. If a pipe can fill a tank in x hours, and another pipe can empty the full tank in y hours, then on opening both the pipes,
the net part filled in 1 hour = (1/x-1/y) if y>x
the net part emptied in 1 hour = (1/y-1/x) if x>y
TIME & DISTANCE :
1. Distance = Speed * Time
2. 1 km/hr = 5/18 m/sec
3. 1 m/sec = 18/5 km/hr
4. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is 2xy/(x+y) kmph.
PROBLEMS ON TRAINS :
1. Time taken by a train x metres long in passing a signal post or a pole or a standing man is equal to the time taken by the train to cover x metres.
2. Time taken by a train x metres long in passing a stationary object of length y metres is equal to the time taken by the train to cover x+y metres.
3. Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph.
4. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u>v, then time taken by the faster train to cross the slower train = (x+y)/(u-v) hours.
5. Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph.
6. If two trains of length x km and y km are moving in the opposite directions at u kmph and v kmph, then time taken by the trains to cross each other = (x+y)/(u+v)hours.
7. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then A’s speed : B’s speed = (√b : √
SIMPLE & COMPOUND INTERESTS :
Let P be the principal, R be the interest rate percent per annum, and N be the time period.
1. Simple Interest = (P*N*R)/100
2. Compound Interest = P(1 + R/100)N – P
3. Amount = Principal + Interest
LOGORITHMS :
If am = x , then m = logax.
Properties :
1. log xx = 1
2. log x1 = 0
3. log a(xy) = log ax + log ay
4. log a(x/y) = log ax – log ay
5. log ax = 1/log xa
6. log a(xp) = p(log ax)
7. log ax = log bx/log ba
Note : Logarithms for base 1 does not exist.
AREA & PERIMETER :
Shape Area Perimeter
Circle ∏ (Radius)2 2∏(Radius)
Square (side)2 4(side)
Rectangle length*breadth 2(length+breadth)
1. Area of a triangle = 1/2*Base*Height or
2. Area of a triangle = √ (s(s-(s-b)(s-c)) where a,b,c are the lengths of the sides and s = (a+b+c)/2
3. Area of a parallelogram = Base * Height
4. Area of a rhombus = 1/2(Product of diagonals)
5. Area of a trapezium = 1/2(Sum of parallel sides)(distance between the parallel sides)
6. Area of a quadrilateral = 1/2(diagonal)(Sum of sides)
7. Area of a regular hexagon = 6(√3/4)(side)2
8. Area of a ring = ∏(R2-r2) where R and r are the outer and inner radii of the ring.
VOLUME & SURFACE AREA :
Cube :
Let a be the length of each edge. Then,
1. Volume of the cube = a3 cubic units
2. Surface Area = 6a2 square units
3. Diagonal = √ 3 a units
Cuboid :
Let l be the length, b be the breadth and h be the height of a cuboid. Then
1. Volume = lbh cu units
2. Surface Area = 2(lb+bh+lh) sq units
3. Diagonal = √ (l2+b2+h2)
Cylinder :
Let radius of the base be r and height of the cylinder be h. Then,
1. Volume = ∏r2h cu units
2. Curved Surface Area = 2∏rh sq units
3. Total Surface Area = 2∏rh + 2∏r2 sq units
Cone :
Let r be the radius of base, h be the height, and l be the slant height of the cone. Then,
1. l2 = h2 + r2
2. Volume = 1/3(∏r2h) cu units
3. Curved Surface Area = ∏rl sq units
4. Total Surface Area = ∏rl + ∏r2 sq units
Sphere :
Let r be the radius of the sphere. Then,
1. Volume = (4/3)∏r3 cu units
2. Surface Area = 4∏r2 sq units
Hemi-sphere :
Let r be the radius of the hemi-sphere. Then,
1. Volume = (2/3)∏r3 cu units
2. Curved Surface Area = 2∏r2 sq units
3. Total Surface Area = 3∏r2 sq units
Prism :
Volume = (Area of base)(Height
ALGEBRA :
1. Sum of first n natural numbers = n(n+1)/2
2. Sum of the squares of first n natural numbers = n(n+1)(2n+1)/6
3. Sum of the cubes of first n natural numbers = [n(n+1)/2]2
4. Sum of first n natural odd numbers = n2
5. Average = (Sum of items)/Number of items
Arithmetic Progression (A.P.):
An A.P. is of the form a, a+d, a+2d, a+3d, …
where a is called the ‘first term’ and d is called the ‘common difference’
1. nth term of an A.P. tn = a + (n-1)d
2. Sum of the first n terms of an A.P. Sn = n/2[2a+(n-1)d] or Sn = n/2(first term + last term)
Geometrical Progression (G.P.):
A G.P. is of the form a, ar, ar2, ar3, …
where a is called the ‘first term’ and r is called the ‘common ratio’.
1. nth term of a G.P. tn = arn-1
2. Sum of the first n terms in a G.P. Sn = a|1-rn|/|1-r|
Permutations and Combinations :
1. nPr = n!/(n-r)!
2. nPn = n!
3. nP1 = n
1. nCr = n!/(r! (n-r)!)
2. nC1 = n
3. nC0 = 1 = nCn
4. nCr = nCn-r
5. nCr = nPr/r!
Number of diagonals in a geometric figure of n sides = nC2-n
Tests of Divisibility :
1. A number is divisible by 2 if it is an even number.
2. A number is divisible by 3 if the sum of the digits is divisible by 3.
3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
4. A number is divisible by 5 if the units digit is either 5 or 0.
5. A number is divisible by 6 if the number is divisible by both 2 and 3.
6. A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
7. A number is divisible by 9 if the sum of the digits is divisible by 9.
8. A number is divisible by 10 if the units digit is 0.
9. A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places, is divisible by 11.
H.C.F and L.C.M :
H.C.F stands for Highest Common Factor. The other names for H.C.F are Greatest Common Divisor (G.C.D) and Greatest Common Measure (G.C.M).
The H.C.F. of two or more numbers is the greatest number that divides each one of them exactly.
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
Two numbers are said to be co-prime if their H.C.F. is 1.
H.C.F. of fractions = H.C.F. of numerators/L.C.M of denominators
L.C.M. of fractions = G.C.D. of numerators/H.C.F of denominators
Product of two numbers = Product of their H.C.F. and L.C.M.
PERCENTAGES :
1. If A is R% more than B, then B is less than A by R / (100+R) * 100
2. If A is R% less than B, then B is more than A by R / (100-R) * 100
3. If the price of a commodity increases by R%, then reduction in consumption, not to increase the expenditure is : R/(100+R)*100
4. If the price of a commodity decreases by R%, then the increase in consumption, not to decrease the expenditure is : R/(100-R)*100
PROFIT & LOSS :
1. Gain = Selling Price(S.P.) – Cost Price(C.P)
2. Loss = C.P. – S.P.
3. Gain % = Gain * 100 / C.P.
4. Loss % = Loss * 100 / C.P.
5. S.P. = (100+Gain%)/100*C.P.
6. S.P. = (100-Loss%)/100*C.P.
Short cut Methods:
1. By selling an article for Rs. X, a man loses l%. At what price should he sell it to gain y%? (or)
A man lost l% by selling an article for Rs. X. What percent shall he gain or lose by selling it for Rs. Y?
(100 – loss%) : 1st S.P. = (100 + gain%) : 2nd S.P.
2. A man sold two articles for Rs. X each. On one he gains y% while on the other he loses y%. How much does he gain or lose in the whole transaction?
In such a question, there is always a lose. The selling price is immaterial.
Formula: Loss % =
3. A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms. For a kg weight. Find his gain percent.
Formula: Gain % =
RATIO & PROPORTIONS:
1. The ratio a : b represents a fraction a/b. a is called antecedent and b is called consequent.
2. The equality of two different ratios is called proportion.
3. If a : b = c : d then a, b, c, d are in proportion. This is represented by a : b :: c : d.
4. In a : b = c : d, then we have a* d = b * c.
5. If a/b = c/d then ( a + b ) / ( a – b ) = ( d + c ) / ( d – c ).
TIME & WORK :
1. If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
2. If A and B work together for n days, then (A+B)’s 1 days’s work = 1/n
3. If A is twice as good workman as B, then ratio of work done by A and B = 2:1
PIPES & CISTERNS :
1. If a pipe can fill a tank in x hours, then part of tank filled in one hour = 1/x
2. If a pipe can empty a full tank in y hours, then part emptied in one hour = 1/y
3. If a pipe can fill a tank in x hours, and another pipe can empty the full tank in y hours, then on opening both the pipes,
the net part filled in 1 hour = (1/x-1/y) if y>x
the net part emptied in 1 hour = (1/y-1/x) if x>y
TIME & DISTANCE :
1. Distance = Speed * Time
2. 1 km/hr = 5/18 m/sec
3. 1 m/sec = 18/5 km/hr
4. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is 2xy/(x+y) kmph.
PROBLEMS ON TRAINS :
1. Time taken by a train x metres long in passing a signal post or a pole or a standing man is equal to the time taken by the train to cover x metres.
2. Time taken by a train x metres long in passing a stationary object of length y metres is equal to the time taken by the train to cover x+y metres.
3. Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph.
4. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u>v, then time taken by the faster train to cross the slower train = (x+y)/(u-v) hours.
5. Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph.
6. If two trains of length x km and y km are moving in the opposite directions at u kmph and v kmph, then time taken by the trains to cross each other = (x+y)/(u+v)hours.
7. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then A’s speed : B’s speed = (√b : √
SIMPLE & COMPOUND INTERESTS :
Let P be the principal, R be the interest rate percent per annum, and N be the time period.
1. Simple Interest = (P*N*R)/100
2. Compound Interest = P(1 + R/100)N – P
3. Amount = Principal + Interest
LOGORITHMS :
If am = x , then m = logax.
Properties :
1. log xx = 1
2. log x1 = 0
3. log a(xy) = log ax + log ay
4. log a(x/y) = log ax – log ay
5. log ax = 1/log xa
6. log a(xp) = p(log ax)
7. log ax = log bx/log ba
Note : Logarithms for base 1 does not exist.
AREA & PERIMETER :
Shape Area Perimeter
Circle ∏ (Radius)2 2∏(Radius)
Square (side)2 4(side)
Rectangle length*breadth 2(length+breadth)
1. Area of a triangle = 1/2*Base*Height or
2. Area of a triangle = √ (s(s-(s-b)(s-c)) where a,b,c are the lengths of the sides and s = (a+b+c)/2
3. Area of a parallelogram = Base * Height
4. Area of a rhombus = 1/2(Product of diagonals)
5. Area of a trapezium = 1/2(Sum of parallel sides)(distance between the parallel sides)
6. Area of a quadrilateral = 1/2(diagonal)(Sum of sides)
7. Area of a regular hexagon = 6(√3/4)(side)2
8. Area of a ring = ∏(R2-r2) where R and r are the outer and inner radii of the ring.
VOLUME & SURFACE AREA :
Cube :
Let a be the length of each edge. Then,
1. Volume of the cube = a3 cubic units
2. Surface Area = 6a2 square units
3. Diagonal = √ 3 a units
Cuboid :
Let l be the length, b be the breadth and h be the height of a cuboid. Then
1. Volume = lbh cu units
2. Surface Area = 2(lb+bh+lh) sq units
3. Diagonal = √ (l2+b2+h2)
Cylinder :
Let radius of the base be r and height of the cylinder be h. Then,
1. Volume = ∏r2h cu units
2. Curved Surface Area = 2∏rh sq units
3. Total Surface Area = 2∏rh + 2∏r2 sq units
Cone :
Let r be the radius of base, h be the height, and l be the slant height of the cone. Then,
1. l2 = h2 + r2
2. Volume = 1/3(∏r2h) cu units
3. Curved Surface Area = ∏rl sq units
4. Total Surface Area = ∏rl + ∏r2 sq units
Sphere :
Let r be the radius of the sphere. Then,
1. Volume = (4/3)∏r3 cu units
2. Surface Area = 4∏r2 sq units
Hemi-sphere :
Let r be the radius of the hemi-sphere. Then,
1. Volume = (2/3)∏r3 cu units
2. Curved Surface Area = 2∏r2 sq units
3. Total Surface Area = 3∏r2 sq units
Prism :
Volume = (Area of base)(Height
Friday, 15 April 2011
Phobia
AAblutophobia - Fear of washing or bathing. Acarophobia - Fear of itching or of insects whose bites cause itching. Acerophobia - Fear of sourness. Achluophobia, Lygophobia, Nyctophobia, Scotophobia - Fear of darkness. Acousticophobia - Fear of noise. Acrophobia, Altophobia - Fear of heights. Aerophobia - Fear of drafts, air swallowing or airborne noxious substances. Aeroacrophobia - Fear of open high places. Aeronausiphobia - Fear of vomiting secondary to airsickness. Agateophobia, Dementophobia, Maniaphobia - Fear of insanity. Agliophobia, Algophobia, Odynophobia, Odynephobia - Fear of pain. Agoraphobia - Fear of the outdoors, crowds or uncontrolled social conditions. Agraphobia, Contreltophobia - Fear of sexual abuse. Agrizoophobia - Fear of wild animals. Agyrophobia, Dromophobia - Fear of streets or crossing the street. Aibohphobia - Fear of palindromes (not necessarily an actual word; aiboh is not of course Greek or Latin for Palindrome, but is simply intended to make the word itself palindromic) Aichmophobia, Belonephobia, Enetophobia - Fear of needles or pointed objects. Ailurophobia, Elurophobia, Felinophobia, Galeophobia, Gatophobia - Fear of cats. Albuminurophobia - Fear of kidney disease. Alektorophobia - Fear of chickens. Alliumphobia - the abnormal fear of garlic that may extend to a variety of plants characterized by their pungent odor including onions, leeks, chives, and shallots. Allium is the onion [[genu Allodoxaphobia - Fear of opinions. Amathophobia, Koniophobia - Fear of dust. Amaxophobia - Fear of riding in a car. Ambulophobia, Stasibasiphobia, Stasiphobia - Fear of walking or standing. Anemophobia - Fear of air. Amerophobia, Columbophobia - Fear of the United States, American culture, etc. Amnesiphobia - Fear of amnesia. Amychophobia - Fear of scratches or being scratched. Anablephobia - Fear of looking up. Ancraophobia, Anemophobia - Fear of wind. Androphobia, Arrhenphobia, Hominophobia - Fear of men. Anginophobia - Fear of angina, choking or narrowness. Anglophobia - Fear of England, English culture, etc. Angrophobia - Fear of anger or of becoming angry. Ankylophobia - Fear of immobility of a joint. Anthrophobia, Anthophobia - Fear of flowers. Anthropophobia - Fear of people or society. Antidaeophobia - Fear that somewhere, somehow, a duck is watching you (fictional, from Gary Larson cartoon). Antlophobia - Fear of floods. Anuptaphobia - Fear of staying single. Apeirophobia - Fear of infinity. Aphenphosmphobia, Chiraptophobia, Haphephobia, Haptephobia - Fear of being touched. Apiphobia, Melissaphobia, Melissophobia - Fear of bees. Apotemnophobia - Fear of persons with amputations. Arachibutyrophobia - Fear of peanut butter sticking to the roof of the mouth. Arachnophobia - Fear of spiders. Arithmophobia - Fear of numbers. Arsonphobia, Pyrophobia - Fear of fire. Asthenophobia - Fear of fainting or weakness. Astraphobia, Astrapophobia, Brontophobia, Keraunophobia - Fear of thunder and lightning. It is especially common in young children. Astrophobia - Fear of stars and celestial space. Asymmetriphobia - Fear of asymmetry. Ataxiophobia - Fear of ataxia. Ataxophobia - Fear of disorder or untidiness. Atelophobia - Fear of imperfection. Atephobia - Fear of ruin or ruins. Athazagoraphobia - Fear of being forgotten, ignored or forgetting. Atomosophobia - Fear of atomic explosions. Atychiphobia, Kakorrhaphiophobia - Fear of failure. Aulophobia - Fear of flutes. Aurophobia - Fear of gold. Auroraphobia - Fear of the Northern Lights or for Chileans, Argentinians, Falkland Islanders or Antarctic explorers, fear of the Southern Lights. Australophobia, Novahollandiaphobia - Fear of Australia, Australians, Australian culture etc. Autodysomophobia - Fear that one has a vile odour. Automatonophobia - Fear of any inanimate object that represents a sentient being, eg. statues, dummies, robots, etc. Automysophobia - Fear of being dirty. Autophobia, Eremophobia, Ermitophibia, Isolophobia, Monophobia - Fear of being alone or fear of oneself. Aviophobia, Aviatophobia, Pteromerhanophobia - Fear of flying. B
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Phobia
Originally from Wikipedia, the free encyclopedia. (many years ago, then edited over the years...)
Originally from Wikipedia, the free encyclopedia. (many years ago, then edited over the years...)
The term phobia, which comes from the Ancient Greek word for fear, denotes a number of psychological and physiological conditions that can range from serious disabilities to common fears to minor quirks.
Phobias are the most common form of anxiety disorder. An American study by the National Institute of Mental Health (NIMH) found that between 5.1 and 21.5 percent of Americans suffer from phobias. Broken down by age and gender, the study found that phobias were the most common mental illness among women in all age groups and the second most common illness among men older than 25.
Understanding and classifying phobias
Social phobias - fears to do with other people and social relationships such as performance anxiety, fears of eating in public etc.
Specific phobias - fear of a single specific panic trigger, like dogs, flying, running water and so on.
Specific phobias - fear of a single specific panic trigger, like dogs, flying, running water and so on.
Agoraphobia - a generalised fear of leaving your home or your small familiar 'safe' area, and of the inevitable panic attacks that will follow. Agoraphobia is the only phobia regularly treated as a medical condition.
Many specific phobias, such as fears of dogs, heights, spider bites, and so forth, are extensions of fears that everyone has. People with these phobias treat them by avoiding the thing they fear.
Many specific phobias can be traced back to a specific triggering event, usually a traumatic experience at an early age. Social phobias and agoraphobia have more complex causes that are not entirely known at this time. It is believed that heredity, genetics and brain-chemistry combine with life-experiences to play a major role in the development of anxiety disorders and phobias.
Phobias vary in severity among individuals, with some phobics simply disliking or avoiding the subject of their fear and suffering mild anxiety. Others suffer fully-fledged panic attacks with all the associated disabling symptoms.
It is possible for a sufferer to become phobic about virtually anything. The name of a phobia generally contains a Greek word for what the patient fears plus the suffix -phobia. Creating these terms is something of a word game. Few of these terms are found in medical literature.
Common phobias include:
Arachnophobia - Fear of spiders.
Anthrophobia - Fear of people or society
Aerophobia - Fear of drafts, air swallowing or airborne noxious substances.
Agoraphobia - Fear of the outdoors, crowds or uncontrolled social conditions.
Claustrophobia - Fear of confined spaces.
Acrophobia - Fear of heights.
Cancerophobia - Fear of cancer.
Astraphobia - Fear of thunder and lightning.
Necrophobia - Fear of death or dead things.
Cardiophobia - Fear of heart disease.
Dental phobia - Fear of dentists, dental surgery, or teeth.
Pornophobia - Fear of pornographic material.
Anthrophobia - Fear of people or society
Aerophobia - Fear of drafts, air swallowing or airborne noxious substances.
Agoraphobia - Fear of the outdoors, crowds or uncontrolled social conditions.
Claustrophobia - Fear of confined spaces.
Acrophobia - Fear of heights.
Cancerophobia - Fear of cancer.
Astraphobia - Fear of thunder and lightning.
Necrophobia - Fear of death or dead things.
Cardiophobia - Fear of heart disease.
Dental phobia - Fear of dentists, dental surgery, or teeth.
Pornophobia - Fear of pornographic material.
Treatment
Some therapists use virtual reality to desensitize patients to the feared thing. Other forms of therapy that may be of benefit to phobics are graduated exposure therapy and cognitive behavioural therapy (CBT). Anti-anxiety medication can also be of assistance in some cases. Most phobics understand that they are suffering from an irrational fear, but are powerless to override their initial panic reaction.
Some therapists use virtual reality to desensitize patients to the feared thing. Other forms of therapy that may be of benefit to phobics are graduated exposure therapy and cognitive behavioural therapy (CBT). Anti-anxiety medication can also be of assistance in some cases. Most phobics understand that they are suffering from an irrational fear, but are powerless to override their initial panic reaction.
Graduated Exposure and CBT both work towards the goal of desensitising the sufferer, and changing the thought patterns that are contributing to their panic. Gradual desensitisation treatment and CBT are often extremely successful, provided the phobic is willing to endure some discomfort and to make a continuous effort over a long period of time. Practitioners of neuro-linguistic programming (NLP) claim to have a procedure that can be used to alleviate most specific phobias in a single therapeutic session, though this has not yet been verified scientifically.
Non-clinical uses of the term
In some cases, a fear or hatred is not considered a phobia in the clinical sense because it is believed to be only a symptom of other psychological problems, or the result of ignorance, or of political or social beliefs. These are phobias in a more general, popular sense of the word:
Afrophobia, fear or dislike of Africans or African culture or people of African ancestry
Islamophobia, fear or dislike of Muslims or Islamic cultur
Homophobia, fear or dislike of homosexual people
Xenophobia, fear or dislike of strangers or the unknown, often used to describe nationalistic political beliefs and movements.
Islamophobia, fear or dislike of Muslims or Islamic cultur
Homophobia, fear or dislike of homosexual people
Xenophobia, fear or dislike of strangers or the unknown, often used to describe nationalistic political beliefs and movements.
Furthermore, the term hydrophobia, or fear of water, is usually not a psychological condition at all, but another term for the disease rabies, referring to a common symptom. Likewise photophobia, is a physical complaint, aversion to light due to an inflamed or painful eye or excessively dilated pupils).
This article is licensed under the GNU Free Documentation License. (http://www.gnu.org/copyleft/fdl.html)It uses material from the Wikipedia. (http://en.wikipedia.org/)
Further Reading & Resources
The opposite of the suffix -phobia is a -philia or -philie (meaning "love of").
Also See: Fear on Wikipedia
Comments on Phobias
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