Time and clock
Clock is a device which is used to measure and display the time. The face or dial of a clock is divided into 60 equal parts called minute space and it is numbered from 1 to 12, in such a way that each subsequent number is equidistant (5 minutes spaces apart) from the preceding number. A clock has two hands, the smaller one is the hour hand/ while larger one is called the minute hand. When hour hand travels five minutes spaces, the minute hand travels 60 minutes spaces. Therefore, in 60 minutes the minute hand gains 55 minute on the hour hand.
Properties of clock
In 60 minutes/ the minute hand gains 55 minutes on the hour hand,
A clock is said to be too fast, if it shows time more than that of shown by a correct clock.
A clock is said to be too slow, if it shows time less than that of shown by a correct clock.
In every hour, both the hands coincide once.
When the two hands are at right angle, they are 15 minutes spaces apart.
When the two hands are in opposite directions, they are 30 minutes spaces apart, this situation occurs once in a hour.
The hands of a clock are in straight line when they are coincident or opposite to each other.
Hour hand of a clock takes 12 hours to trace the angle of \[360{}^\circ \].
Minute hand of a clock takes 1 hour to trace the angle of \[360{}^\circ \].
Example 1
Choose the time from the following options when the hands of a clock will be in the same straight line.
(a) 4:00 p.m. (b) 8:00 p.m.
(c) 7:00 p.m. (d) 6:00 p.m.
(e) None of these
Answer (d)
Explanation: The two hands of a clock are in the same straight line when they are either coincident or 30 minutes spaces apart from each other.
At 4:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.
So option (a) is incorrect.
At 8:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.
So option (b) is incorrect.
At 7:00 p.m., the minute hand will be 25 minutes spaces apart from the hour hand.
So option (c) is incorrect.
At 6:00 p.m., the minute hand will be 30 minutes spaces apart from the hour hand.
So option (d) is correct.
Therefore, the correct answer is 6 : 00 p.m.
Between 2 O'clock to 10 O'clock, how many times the hands of a clock are at right angle?
(a) 14 (b) 12
(c) 16 (d) 15 more...
What is Non-verbal Reasoning
Non-Verbal reasoning is a figure based reasoning. It has no language at all. To solve non-verbal problems one has to find out the pattern of pictorial presentation in the given figure. To get a more clear concept about non-verbal reasoning. Let us see the types of problems coming before you.
Types of Problems
Problems Based on Mirror Image
In a mirror image, left part of an object becomes right part and right part becomes left part.
Remember the rule given below,
Left Hand Side (LH.S.) \[\overset{{}}{leftrightarrows}\] Right hand Side (R.H.S.)
Example 1
Number System
A system of naming or representing numbers.
Number
A number is a mathematical object which is used to count, label and measure,
Example
1, 5, 19, 325
Main Type
Natural numbers/whole-numbers, integers, rational numbers, irrational numbers, real numbers.
Natural Numbers
Counting numbers 1, 2, 3, 4, 5, 6... are called natural numbers. These numbers are also referred to as the positive integers.
Properties
The set of natural numbers, commonly denoted by N.
1 is the smallest natural number.
No largest natural number can be found because the set of natural numbers is infinite,
The successor of a natural number is 1 more than the number.
The predecessor of a natural number is 1 less than the number.
Whole Numbers
The natural numbers along with zero form the collection of whole numbers.
Example 0, 1, 2, 3, 4, 5, 6 ....
Properties
The set of whole numbers, commonly denoted by W.
0 is the smallest whole number.
No largest whole number can be found because the set of whole numbers is infinite.
The successor of a whole number is 1 more than the number
The predecessor of a whole number is 1 less than the number.
Factors
A factor of a number is an exact divisor of that number.
Example 1
Factors of \[4=1,\,2,\,4\]
Example 2
Factors of \[15=1,\,3,\,5,\,15\]
Properties
1 is the factor of every number.
Every number is a factor of itself.
The factors of a number are smaller or equal to the number.
Numbers of factors of a given number are finite.
Every factor of a number is an exact divisor of that number.
A number for which sum of all of its factors is equal to twice of twice the number is called a perfect number.
1 is the only number which has exactly one factor, namely itself.
Multiple
A multiple of any natural number is a number formed by multiplying that number by any whole number or a multiple is the product of any quantity and an integer or a number is said to be multiple of any of its factors.
Example 1
First three multiple of 4 are \[4\times 1= 4,4\times 2 = 8\] and \[4\times 3 =12\]
Example 2
First three multiple of 19 are \[19\times 1=19,19\times 2=38\] and \[19\times 3=57\]
Properties
0 is the multiple of everything.
Every number is a multiple of itself,
Every multiple is greater than or equal to that number
The number of multiples of a given number is infinite.
A number is a multiple of each of its factors,
Prime Numbers
The numbers which have exactly two factors, 1 and the number itself, are called prime numbers.
Example more...
Algebra
Algebra is generalized arithmetic in which unknown or unspecified numbers are represented by using letters known as literals.
Constant and variable: A symbol having a fixed numerical value is called a constant and a symbol which takes on various numerical values is known as variables.,
Example: \[8,-25,\text{ }6\frac{6}{11},\,3\frac{1}{2}\] are examples of constants whereas a, b, c, u, u x and y are examples of variables.
Algebraic expression: An algebraic expression composed of arithmetic numbers, letters and signs of operation.
Example: \[5x+8,\text{ }9y+3x\] and 8z are examples of algebraic expressions.
Terms of an expression: Various parts of an algebraic expression separated by the signs plus (+) or minus (-) are known as the terms of the expression.
Example: The algebraic expression \[6x+8y+9\] have three terms, 6x, 8y and 9.
Monomial: An algebraic expression having only one term is known as monomial.
Example: \[2,5x,6xy\] and\[-89xyz\] are examples of monomials.
Binomial: An algebraic expression having two terms is known as binomial.
Example: \[2x+y,3z+5y\] and \[x+8\]are examples of binomials,
Trinomial: An algebraic expression having three terms is known as trinomial
Example: \[x+y-9,\text{ }5a+6b+c\] and \[5x+xy+9\] are examples of trinomials.
Polynomial: An algebraic expression containing two or more terms is called polynomial,
Example: \[5x+6,\text{ }7x+8y+9\]and \[15+xy+9y+8x\] are examples of polynomials,
Factor: A factor is any one of two or more numbers that are multiplied together.
Example: 5 and x are factors of 5x.
Coefficients: In a product of numbers and literals, any of the factors is called the coefficient of the product of other factors.
Example: In 7xy, the coefficient of x is 7y and the coefficient of y is 7x.
Like terms: The terms which have the same literal factors are called like or similar terms.
Example: 7x, 9x, x are examples of like terms.
Unlike terms: The terms which have different literal factors are called unlike or dissimilar terms.
Example: \[5x,3xy,7xz\] are examples of unlike terms.
Algebraic equation: An equation is a mathematical statement equating two quantities.
Example: \[x+9=15,\text{ }5x-8=3x\] and \[3x-7=4\] are examples of algebraic equations.
Solution of equation: The value of the variable in an equation which satisfies the equation is called solution of the equation.
Example: \[x+9=20\], here the value \[~x=11\] satisfies the equation/ therefore \[~x=11\] is the solution of the equation \[x+9=20\].
Ratio
The ratio of two quantities of the same kind and in the same units is a fraction which shows how many times the one quantity is of other.
Example
If a and b are two physical quantities of same kind and in the same units, then the fraction \[\frac{a}{b}\]is called the ratio of a to b and denoted as a : b. Here a and b are called terms of the ratio.
The former 'a' is called the first term or antecedent and the latter b is called second term of consequent
Note 1: A ratio is unchanged if the two more...
Geometry
The branch of mathematics which deals with mathematical objects like points, lines, panes and space is called geometry.
Point: A point is to be thought of as a location in space. In other words, a point determines location in a space.
Line segment: Let A and B be two point on a plane. Then the straight path between points a and B is known as Sine segment AB.
The above line segment is denoted as\[\overline{AB}\].
Ray: A line segment extended endlessly in one direction Is. called a ray.
The above ray Is denoted as \[\overrightarrow{AB}\].
Line: A line is a straight path that extends on and on in both directions endlessly.
The above ray Is denoted as \[\overrightarrow{AB}\].
Line: A line is a straight path that extends on and on in both directions endlessly.
Parallel lines: If two or more lines do not meet each other however far they are extended, then they are called parallel lines
Intersecting lines: If two or more lines meet each other at one point they are called intersecting lines.
Concurrent lines: Three or more lines in a place are concurrent if all of them pass through the same point. The common point is called point of concurrence.
Mensuration
Mensuration is the branch of mathematics which deals with the measurement of lengths, area and volume of the plane and solid figures.
Perimeter of a plane figure: The distance all round a plane figure is called perimeter of the figure or the lengths of boundary of a plane figure is known as its perimeter
\
Perimeter of the quadrilateral \[ABCD=AB+BC+CD+DA\]
\[=40\text{ }cm+10\text{ }cm+40\text{ }cm+10\text{ }cm\]
\[=100\text{ }cm\]
Perimeter of the hexagon \[ABCDEF=AB+BC+CD+DE+EF+FA\]
\[=100\text{ }m+120\text{ }m+90\text{ }m+45\text{ }m+60\text{ }m+80\text{ }m\]
\[=495\text{ }m\]
Perimeter of a scalene triangle = Sum of all the three sides of the triangle.
Example: Find the perimeter of the triangle ABC.
Perimeter of the triangle \[ABC=AB+BC+CA\]
\[=4\text{ }cm+12\text{ }cm+8\text{ }cm\]
\[=24cm\]
Perimeter of a rectangle \[=2\times \left( length+breadth \right).\]
Example: Find the perimeter of the following rectangle ABCD.
Perimeter of rectangle \[ABCD=2\times \left( AB+BC \right)\]
\[=2\times \left( 15cm+9cm \right)\]
\[=48\text{ }cm\]
Perimeter of regular shapes
Perimeter of an equilateral triangle \[\text{=3 }\!\!\times\!\!\text{ length of one side}\].
Example: Find the perimeter of the given triangle.
Perimeter of the triangle \[=3\times 4\text{ }cm\]
\[=12\text{ }cm\]
Perimeter of a square: \[\text{4 }\!\!\times\!\!\text{ length of one side}\text{.}\]
Example: Find the perimeter of the given square.
Perimeter of the square \[=4\times 1\text{ }m\]
\[=4\text{ }m\]
Perimeter of regular pentagon \[=5\text{ }\times \text{ }length\text{ }of\text{ }one\text{ }side.\]
Example: Find the perimeter of the given pentagon.
Perimeter of the pentagon \[=5\times 4\text{ }cm\]
\[=20\text{ }cm\]
Perimeter of the regular hexagon \[=6\times length\text{ }of\text{ }one\text{ }side.\]
Perimeter of the hexagon \[=6\times 5\text{ }cm\]
\[=30\text{ }cm.\]
Area of a plane figure: The measurement of the region enclosed by a plane figure is called area of the figure or area is the amount of surface covered by the shape.
Area of triangle \[=\frac{1}{2}\times base\times height.\]
Example: Find the area of the given triangle.
Area of the triangle \[=\frac{1}{2}\times 4cm\times 6cm=12c{{m}^{2}}\]
Area of rectangle: \[length\times breadth.\]
Example: Find the area of the given rectangle.
Area of the rectangle \[=8\text{ }cm\times 6\text{ }cm=48\text{ }c{{m}^{2}}\] more...
Data
A collection of information in the form of numerical figures is called data.
Raw data: Data obtained in the original form is called raw data.
Tabulation of data: Arranging the data in a systematic form in the form of a table is known as tabulation of data.
Statistics
The branch of mathematics which deals with the collection, presentation, analysis and interpretation of numerical data is called statistics.
Example
A dice was thrown 30 times and the following outcomes were noted:
4, 3, 3, 2, 5, 4, 4, 6, 1, 2, 2, 3, 4, 6, 2, 3, 3, 4, 1, 2, 3, 3, 4, 5, 6, 3, 2, 1, 3, 4.
Represent the above data in the form of frequency distribution.
Explanation: We may present the data as shown below:
MENTAL ABILITYFUNDAMENTALSMental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.
Mental ability develop logical thinking among students.
Mental ability is based on some concepts.
Series completion
Number series
Alphabet series
Number Series: The three or more numbers having a sequence of pattern is given. The numbers follow a certain rule which relates the consecutive terms. Students should be able to recognize the rule or pattern. This will be help them to find the next term or number.
Look at the example given below1.Series of odd number1, 3, 5, 7, 9, ___________Ans.: Next number is 11.2.Series of even number. more...
GEOMETRYGEOMETRYGeometry is derived from two greek words "Geo" means "Earth" metron means "Measurement". That means measurement of Earth is called geometry.Basics terms of geometry
There are three basics undefined terms of geometry.
(i) Point (ii) Line (iii) PlanePoint: Point is a mark of position, it is made by sharp tip of pen, pencil and nail.
It is denoted by capital letter.
It is represented by
A point has no length, no breadth and no thickness.
Line segment: The distance between two points in a same plane is called a line segment.
It is denoted by\[\overline{AB}\]. It is measured in 'cm' or 'inch'.