Formula list which helps during Interview/Placement

ALGEBRA:

1.      Natural numbers: 1, 2, 3,..

2.      However, 1 is not a prime number.

Formulae:

〖(a+b)〗^2= a^2+ b^2+ 2ab

〖(a-b)〗^2= a^2+ b^2- 2ab

a^2- b^2= (a+b)(a-b)

a^3- b^3= (a-b)(a^2+ b^2+ ab)

a^3+ b^3= (a+b)(a^2+ b^2- ab)

〖(a+b)〗^2 - 〖(a-b)〗^2=4ab

〖(a+b)〗^2 + 〖(a-b)〗^2= 2(a^2+b^2)

〖(a+b)〗^3= a^3+ b^3+ 3ab(a+b)

〖(a-b)〗^3= a^3- b^3- 3ab(a - b)

a^m * a^n= a^(m+n)

a^m / a^n= a^(m-n)

Divisibility Rules:

1.      By 2: If the last digit of number is divisible by 2.

2.      By 3: If the sum of digits of the number is 3 or a multiple of 3.

3.      By 4: If the number formed by the last two digits is divisible by 4.

4.      By 5: if the units place digit is 0 or 5.

5.      By 6: If the number is divisible by both 2 and 3.

6.      By 8: If the number formed by the last two digits is divisible by 8.

7.      By 9: If the sum of the digits of the number is divisible by 9.

8.      By 11: if the difference of the sum of digits at odd places and even places is 0 or a multiple of 11.

9.      By 12: If the number is divisible by 3 and 4.

RATIO AND PROPORTION:

1.      A ratio x:y does not change when both its terms are multiplied or divided by the same number.

2.      A ratio is always expressed in simplest form.

3.      x/y  y/x when x y

4.      In a proportion a:b :: c:d, a and d are known as extremes and b and c are known as means.

5.      In a proportion a:b :: c:d, ad=bc.

6.      If a sum of money X is divided in the ratio a:b:c, then the three parts are:

aX/a+b+c, bX/a+b+c, cX/a+b+c

7.      If A:B= a:b and B:C= p:q, then A:B:C= ap:bp:bq

8.      If two investments are in the ratio a:b, and period in the ratio p:q, then profit will be shared in the ratio ap:bq.

ARITHMETIC PROGRESSION:

1.      Let a be the first term and d be its common difference, then A.P is a, a+d, a+2d, a+3d…. a+ (n-1)d.

2.      The nth term will be: a + (n-1)d.

PROBABILITY:

1.      An event’s probability is the proportion of times that we expect the event to occur, if the experiment were repeated a large number of times.

2.      Experiment: Phenomenon where outcomes are uncertain. For example: Single throws of a six-sided die

3.      Sample space: Set of all outcomes of the experiment. For example:S=(1; 2; 3; 4; 5; 6); (1; 2; 3, 4; 5; or 6dots show)

4.      Event: A collection of outcomes; a subset of S.A = (3)(3 dots show), B =(3; 4; 5; or 6)(3, 4, 5, or 6 dots show)or ’at least three dots show’.

5.      For any event A, the probability that A will occur is a number between 0 and 1, inclusive:

                                                                 0 P(A) 1;

P( ) = 0; P(S) = 1:

6.      Probability: A number between 0 and 1 assigned toan event.

7.      P(A.B) = P(A)P(B)

8.      Events are said to be mutually exclusive if they have no outcomes in common. In other words, it isimpossible that both could occur in a single trial of the experiment. For mutually exclusive events holds

P(A.B) = P( ) = 0:

9.      For mutually exclusive events, the probability that at least one of them occurs is

P(A C) = P(A) + P(C).

10.  For any two events A and B, the probability that either A or B will occur is given by the inclusion-exclusion rule

P(A B) = P(A) + P(B)- P(A.B)

11.  P(A B C) = P(A) + P(B) + P(C)- P(A.B)- P(A.C)- P(B.C) + P(A.B.C)

12.  P(E)= n(E)/n(S)

Where S is the sample space and let E be the event.

PERMUTATION AND COMBINATION:

1.      If any event can occur in m ways and after it happens in any one of these ways, a second event can occur in n ways, then both the events together can occur in m´nways.

2.      The total number of permutations of n objects is n (n – 1) ....2.1.=n´(n -1) !

3.      = n(n -1)(n - 2)...(n - r +1)

4.      Let n ³1 be an integer and r £ n . Let us denote the number of ways of choosing r objects out of n objects by . Then

/ r! = n!/ (n-r)!r!

PROFIT, LOSS AND DISCOUNT:

1.      Gain= S.P-C.P

2.      Loss= C.P- S.P

3.      Gain%=  (Gain*100)/C.P

4.      Loss%= (Loss*100)/C.P

5.      Discount is always calculated on MRP or list price unless and until mentioned otherwise.

6.      SP= MRP- Discount

7.      Successive Discounts: If a shopkeeper gives a discount D% and E% in two stages then final equivalent discount (D)= D + E – (D*E)/100

AVERAGE:

1.      Average= Sum of n quantities/ n

TIME SPEED AND WORK:

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =	1	.
	n

2. Days from Work:

If A's 1 day's work =	1	,	then A can finish the work in n days.
	n

3. Ratio:

If A is n times as good a workman as B, then:

Ratio of work done by A and B = n : 1.

Ratio of times taken by A and B to finish a work = 1 : n.

4.      If A completes a piece of work in n days and B in m days, then they both working together can complete the work in (nm/m+n) days.

TIME, DISTANCE AND SPEED:

1.      Speed= Distance/time

2.      To convert the speed, from kmh to m/s we multiply it by a factor 5/18.

3.      To convert the speed, from m/s to kmp we multiply it by a factor 18/5.

SIMPLE AND COMPOUND INTREST:

SIMPLE INTREST:

1.      SI= PRT/100

2.      A = P(1 + rt)= P+SI

COMPOUND INTREST:

1.     

2.      CI= A-P= -P= P

3.      If difference between CI and SI is Rs. D on the principal at R% rate per annum for two years, then D= .

P= Principle amount; r/R= Rate of interest; T/n= time(in years); A= amount

MENSURATION:

RECTANGLE:

1.      Area of Rectangle= l*b

2.      Perimeter of Rectangle= 2(l+b)

SQUARE:

1.      Area of square=

2.      Diagonal of square= * Side

TRIANGLE:

1.      Area of triangle= ½*base*height

2.      Perimeter of triangle= a+b+c

3.      Area of equilateral triangle= /4*

PARALLELOGRAM:

1.      Area= Base*height

2.      Area of Rhombus= ½*(product of diagonals)

3.      Area of trapezium= ½*(sum of parallel sides)*(distance between them)

CIRCLE:

1.      Area of Circle=

2.      Circumference of a circle= 2 r

CUBOID:

1.      Volume= l*b*h

2.      Surface area= 2(lb+bh+hl)

CUBE:

1.      Volume= .

2.      Surface area= 6

3.      Diagonal= *a

CYLINDER:

1.      Volume= h

2.      Curved surface area= 2 rh

3.      Total surface area= 2 rh+ 2

CONE:

1.      Slant height= l=

2.      Volume= 1/3* h

4.      Curved surface area= rl

5.      Total surface area= rl+

SPHERE:

1.      Volume= 4/3*

2.      Surface area=