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PERMUTATIONS AND COMBINATIONS

2009-04-17T00:32:00.000-07:00

THIS POST PROVIDES YOU SOME OF THE BASICS
TERM RELATED TO PERMUTATIONS AND COMBINATIONS
AND ITS RELATED FORMULAS ,WHICH WE USE IN
OUR DAY TO DAY ACTIVITIES .

BASICS

1. WHAT IS A PERMUTATION ?

PERMUTATION :-
* PERMUTATION IS SIMPLY REFERED TO AS THE
ARRANGEMENT OF THINGS OR OBJECTS.
* THIS IS AS SHOWN IN BELOW FIGURE .

2. WHAT IS A COMBINATION ?

COMBINATION :-
* COMBINATION IS SIMPLY REFERED TO AS THE SELECTION
OF THINGS OR OBJECTS .
* THIS IS SHOWN IN BELOW FIGURE .

3. WHAT ARE THE TYPES OF PERMUTATIONS ?

TYPES OF PERMUTATIONS :-
* THERE ARE MAINLY TWO TYPES OF PERMUTATIONS .
* THEY ARE
(a) LINEAR PERMUTATION .
(b) CIRCULAR PERMUTATION .
* THESE ARE AS SHOWN IN BELOW FIGURE .

4. WHAT IS A LINEAR PERMUTATION ?

LINEAR PERMUTATION :-
LINEAR PERMUTATION IS A PERMUTATION WHERE THE
ARRANGEMENT OF THINGS ARE DONE IN A LINE (ROW) WISE .

5.WHAT IS A CIRCULAR PERMUTATION ?

CIRCULAR PERMUTATION :-
CIRCULAR PERMUTATION IS A PERMUTATION WHERE THE
ARRANGEMENT OF THINGS ARE DONE IN A CIRCLE WISE .

FORMULAS

LET US CONSIDER,
P= PRMUTATION ,
C= COMBINATION .
THEN,

1. nPr=P(n,r)=n!/(n-r)! = PERMUTATIONS FORMED BY
TAKING r THINGS FROM n DISSIMILAR THINGS .

2. nCr=C(n,r)=n!/((n-r)!r!) = COMBINATIONS FORMED BY
TAKING r THINGS FROM n DISSIMILAR THINGS.

3. n! = n*(n-1)*(n-2)*(n-3)....... .

4. C(n,r)+C(n,r-1)=C(n+1,r) .

5. C(n,r)/C(n,r-1)=(n-r+1)/r .

6. IF ONE WORK DONE IN m ROUTES ,OTHER IN n ROUTES
(BOTH ASSOCIATED ) ,THEN BOTH CAN BE DONE IN
SUCCESSION IN mn ROUTES.

7. THE ARRANGEMENT OF WAYS FOR n PENS n PENCILS ,
BOTH ALTERNATIVELY IN A LINE DONE IN 2 n! n! .

8. THE NUMBER OF CIRCULAR PERMUTATIONS FORMED BY
n DISSIMILAR THINGS IS (n-1)! .

9. THE POSSIBLE WAYS OF DISTRIBUTING n THINGS EQUALLY
AMONG 2 PERSONS IS (2n)!/(n!n!) .

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2009-04-16T02:59:00.000-07:00

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2009-04-16T02:51:00.000-07:00

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EQUATIONS

2009-03-28T08:46:00.000-07:00

EQUATIONS

EQUATIONS :-

THIS POST PROVIDES YOU THE BASIC KNOWLEDGE OF EQUATIONS.
IN THIS POST YOU WILL FIND OUT ,

(1) WHAT ARE THE BASIC TERMS REGARDING EQUATIONS ?
(2) HOW TO ESTIMATE AND FIND OUT THE ROOTS OF QUADRATIC EQUATIONS ?

(1) WHAT ARE THE BASIC TERMS REGARDING EQUATIONS ?

EXPRESSION :-
EXPRESSION CAN BE UNDERSTOOD EASILY BY THE BELOW EXAMPLE .

EXAMPLE OF EXPRESSION :-
IF GIVEN ax^2+bx+c=0 ,THEN WE GET THE LEFT HAND PART (i.e) ax^2+bx+c WHICH IS CALLED AS EXPRESSION .

EQUATION :-
EQUATION IS SIMPLY A EXPRESSION EQUATING TO ANOTHER EXPRESSION .

EXAMPLES OF EQUATIONS :-
ax^2+bx+c=0 ,
bx+c=0 ,
c=0 .

QUADRATIC EQUATION :-
QUADRATIC EQUATION IS THE EQUATION,HAVING OF FORM ax^2+bx+c=0 ,WITH THE CONDITION THAT a NEVER BE 0.

EXAMPLES OF QUADRATIC EQUATION :-
2x^2+x+3=0,
4x^2+5=0 .

DETAILS OF QUADRATIC EQUATION :-
THE DETAILS OF QUADRATIC EQUATION IS GIVEN IN BELOW FIGURE 1 .

(2) HOW TO ESTIMATE AND FIND OUT THE ROOTS OF QUADRATIC EQUATIONS ?

ESTIMATING THE ROOTS OF QUADRATIC EQUATIONS :-

CONSIDERING ax^2+bx+c=0 AS A STANDARD QUADRATIC EQUATION ,WE ESTIMATE THE ROOTS BY JUST CALCULATING b^2-4ac .

IF b^2-4ac IS KNOW THEN WE COMPARE THIS AS FOLLOWS ,
(a) >0,THE ROOTS ARE REAL AND DISTINCT .
(b) <0,THE ROOTS ARE IMAGINARY .
(c) =0,THE ROOTS ARE REAL AND EQUAL .

EXAMPLE OF ESTIMATING THE ROOTS OF QUADRATIC EQUATION :-
IF GIVEN 2x^2+x+3=0 ,
a=2,
b=1,
c=3,
THEN
b^2-4ac =1-24=-23 <0
THAT IS THE ROOTS ARE IMAGINARY .

ROOTS OF QUADRATIC EQUATION :-

CONSIDERING ax^2+bx+c=0 AS A STANDARD QUADRATIC EQUATION ,WE WRITE THE ROOTS AS (-b+ SQUARE ROOT(b^2-4ac))/(2a) AND (-b- SQUARE ROOT(b^2-4ac))/(2a) .
THESE ROOTS ARE REPRESENTED IN BELOW FIGURE 2 .

IF WE ASSUME p,q AS THE ROOTS OF STANDARD QUADRATIC EQUATION ax^2+bx+c=0 ,THEN WE WRITE ,
p+q=-b/a (SUM OF THE ROOTS ) .
p*q=c/a (PRODUCT OF THE ROOTS) .

NOTE THAT THE NUMBER OF ROOTS FOR A EQUATION IS EQUAL TO THE MAXIMUM POWER OF x PRESENT IN THE EQUATION .

EXAMPLE OF FINDING THE ROOTS OF A QUADRATIC EQUATION :-
IF GIVEN 2x^2+x+3=0 ,
a=2,
b=1,
c=3,
THEN
(-b+ SQUARE ROOT(b^2-4ac))/(2a) =(-1+SQUARE ROOT(-23))/(4) AND
(-b- SQUARE ROOT(b^2-4ac))/(2a) =(-1-SQUARE ROOT(-23))/(4) .
THE ROOTS ARE =(-1+SQUARE ROOT(-23))/(4) AND =(-1-SQUARE ROOT(-23))/(4) .

SOLID GEOMETRY

2009-03-25T23:21:00.000-07:00

SOLID GEOMETRY

SOLID GEOMETRY :-

THIS POST PROVIDES YOU , SOME OF THE BASICS OF STANDARD
SOLIDS LIKE RECTANGULAR SOLID ,CUBE ,CYLINDER .

BASIC DEFINITIONS :-

(1)WHAT IS A VOLUME ?

VOLUME :-
VOLUME IS DEFINED AS THE AMOUNT OF SPACE TAKEN BY AN OBJECT .

(2)WHAT IS A RECTANGULAR SOLID ?

RECTANGULAR SOLID :-
RECTANGULAR SOLID IS A SOLID THAT IS FORMED BY 6 RECTANGLES.
RECTANGULAR SOLID IS SIMPLY REFERED AS BOX.
THIS IS SHOWN IN BELOW FIGURE 1 .

(3)WHAT ARE THE FACES OF RECTANGULAR SOLID ?

FACES OF A RECTANGULAR SOLID :-
THE FACES OF RECTANGULAR SOLID ARE NOTHING BUT THE 6 RECTANGLES SORROUNDED IT .
THIS IS SHOWN BELOW IN FIGURE 1 .

(4)WHAT ARE EDGES OF RECTANGULAR SOLID ?

EDGES OF A RECTANGULAR SOLID :-
THE EDGES OF A RECTANGULAR SOLID ARE NOTHING BUT THE SIDES OF THE RECTANGLES SORROUNDED IT .
THIS IS SHOWN IN BELOW FIGURE 1 .

(5)WHAT IS A CUBE ?

CUBE :-
CUBE IS A RECTANGULAR SOLID WHERE ALL SIDES ADJUSTED AS EQUAL TO ONE ANOTHER .

(6)WHAT IS A BOX DIAGONAL OR RECTANGULAR SOLID DIAGONAL ?

DIAGONALS OF A RECTANGULAR SOLID :-
SIMPLY , BOX DIAGONAL IS THE LINE SEGMENT JOINING ANY VERTEX OF BOX TO EXACTLY THE OPPOSITE VERTEX OF A BOX.
THIS IS SHOWN IN BELOW FIGURE 2 .

(7)HOW MANY DIAGONAL EXISTS FOR A RECTANGULAR SOLID ?

DIAGONALS OF A RECTANGULAR SOLID :-
EXACTLY 4 DIAGONALS EXITS FOR A RECTANGULAR SOLID ,HAVING LENGTH AS SAME FOR ALL .
NOTE THAT, BOX DIAGONAL IS THE LONGEST LINE SEGMENT THAT CAN BE DRAWN BETWEEN 2 POINTS OF A BOX .

(8)WHAT IS A CYLINDER ?

CYLINDER :-
CYLINDER IS SIMPLY A RECTANGULAR SOLID WITH THE EXCEPTION OF THE BASE THAT IS ACTING AS CIRCLE ( i.e IN PLACE OF RECTANGLE ) .
THIS IS SHOWN IN BELOW FIGURE 3 .

FORMULAS REGARDING TO SOLID GEOMETRY :-

LET US CONSIDER ,
V=VOLUME ,
S=SURFACE AREA ,
A=AREA ,
a=SIDE OF CUBE ,
l=LENGTH ,
b=BREADTH ,
h=HEIGHT ,
d=DIAGONAL LENGTH ,
THEN,

(1)VOLUME OF A RECTANGULAR SOLID (V)=lbh .

(2)SURFACE OF A RECTANGULAR SOLID (S) =2(lb+bh+hl) .

(3)VOLUME OF A CUBE (V) =a^3 .

(4)SURFACE AREA OF A CUBE (S) = 6*a^2 .

(5)d^2=l^2+b^2+h^2 . (PROPERTY OF RECTANGULAR SOLID OR CUBE ) .

(6)VOLUME OF A CYLINDER (V)=(pie)*r^2*h .

(7)SURFACE AREA OF A CYLINDER (S) = 2*(pie)*r*h .

(8)AREA OF A CYLINDER (A) = 2*(pie)*r*h + (pie)*r^2*h .

CIRCLES

2009-03-24T05:31:00.001-07:00

CIRCLES
CIRCLES :-

THIS POST PROVIDES YOU THE BASICS OF CIRCLES,SEMICIRCLES,ARCS AND SECTORS .

BASICS OF CIRCLES :-

WHAT IS A CIRCLE ?
CIRCLE :-
CIRCLE IS THE ROUNDED FIGURE ,SUCH THAT EVERY POINT IN IT IS A FIXED DISTANCE FROM A SEPARATE POINT .
THIS IS SHOWN IN FIGURE 1 (a).

WHAT IS A SEMICIRCLE ?
SEMICIRCLE :-
SEMICIRCLE IS THE HALF PART OF A CIRCLE OF EXACTLY CIRCUMFERENCE (pie)r .
THIS IS SHOWN IN FIGURE 1 (b).

WHAT IS A RADIUS OF CIRCLE ?
RADIUS :-
RADIUS IS THE ONE ,REPRESENTS THE ABOVE DISCUSSED FIXED DISTANCE .
THIS IS SHOWN IN FIGURE 1 (c).

WHAT IS A CENTRE OF CIRCLE ?
CENTRE :-
CENTRE IS THE ONE ,REPRESENTS THE SEPARATE POINT WHICH WE DISCUSSED ABOVE .
THIS IS SHOWN IN FIGURE 2 (a).

WHAT IS A CHORD ?
CHORD :-
CHORD IS THE ONE ,THAT IS DRAWN BETWEEN ANY TWO POINTS OF A CIRCLE .
THE LONGEST CHORD THAT CAN BE REPRESENTED IN CIRCLE IS THE DIAMETER ITSELF .
THIS IS SHOWN IN FIGURE 2 (b).

WHAT IS A CIRCUMFERENCE ?
CIRCUMFERENCE :-
CIRCUMFERENCE IS THE ONE ,SIMPLY THE TOTAL LENGTH AROUND CIRCLE .
THIS IS SHOWN IN FIGURE 2 (c).

WHAT IS AN ARC ?
ARC :-
ARC IS THE ONE CONTAIN TWO POINTS OF CIRCLE AND ALL THE POINTS LYING IN BETWEEN
THEM .
THIS IS SHOWN IN FIGURE 3 (1ST FIGURE ).

FORMULAS RELATED TO CIRCLES :-

LET US CONSIDER ,
pie =22/7 .
r = RADIUS .
d=DIAMETER .
c=CIRCUMFERENCE .
x=ANGLE IN DEGREES .

AREA OF A CIRCLE (A)= (PIE) r^2 .

DIAMETER OF A CIRCLE (d)=2r .

CIRCUMFERENCE TO DIAMETER RATIO OF A CIRCLE IS EQUAL TO (PIE) .

CIRCUMFERENCE OF A CIRCLE (c)= 2(PIE)r =(PIE)d .

LENGTH OF A ARC =(x/360)*(2(pie)r) .

AREA OF A SECTOR =(x/360)*((pie)r^2) .

ABOUT MAHESH POLINENI

2009-03-18T23:33:00.000-07:00

ABOUT MAHESH POLINENI

ABOUT MAHESH POLINENI :-

INTRODUCING MYSELF,
IAM MAHESH POLINENI (PULI) (19) BORN ON 14TH JUNE 1989 IN RAILWAY KODUR,KADAPA,ANDHRAPRADESH,INDIA.

MY FATHER AND MOTHER ARE RESPECTED MALLIKARJUNA POLINENI AND RANAMMA POLINENI(NELAPATI-OWN).

AT FIRST MY FATHER IS A FARMER ,AND MY MOTHER A TAILOR.LATER FOR THE BRIGHT FUTURE OF MY BROTHER AND ME,MY FATHER LEFT TO GULF COUNTRIES.

MY BROTHER IS RAJESH POLINENI ,RUNNING AN OWN INSTITUTE OF COMPUTER EDUCATION AT RAILWAY KODUR.

I STUDIED MY L.K.G,U.K.G,1ST,2ND,3RD IN EVEREST RESEDENTIAL SCHOOL,T.KAMMAPALLI,PULLAMPET,KADAPA,ANDHRAPRADESH,INDIA.

I DID MY 3RD CLASS ONCE AGAIN,WITH SKIPPING OF 4TH STANDARD,CONTINUING MY 5TH,6TH IN EVEREST RESEDENTIAL SCHOOL,RAJAMPET,KADAPA,ANDHRAPRADESH,INDIA.

I DID MY 7TH,8TH,9TH,10TH IN DOLPHIN DALE HIGH SCHOOL,RAILWAY KODUR,KADAPA,ANDHRAPRADESH,INDIA (MY BIRTH PLACE).

I DID MY INTERMEDIATE IN VIKAS JUNIOR COLLEGE,ANNAMACHARI
CIRCLE,TIRUPATHI,ANDHRAPRADESH,INDIA.PRESENTLY IAM DOING MY ENGINEERING IN SVEC, A.RANGAMPETA,TIRUPATHI,ANDHRAPRADESH,INDIA.

WHATEVER GREAT POSITION I REACH,MOTIVATION FORCE LIES IN MY FATHER,MOTHER AND MY UNCLE (CHENGIAH NAIDU NELAPATI (FARMER,BUSSINESS MAN)).

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2009-03-18T11:49:00.000-07:00

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COORDINATE GEOMETRY

2009-03-17T12:02:00.000-07:00

COORDINATE GEOMETRY

COORDINATE GEOMETRY:-

THIS POST PROVIDES YOU ABOUT THE THINGS THAT WE HAVE TO APPLY
TO THE CONSTRUCTIONS,TAKING CORRECT MEASUREMENTS ,CALCULATING
DISTANCES AND SO ON ...

INTRODUCTION :-

WHAT IS A GEOMETRY ?
GEOMETRY:-
GEOMETRY IS DEFINED AS THE STUDY OF OBJECTS THAT ARE REAL OR IMAGINARY.

WHAT IS A COORDINATE GEOMETRY ?
COORDINATE GEOMETRY:-
(a)COORDINATE GEOMETRY IS THE GEOMETRY THAT IS USED TO REPRESENT A OBJECT IN A PLANE USING COORDINATES.
(b)EXAMPLE:-
IN 2D,(X,Y) IS USED TO REPRESENT ANY POINT.

QUADRANTS :-

WHAT IS A QUADRANT ?
QUADRANT:-
QUADRANT IS DEFINED AS A 1/4 PORTION OF A COORDINATE SYSTEM.
THE QUADRANTS ARE Q1,Q2,Q3,Q4 AS SHOWN IN BELOW FIGURE.

LINES :-

WHAT IS A LINE?
LINE:-
LINE IS THE 2D STRAIGHT CURVE THAT EXTENDS TO INFINITY HAVING ONLY 2 END POINTS.

WHAT IS A PARALLEL LINE ?
PARALLEL LINE:-
PARALLEL LINE IS THE LINE WHOSE SLOPES ARE EQUAL.

WHAT IS A PERPENDICULAR LINE ?
PERPENDICULAR LINE:-
PERPENDICULAR LINE IS THE LINE WHOSE PRODUCT OF SLOPES EQUALS -1.

SLOPES :-

WHAT IS A SLOPE?
SLOPE:-
(a)SLOPE IS REFERRED TO AS THE SLANT WHICH EQUALS TAN(A) WHERE A IS THE ANGLE BETWEEN 2 LINES
(b)IT IS DENOTED BY m
(c)SLOPE OF A LINE PASSING THROUGH (X1,Y1),(X2,Y2) IS (Y2-Y1)/(X2-X1).

FORMULAS OF COORDINATE GEOMENTRY :-

MIDPOINT OF A LINE :-

MIDPOINT OF THE LINE WHOSE END POINTS A(X0,Y0),B(X1,Y1) IS GIVEN BY
P(X,Y)=P((X0+X1)/2,(Y0+Y1)/2).
(SHOWN IN BELOW FIGURE (a) )

CENTROID OF A TRIANGLE :-

(a)CENTROID OF A TRIANGLE WHOSE VERTICES (X1,Y1),(X2,Y2),(X3,Y3) IS GIVEN BY
((X1+X2+X3)/3,(Y1+Y2+Y3)/3). (HERE 3 MEDIANS INTERSECT AT CENTRE)
(b)CENTROID DIVIDES MEDIAN IN THE RATIO OF 2:1.
(SHOWN IN BELOW FIGURE (b) )

DISTANCE BETWEEN TWO POINTS :-

DISTANCE BETWEEN 2 POINTS OF A LINE (X1,Y1),(X2,Y2) IS GIVEN BY
d= SQRT((X2-X1)^2+(Y2-Y1)^2)
(SHOWN IN BELOW FIGURE (c) )

EQUATION OF A LINE :-

(a)EQUATION OF A LINE WHOSE SLOPE =M AND INTERCEPT=C IS GIVEN BY Y=MX+C.
(b)EQUATION OF A LINE PASSING THROUGH (X1,Y1),(X2,Y2) IS X-X1=((X2-X1)/(Y2-Y1))(Y-Y1)
(c)EQUATION OF THE LINE WHOSE INTERCEPTS ARE a,b IS GIVEN BY X/a+Y/b=1.
(d)EQUATION OF A LINE PASSING THROUGH (X1,Y1) WITH SLOPE=M IS GIVEN BY
Y-Y1=M(X-X1)

DIVISIONS :-

INTERNAL DIVISION :-
IF A(X1,Y1),B(X2,Y2) ARE TWO POINTS OF A LINE THEN A POINT P DIVIDES THE LINES INTERNALLY IN THE RAIO OF ((mX2+nX1)/(m+n),(mY2+nY1)/(m+n)) .
BELOW FIGURE (a) SHOWS THE INTERNAL DIVISION.

EXTERNAL DIVISION :-
IF A(X1,Y1),B(X2,Y2) ARE TWO POINTS OF A LINE THEN A POINT P DIVIDES THE LINES EXTERNALLY IN THE RAIO OF ((mX2-nX1)/(m-n),(mY2-nY1)/(m-n)) .
BELOW FIGURE (b) SHOWS THE POSSIBLE EXTERNAL DIVISIONS.

LOGARITHMS

2009-03-07T05:36:00.000-08:00

LOGARITHMS

LOGARITHMS :-

THIS POST PROVIDES YOU ABOUT THE TERMS,
1.WHAT IS LOGARITHM ?
2.WHAT ARE THE PARTS OF LOGARITHM ?
3.WHAT ARE THE SYSTEMS REGARDING LOGARITM ?
4.WHAT ARE IMPORTANT PROPERTIES OF LOGARITHMS ?

1.WHAT IS LOGARITHM ?
LOGARITHM :-
LOGARITHM IS DEFINED AS WRITTEN IN BELOW FIGURE .

2.WHAT ARE THE PARTS OF LOGARITHM ?
PARTS OF LOGARITHM :-
* LOGARITHM CONSISTS OF 2 PARTS .
(a) CHARACTERISTIC .
(b) MANTISSA .
* CHARACTERISTIC REFER TO THE INTEGRAL PART OF THE LOGARITHM .
* MANTISSA REFER TO THE DECIMAL PART OF THE LOGARITHM .

3.WHAT ARE THE SYSTEMS REGARDING LOGARITM ?
SYSTEMS REGARDING LOGARITHMS :-
* THERE ARE MAINLY TWO TYPES OF LOGARITHMIC SYSTEMS IN USE .
* THEY ARE ,
(a) LOGARITHM TO THE BASE e .
(b) LOGARITHM TO THE BASE 10 .
* LOGARITHM TO THE BASE e IS REFERED AS NATURAL LOGARITHM ,SOME TIMES CALLED AS NAPLIERIAN LOGARITHM .
* LOGARITHM TO THE BASE 10 IS CALLED AS COMMON LOGARITHM .
* IF NO SYSTEM IS MENTIONED ,TAKING BASE AS 10 IS TO BE CONSIDERED WHILE SOLVING PROBLEMS .

4. WHAT ARE IMPORTANT PROPERTIES OF LOGARITHMS ?
IMPORTANT PROPERTIES OF LOGARITHMS :-
IMPORTANT PROPERTIES OF LOGARITHM IS WRITTEN AS SHOWN IN BELOW FIGURE .

SURDS

2009-03-07T05:26:00.000-08:00

SURDS

SURDS :-

THIS POST PROVIDES YOU THE CONCEPT OF SURDS,AND
HOW TO DEAL WITH THE NUMBERS OF SURD TYPE .

WHAT IS A SURD ?
SURD :-
SURD IS DEFINED AS WRITTEN IN BELOW FIGURE .

WHAT ARE THE TYPES OF SURDS ?
TYPES OF SURDS :-
MAINLY SURDS ARE OF 4 TYPES.
THEY ARE,
1.SIMPLE SURD
2.MIXED SURD
3.COMPOUND SURD
4.SIMILAR SURD

WHAT IS SIMPLE SURD ?
SIMPLE SURD :-
SIMPLE SURD IS THE SURD THAT CONSISTS OF A SINGLE TERM .

WHAT IS A MIXED SURD ?
MIXED SURD :-
MIXED SURD IS DEFINED AS WRITTEN IN BELOW FIGURE .

WHAT IS A COMPOUND SURD ?
COMPOUND SURD :-
COMPOUND SURD IS THE SURD THAT IS SUM OR DIFFERENCE
OF 2 OR MORE SURDS

WHAT IS A SIMILAR SURD ?
SIMILAR SURD :-
SIMILAR SURD IS THE SURD WHERE THE TWO SURDS ARE THE
DIFFERENT MULTIPLES OF THE SAME SURD

MENTION IMPORTANT PROPERTIES OF SURDS ?
IMPORTANT PROPERTIES OF SURDS :-
THE IMPORTANT PROPERTIES OF SURDS ARE WRITTEN IN BELOW FIGURE .

SIMPLE AND COMPOUND INTERESTS

2009-02-24T05:15:00.000-08:00

SIMPLE AND COMPOUND INTEREST

SIMPLE AND COMPOUND INTEREST:-

THIS POST PROVIDES YOU,THE REAL LIFE MONEY MANAGING TERMS LIKE
INTERESTS,SIMPLE INTERESTS,COMPOUND INTERESTS .

INTRODUCTION:-

WHAT IS INTEREST?
INTEREST IS THE AMOUNT THAT HAS TO PAY TO LENDER FOR USING IT OVER A TIME.

WHAT IS PRINCIPAL?
PRINCIPLE IS NOTHING BUT THE "MONEY TAKEN".

WHAT IS RATE OF INTEREST?
RATE OF INTEREST IS THE INTEREST BASED ON PRINCIPAL.

TYPES OF INTERESTS:-

SIMPLE INTEREST (SI):-
SIMPLE INTEREST IS THE INTEREST THAT IS BASED ON ORIGINAL INTEREST.

FORMULA'S:-

SI=PNR/100=A-P,

WHERE,
SI=SIMPLE INTEREST.
P=PRINCIPAL
N=NO. OF YEARS
R=RATE OF INTEREST PER YEAR
A=AMOUNT.

COMPOUND INTEREST (CI):-
COMPOUND INTEREST IS THE INTEREST THAT IS BASED ON PRINCIPAL AT THE END OF EACH PERIOD.

FORMULA'S:-

CI=P((1+R/100)^n-1)=A-P,

WHERE,
CI=COMPOUND INTEREST
P=PRINCIPAL
R=RATE OF INTEREST PER UNIT TIME
n=NO. OF TIMES (AMOUNT INVESTED, INTEREST CALC.)
A=AMOUNT.

NUMBER SYSTEMS

2009-02-24T05:08:00.000-08:00

NUMBER SYSTEMS :-

THIS POST PROVIDES YOU THE SOME OF THE BASICS OF NUMBER SYSTEMS THAT
WE USE IN OUR DAILY LIFE .

(1) NUMBERS:-

(a) WHAT ARE NATURAL NUMBERS (N)?

NATURAL NUMBERS :-
NATURAL NUMBERS ARE THE NUMBERS BELONGS TO SET {1,2,.....}

(b)WHAT ARE INTEGERS (Z)?

INTEGERS :-
INTEGERS ARE THE NUMBERS THAT BELONGS TO SET {....-2,-1,0,1,2,3....}

(c) WHAT ARE WHOLE NUMBERS (W)?

WHOLE NUMBERS :-
WHOLE NUMBERS ARE THE NUMBERS BELONGS TO SET {0,1,2,3....}

(d) WHAT ARE REAL NUMBERS (R)?

REAL NUMBERS :-
REAL NUMBERS ARE THE NUMBERS WHICH ARE COMBINATION OF BOTH RATIONAL AND IRRATIONAL NUMBERS.

(e) WHAT ARE COMPLEX NUMBERS (Z)?

COMPLEX NUMBERS :-
COMPLEX NUMBERS ARE THE NUMBERS THARE IN THE FORM SQRT(-P),P=+VE NUMBER.

(f) WHAT ARE RATI0NAL NUMBERS (Q)?

RATIONAL NUMBERS :-
RATIONAL NUMBERS ARE THE NUMBERS THAT ARE OF FORM p/q,q!=0

(g) WHAT ARE IRRATIONAL NUMBERS (Q')?

IRRATIONAL NUMBERS :-
IRRATIONAL NUMBERS ARE THE NUMBERS THAT ARE NOT RATIONAL.

(i) DRAW THE RELATIONSHIP BETWEEN DIFFERENT KINDS OF NUMBERS ?

RELATIONSHIP :-
THE RELATIONSHIP IS SHOWN CLEARLY IN BELOW FIGURE 1.

(2) TYPES OF NUMBERS :-

(a) WHAT IS AN EVEN NUMBER?

EVEN NUMBER :-
EVEN NUMBER IS THE NUMBER THAT IS DIVISIBLE BY 2 LEAVING REMAINDER 0.

(b) WHAT IS AN ODD NUMBER?

ODD NUMBER :-
ODD NUMBER IS THE NUMBER THAT IS NOT EVEN.

(c) WHAT IS A PRIME NUMBER ?

PRIME NUMBER :-
PRIME NUMBER IS THE NUMBER WHICH IS DIVISIBLE BY 1 AND ITSELF.

(d) WHAT IS A COMPOSITE NUMBER?

COMPOSITE NUMBER :-
COMPOSITE NUMBER IS THE NUMBER WHICH IS NOT PRIME.

(e) WHAT IS A PERFECT NUMBER?

PERFECT NUMBER :-
PERFECT NUMBER IS THE NUMBER WHERE THE SUM OF ALL FACTORS EXCLUDING ITSELF IS THE NUMBER ITSELF.

(3) TYPES OF FRACTIONS :-

(a) WHAT IS A PROPER FRACTION?

PROPER FRACTION :-
PROPER FRACTION IS THE FRACTION WHERE THE NUMERATOR ALWAYS LESS THAN DENOMINATOR.

(b) WHAT IS AN IMPROPER FRACTION?

IMPROPER FRACTION :-
IMPROPER FRACTION IS THE FRACTION WHERE THE NUMERATOR ALWAYS GREATER THAN DENOMINATOR.

(c) WHAT IS A MIXED FRACTION?

MIXED FRACTION :-
MIXED FRACTION IS THE FRACTION THAT HAS BOTH INTEGER AND FRACTIONAL PART.

TRIANGLE PROPERTIES

2009-02-11T07:07:00.000-08:00

TRIANGLE PROPERTIES & FORMULAS

TRIANGLE PROPERTIES & FORMULAS :-

THIS POST PROVIDES YOU THE SOME OF THE PROPERTIES/FORMULAS
THAT EVERY TRIANGLE SATISFIES.
THESE PROPERTIES SHOULD BE ON FINGERTIPS FOR QUICK PROBLEM SOLVING .

FOR ANY TRIANGLE ABC,
CONSIDERING,
A,B,C AS THE ANGLES OF A TRIANGLE.
R AS THE CIRCUMFERENCE .
DELTA AS THE AREA OF THE TRIANGLE .
a,b,c AS THE SIDES LENGTHS OF A TRIANGLE .

THEN,

1.sinA+sinB+sinC=4cos(A/2)cos(B/2)cos(C/2).

2.cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(c/2).

3.sin2A+sin2B+sin2C=4sinAsinBsinC.

4.S=4Rcos(A/2)cos(B/2)cos(C/2).

5.a/sinA=b/sinB=c/sinC=2R.

6.cosA=(b^2+c^2-a^2)/(2bc).

7.bcsinA=acsinB=absinC=2delta.

8.delta=rS=abc/(4R)=2R^2sinAsinBsinC=sqrt(r*r1*r2*r3).

9.tan((B-C)/2)=((b-c)/(b+c))*cot(A/2).

10.tan(A/2)=sqrt((s-b)(s-c)/(s(s-a)))=(s-b)(s-c)/delta=delta/(s(s-a)).

11.cotA+cotB+cotC=(a^2+b^2+c^2)/(4delta).

12.r1+r2=4Rcos^2(C/2).

13.r1-r=4Rsin^2(A/2).

14.1/r=(1/r1)+(1/r2)+(1/r3).

15.r1+r2+r3-r=4R.

16.r1*r2+r2*r3+r3*r1=S^2.

17.r(r1+r2+r3)=ab+bc+ca-s^2.

18.if P1,P2,P3 are lengths of altitudes drawn from vertices a,b,c to opposite sides,then P1=2delta/a......

19.if feet of perpendiculars from vertices A,B,C to the opposite sides are at D,E,F,then triangle DEFis called pedal triangle of triangle ABC.
20.circum radius of pedal triangle=R/2.

21.area of pedal triangle=2deltacosAcosBcosC.

22.

Then,AI1=r1cosec(A/2)……

23.

Then,AI=rcosec(A/2)……

PROGRESSIONS

2009-01-22T21:04:00.000-08:00

PROGRESSIONS

PROGRESSIONS :-

THIS POST PROVIDES YOU THE CONCEPTS REGARDING
PROGRESSIONS BASICS AND ITS TYPES LIKE AP,GP,HP .

(1)BASICS OF PROGRESSIONS :-

(a)The origin of natural numbers also lead to the origin of progressions

(b)MATHEMATICIANS:-

NAME-------------------------FORMULA
1.ARCHIMEDES(GREEK)---SUM OF ARITHMETIC PROGRESSION.
2.ARYABHATTA (INDIAN)----SUM OF SQUARES AND CUBES OF N.

{Sum of squares=n(n+1)(2n+1)/6,Sum of cubes=((n(n+1)/2)^2.)

(2)TERMS:-

(a)WHAT IS A PROGRESSION?

PROGRESSION:-
Simply,Progression is nothing but a sequence.

(b)WHAT IS A SEQUENCE?

SEQUENCE:-
Simply,Sequence is a function whose domain is N and
* if range is R ,it is Real sequence.
* if range is complex numbers,it is a complex sequence.

(3)ARITHMETIC PROGRESSION (AP) :-

(a)WHAT IS AN ARITHMETIC PROGRESSION (AP)?

ARITHMETIC PROGRESSION (AP):-
* Arithmetic progression (AP) is sequence,where there is a
constant difference between 2 successive numbers.
* The constant difference is called common difference denoted by d.

(b)FORMULA'S OF ARITHMETIC PROGRESSION (AP):-

If a=first term,d=common difference,then

1.nth term=a+(n-1)d.
2.sum of n terms=Sn=n/2*(2a+(n-1)d).
3.Arithmetic mean (AM) of a,b,c is b=(a+c)/2.

(4)GEOMETRIC PROGRESSION (GP) :-

(a)WHAT IS A GEOMETRIC PROGRESSION (GP)?

GEOMETRIC PROGRESSION (GP):-
* Geometric progression (GP) is sequence,where there ratio of
each term to its previous term is constant.
* The constant is called common ratio denoted by r.

(b)FORMULA'S OF GEOMETRIC PROGRESSIONS (GP):-

If a=first term,r=common ratio,then

1.nth term=a*r^(n-1).
2.Sum of first n terms=Sn=a(1-r^n)/(1-r).
3.Geometric mean (GM) of a,b,c is b=square root(ac).

(5)HARMONIC PROGRESSION (HP) :-

(a)WHAT IS A HARMONIC PROGRESSION (HP)?

HARMONIC PROGRESSION (HP):-
Harmonic progression is sequence,where the reciprocal terms are
in arithmetic progression.

(b)FORMULA'S OF HARMONIC PROGRESSIONS (HP):-

If 1/a=first term,d=common difference,then

1.nth term=1/(a+(n-1)d).
2.Harmonic mean (HM) of a,b,c is b=2ac/(a+c).

(6)RELATION SHIP BETWEEN ARITHMETIC PROGRESSION (AP),GEOMETRIC
PROGRESSION (GP) AND HARMONIC PROGRESSION (HP):-

AM.HM=GM.GM=GM^2.

(i.e) AM,GM,HM FOLLOWS GP.

PROBABILITY

2009-01-22T02:00:00.000-08:00

PROBABILITY

PROBABILITY :-

THIS POST PROVIDES YOU THE BASIC TERMS REGARDING PROBABILITY
AND SOME OF THE BASIC FORMULAS,PROPERTIES AND THEOREM
STATEMENTS .

BASICS OF PROBABILITY :-

WHAT IS PROBABILITY?
PROBABILITY :-
Simply,Probability is the chance of occurence of an event.

BASIC TERMS OF PROBABILITY :-

1.WHAT IS A RANDOM EXPERIMENT?
RANDOM EXPERIMENT :-
Random experiment is the one,whose result is not certain,
but one of the possible outcomes.
EXAMPLE :-
Tossing a coin,rolling a dice .......

2.WHAT IS A SAMPLE SPACE?
SAMPLE SPACE :-
Sample space is the set of all possible outcomes of a
random experiment,denoted by S.
EXAMPLE :-
Tossing a coin,S={Head,Tail};

3.WHAT IS AN EVENT, SIMPLE EVENT,CERTAIN EVENT
AND AN IMPOSSIBLE EVENT?
EVENT :-
Event is the every subset of a sample space.
SIMPLE EVENT :-
Simple event is the event,whose sample space has only
one element.
CERTAIN EVENT :-
Certain event is the event which will definitely happen.
IMPOSSIBLE EVENT :-
Impossible event is the event which will not happen
(i.e propability always 0).

4.WHAT IS AN EQUALLY LIKELY EVENT?
EQUALLY LIKELY EVENT :-
Equally likely event is the one whose chances for happening
of event are equal.

5.WHAT IS AN MUTUALLY EXCLUSIVE EVENT?
MUTUALLY EXCLUSIVE EVENT:-
Mutually exclusive event is the event,that the happening of
one of the events prevent the hapening of the remaining events.

6.WHAT IS AN EXHAUSTIVE EVENT?
EXHAUSTIVE EVENT :-
Exhaustive event is the one, that consists of all possible
events of a random experiment.

FORMULA'S OF PROBABILITY:-

1.P(S)=1
2.P(A')=1-P(A)
3.P(E)=n(E) / n(S), where E is an event of S.
4.P(AUB)=P(A)+P(B)-P(A^B)
5.P(AUBUC)=P(A)+P(B)+P(C)-P(A^B)-P(B^C)-P(C^A)+P(A^B^C)

6.P(A ^ B')=P(A)-P(A^B)
7.P(A' ^ B')=1-P(AUB)
8.P(A'UB')=1-P(A^B)

9.P(B/A)=P(A^B)/P(A) (FOR CONDITIONAL EVENTS)
10.P(A^B)=P(A).P(B/A) (FOR DEPENDENT EVENTS)
11.P(A^B)=P(A).P(B) (FOR INDEPENDENT EVENTS)

12.IF A COIN TOSSED n TIMES OR n COINS TOSSED AT A TIME ,THEN n(S)=2^n

13.ODD IN & AGAINST FAVOUR OF EVENT :-
A)ODDS IN FAVOUR OF A =P(A):P(A')
B)ODDS AGAINST FAVOUR OF A=P(A'):P(A)

14.BAYE'S THEOREM :-
IF A1,A2,...An ARE n MUTUALLY EXCLUSIVE AND EXHAUSTIVE
EVENTS OF A RANDOM EXPERIMENT AND E BE ANY EVENT
THEN,
P(Ak/E)={P(Ak)P(E/Ak)} / { (SUMMATION I= 1 TO n) P(Ai)P(E/Ai)}