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 1.2 |
Exercise 1.4 |
Sequence and Series
Algebra
MATRIX
Exercise 4.2 |
Exercise 4.3 |
Coordinate Geometry
Exercise 5.3 | |||
Geometry
Trigonometry
Mensuration
Statistics
Probability
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WORD PROBLEMS
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Word problems on direct variation and inverse variation
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Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
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Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
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Word problems on sets and venn diagrams
Pythagorean theorem word problems
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OTHER TOPICS
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 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