Set Theory Practice Questions2

In this page set theory practice questions2 we are going to see some practice questions. For each questions you can find solution.

(1) If A and B are two sets and U is the universal set such that n (U) = 700, n (A) = 200, n(B) = 300 and n (A ∩ B) = 100,find n (A' ∩ B').            Solution

(2) Given n (A) = 285,n (B) = 195,n (U) = 500,n (A U B) = 410,find n(A'UB')            Solution

(3) For any three sets A,B and C if n (A) = 17, n (B) = 17, n(C)=17,n(A∩B) = 7,n (B∩C) = 6 , (A ∩C)= 5 and n (A ∩ B ∩C).              Solution

(4) verify n (AUBUC)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n (A∩C)+n(A∩B ∩C)

(i) A = {4,5,6},B = {5,6,7,8} and C = {6,7,8,9}

(ii) A = {a,b,c,d,e} B = {x,y,z} and C = {a,e,x}   Solution

(5) In a college,60 students enrolled in chemistry,40 in physics,30 in biology,15 in chemistry and physics,10 in physics and biology,5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects.   Solution

(6) In a town 85 % of the people speak Tamil,40 % speak English and 20 % speak Hindi. Also 32% speak English and Tamil, 13 % speak Tamil and Hindi and 10 % speak English and Hindi, find the percentage of people who can speak all the three languages.    Solution

(7) An advertising agency finds that, of its 170 clients,115 use Television,110 use Radio and 130 use Magazines. Also 85 use Television and Magazines,75 use Television and Radio,95 use Radio and Magazines,70 use all the three. Draw Venn diagram to represent these data. Find 

(i) how many use only Radio?

(ii) how many use only Television?

(iii) how many use Television and Magazine but not radio?    Solution

(8) In a school of 4000 students,2000 know French,3000 know Tamil and 500 know Hindi,1500 know French and Tamil,300 know French and Hindi,200 know Tamil and Hindi and 50 know all the three languages.

(i) How many do not know any of the three languages?

(ii) How many know at least one languages?

(iii) How many know only two languages?

(9) In a village of 120 families,93 families use firewood for cooking,63 families use kerosene,45 families use cooking gas,45 families use firewood and kerosene,24 families use kerosene and cooking gas,27 families use cooking gas and firewood. Find how many use firewood,kerosene and cooking gas.

Sets and Functions

Exercise 1.1

Exercise 1.2

Exercise 1.3

Exercise 1.4


Exercise 4.1

Exercise 4.2

Exercise 4.3

Coordinate Geometry



Exercise 11.1

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Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power


Quantitative aptitude

Multiplication tricks


Aptitude test online


Test - I

Test - II


Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices





Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet



Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem


Mensuration formulas

Area and perimeter



Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem


Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance


Area of triangle

Area of quadrilateral



Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator


Missing addend 

Double facts 

Doubles word problems


Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work


Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry


Converting metric units

Converting customary units


HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree


Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6