Quant Theory

QUANT THEORY
1) nPr = n!/(n-r)!
2) nPn = n!
3) nCr = n!/(n-r)!r!
4) nCn = 1
5) nP0 = 1
6) nC0 = 1
7) AP An = a + (n-1)d
Sn = n/2[2a + (n-1)d]
8) GP An = ar(n-1)
Sn = a(rn – 1 )/ (r-1)
S8 = a/(1-r)
9) 1 mile = 1760 yards
10) 1 yard = 3 feet
11) 1 mile2 = 640 acres
12) I gallon = 4 quarts
13) 1 quart = 2 pints
14) 1 pint = 2 cups
15) 1 cup = 8 ounces
16) 1 pound = 16 ounces
17) 1 ounce = 16 drams
18) 1 kg = 2.2 pounds
19) 30-60-90 triangle ? 1:v3:2 sides
20) 45-45-90 triangle ? 1:1:v2 sides
21) a3>b3 ? a>b
22) If A than B => not B than not A
23) Zero divided by any nonzero integer is zero.
24) Division by 0 is undefined.
26) The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you have a relatively large standard deviation.
27) n(A ? B U C) = n(A) + n (B)+ n(C) – n(A n B) – n(A n C) – n(B n C) + n(A n B n C)
28) n(Aonly) = n(A) – n(A n C) – n(A n B) + n(A U B U C)
29) Dividend = Divisor * Quotient + Remainder
30) LCM * HCF = Product of 2 numbers.
31) 1 + 2 + 3 ………………..n = n * n+1 / 2
32) Sum of squares of 1st n natural numbers = n (n+1)(2n+1) / 6
33) Sum of cubes of 1st n natural numbers = [n (n+1)/2]2
Number ( x ) Square ( x 2 ) Cube ( x 3 )
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
6 36 216
7 49 343
8 64 512
9 81 729
10 100 1000
11 121 1331
12 144 1728
13 169 2197
14 196 2744
15 225 3375
16 256 -
17 289 -
18 324 -
19 361 -
21 441 -
22 484 -
23 529 -
24 576 -
25 625 -
35)
Fractions and Percentage:
Fraction Decimal Percentage
1 / 2 0.5 50
1 / 3 0.33 33 1/3
2 / 3 0.66 66 2/3
1 / 4 0.25 25
3 / 4 0.75 75
1 / 5 0.2 20
2 / 5 0.4 40
3 / 5 0.6 60
4 / 5 0.8 80
1 / 6 0.166 16 2/3
5 / 6 0.833 83 2 / 3
1 / 8 0.125 12 1 / 2
3 / 8 0.375 37 1 / 2
5 / 8 0.625 62 1 / 2
7 / 8 0.875 87 1 / 2
1 / 9 0.111 11
2 / 9 0.222 22
1 / 10 0.1 10
1 / 20 0.05 5
1 / 100 0.01 1
36) Average speed = Total distance / Total Time
1. When equal distances are covered in different speed then we take the harmonic mean
Av Speed = 2ab / a + b
1. Different distances in same time we take AM
Av Speed is = a + b / 2
37) Simple Interest: SI = PRT / 100, A = P + SI
38) 1 Nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
1 half = 50 cents
1 dollar = 100 cents
39) Equilateral triangle, Area = (v3 * a2)/4
40) Area of trapezium = ½ (Height * Sum of parallel sides)
41) Arc Length = (?/ 360) 2 ? r
42) Area of sector = (?/ 360) ? r2
43) Equal chords are equidistant from the center.
44) (x+y) 8 = 8C8x8 + 8C7x7y + 8C6x6y2 + 8C5x5y3 + … + 8C2x2y6 +8C1xy7 + 8C0y8
45) Sometimes we get so involved with the nitty-gritties of mathematics that we start functioning like automatons and stop thinking. Don’t fall prey to this trap. For example, what is the probability that a number amongst the first 1000 positive integers is divisible by 8? Don’t start counting the multiples of 8! The figure of 1000 is a red herring. Use a little common sense. The numbers will be 8,16,24,32…So, 1 in every 8 numbers is a multiple of 8, even if you consider the first million integers. So Probability is 1/8
46) The number of integers from A to B inclusive is = B -A +1
47) Average of consecutive numbers:
Eg from 13 to 77 = (13+77)/2
48) Slope = (change in y)/(change in x)
49) 00 = undefined