|Quantitative Aptitude Important Formulas Logical ReasoningGeneral Knowledge of MPGeneral Knowledge of India|
Area and Perimeter - Important Formulas,Tricks and Examples
Perimeter = (a+b+c) ,there a,b,c are the sides of a triangle
Area = 1/2(base*height) = √[s(s-a)(s-b)(s-c)] there s = (a+b+c)/2
Perimeter = base + height + hypotenuse
Area = 1/2(base*height)
Hypotenuse = √(base2+height2)
Perimeter = 3*length of a side
Area = 1/2(base*height) = (√3/4)*(length of a side2)
height=√3* length of a side/2
Perimeter = 4 * length of a side
Area = length of a side2
Diagonal, d = √2 * length of a side
Perimeter = 2(length + breadth)
Area = length * breadth
Diagonal, d = √( length2+breadth2)
Perimeter = 2(base+ height)
Area = base* height
Perimeter of Rhombus = 4 x length of a side
Area = (1/2) * product of the diagonals
Circumference = 2*π*radius = π*diameter
Area = π*radius2 = diameter2/4
Diameter = 2*radius
Length of an arc = (2*π*radius*θ)/360 ,where θ is the central angle
Area of a sector = (1/2) (arc x radius) = π*radius2*θ/360
Circumference of a semi-circle = π*radius+2*radius=1/2(π*diameter)+diameter
Area of a semi-circle = π*radius2/2
Sum of the angles of a triangle is 180 degrees
Pythagoras theorem(right angle triangle) => (Hypotenuse)^2 = (base)^2 + (Height)^2
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Numbers - Important Formulas,Tricks and Examples
The common number system is decimal number system.
Types of Numbers
Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 .
Whole numbers:The whole numbers are just all the natural numbers plus zero.
Integers: Integers incorporate all positive and negative numbers with zero.
Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.
Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7.
Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers.
Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers.
Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers.
Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself.
Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself.
Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2.
(a+b)2 = a2 + 2ab + b2
(a+b)2 - (a-b)2 = 4ab
a2-b2 = (a-b)(a+b)
(a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2
a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2)
Test of Divisibility
Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..).
Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.
Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5.
Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3.
Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible
Divisibility By 10 : A number is divisible by 10, if it ends with 0.
Divisibility By 11 : 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 either 0 or a number divisible by 11.
Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3.
Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13.
Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7.
Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5.
Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros.
Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17.
Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9.
Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19.
Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.
Choose appropriate article for the given sentence:
|Child Development & Pedagogy|
Which of the following is the most effective way to create interest for learning in a student?
The rules of presenting the content to make them easy are called_________?
The term SLD in children’s mental health denotes for?
The child will be able to use proper sentences by the age of?
______is an institutional mechanism to provide representation to the states of India?
|Books and Authors|
Which text is not written by Kalidasa?
Which Constitutional Amendment introduced Right to Education as a Fundamental Right?
Which animal is engraved on Harappan seals?
Who is known for initiating electoral reforms in India to ensure free and fair elections?
The sequence in which the given terms are mentioned in the preamble to the Constitution of India is?
Which of the following parts of the Constitution of India provides fundamental rights ?
|Books and Authors|
Who among the following is the author of ‘Politics’?
Which one is the text not written by Abul Fazl?
Which King was the author of Ratnawali, Nagananda, Priyadarsika?
|Fill in the blank|
Fill in the blanks with the most appropriate preposition in the given sentence.
The workers were so skilled that their _____ was quite visible even to a layman.
Choose appropriate article for the given sentence:
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