CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 4 - MCQExams.com

Examine whether the following statements are true or false:
$$(a)\epsilon (a,b,c)$$
  • True
  • False
Examine whether the following statements are true or false:$$\left\{a \right\}  \subset \left\{a,b,c \right\}$$
  • True
  • False
State true or false for each of the following. Correct the wrong statement.
If T = {a, l, a, h, b, d, h}, then $$n (T) = 5$$
  • True
  • False
For sets $$\phi  , A = \left \{ 1,3 \right \} = B = \left \{ 1, 5, 9 \right \} , C = \left \{ 1, 5, 7, 9 \right \}$$ True option is 
  • $$ A \subset B $$
  • $$ B \subset C $$
  • $$ C \subset B $$
  • $$ A \subset C $$
The equation x + cosx $$=$$ a has exactly one positive root. Complete set of values of 'a' is
  • (0, 1)
  • $$(-\infty, 1)$$
  • (-1,1)
  • $$(1,\infty)$$
  • $$(0,\infty)$$
Let $$S$$ be a non-empty subset of $$R$$. Consider the following statement:
$$p$$ : There is a rational number $$x$$  such that $$x > 0$$.
which of the following statements is the negation of the statement P ? 
  • There is no rational number $$\mathrm{x}\in \mathrm{S}$$ such that $$\mathrm{x}\leq 0$$
  • Every rational number $$\mathrm{x}\in \mathrm{S}$$ satisfies $$\mathrm{x}\leq 0$$
  • $$\mathrm{x}\in \mathrm{S}$$ and $$\mathrm{x}\leq 0= \mathrm{x}$$ is not rational
  • There is a rational number $$\mathrm{x}\in \mathrm{S}$$ such that $$\mathrm{x}\leq 0$$
The smallest set $$A$$ such that $$A\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $$ is 
  • $$\left\{ 2,3,5 \right\} $$
  • $$\left\{ 3,5,9 \right\} $$
  • $$\left\{ 1,2,5,9 \right\} $$
  • $$\left\{ 1,2 \right\} $$
If $$A$$ and $$B$$ have some elements in common, then $$n(A \cup B)$$ is:
  • $$= n(A) + n (B)$$
  • $$ > n (A) + n(B)$$
  • $$< n(A) + n(B)$$
  • $$\geq n (A)+ n (B)$$
If $$A \cap B = \phi$$, then $$A \Delta B$$ =
  • $$A \cap B$$
  • $$A \cup B$$
  • $$A - B$$
  • $$B - A$$
In an examination $$80\%$$  passed in English, $$85\%$$ in Maths, $$75\%$$ in both and $$40$$ students failed in both subjects. Then the number of  students appeared are
  • $$300$$
  • $$400$$
  • $$500$$
  • $$600$$
$$p\cap (q\cup r)=?$$
  • $$p\cup (q\cap r)$$
  • $$(p\cap q)\cap (q\cap p)$$
  • $$(p\cap q)\cup r$$
  • $$(p\cap q)\cup (p\cap r)$$
There are 19 hockey players in a club. On a  particular day 14 were wearing the prescribed hockey shirts, while 11 were wearing the  prescribed hockey pants. None of then was without hockey pant  or hockey shirt. How many of  them were in complete  hockey uniform?
  • 8
  • 6
  • 9
  • 7
In an examination, $$34\%$$ of  the candidates fail in Arithmetic and $$42\%$$ in  English. If $$20\%$$ fail in Arithmetic and English, the  percentage of those passing in both subjects is :
  • $$44$$
  • $$45$$
  • $$46$$
  • $$47$$
In a science talent examination, 50% of the candidates fail in Mathematics and 50% fail in Physics. If 20% fail in both these subjects, then the  percentage who pass in both Mathematics and Physics is:
  • 0%
  • 20%
  • 25%
  • 50%
All the students of a batch opted Psychology, Business, or both. 73% of the students opted Psychology and 62% opted Business. If there are  220 students, how many of them opted for both Psychology and business?
  • $$60$$
  • $$100$$
  • $$77$$
  • $$35$$
In a group of $$15, 7$$ have studied German, $$8$$ have studied French, and $$3$$ have not studied either. How many of these have studied both German and  French?
  • $$0$$
  • $$3$$
  • $$4$$
  • $$5$$
One Hundred Twenty-five $$(125)$$ aliens descended on a set of film as Extra Terrestrial Beings. $$40$$ had two noses, $$30$$ had three legs, $$20$$ had four ears, $$10$$ had two noses and three legs, $$12$$ had three legs and four ears, $$5$$ had two noses and four ears and $$3$$ had all the three unusual features. How many  were there without any of these unusual features?
  • $$5$$
  • $$35$$
  • $$80$$
  • None of these
In a class consisting of 100 students, 20 know  English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students  knowing both Hindi and English is:
  • 5
  • 10
  • 15
  • 20

If $$Y\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $$, then 
  • The smallest set of $$Y$$ is $$\left\{ 3,5,9 \right\} $$
  • The smallest set of $$Y$$ is $$\left\{ 2,3,5,9 \right\} $$
  • The largest set of $$Y$$ is $$\left\{ 1,2,3,5,9 \right\} $$
  • The largest set of $$Y$$ is $$\left\{ 2,3,4,9 \right\} $$
State true or false:
A set of rational number is a subset of a set of real numbers.
  • True
  • False
In a survey of brand preference for toothpastes, $$82$$ of the population (number of people covered for the survey is $$100$$) liked at least one of the brands: I,  II and III. $$40$$ of those liked brand I, $$25$$ liked brand II and $$35$$ liked brand III. If $$8$$ of those asked, showed liking for all the three brands, then what percentage of those liked more than one of the three brands?
  • $$13$$
  • $$10$$
  • $$8$$
  • $$5$$
In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?
  • $$0$$
  • $$2$$
  • $$3$$
  • $$7$$
In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other subjects. The class contains how many students?
  • $$35$$
  • $$42$$
  • $$52$$
  • $$60$$
In a community of 175 persons, 40 read the Times, 50 read the Samachar and 100 do not read any. How many persons read both the papers?
  • 10
  • 15
  • 20
  • 25
Out of 450 students in a school, 193 students read Science Today, 200 students read Junior Statesman, while 80 students read neither. How many students read both the magazines?
  • $$137$$
  • $$80$$
  • $$57$$
  • $$23$$
In a party, 70 guests were to be served tea or coffee after dinner. There were 52 guests who preferred tea while 37 preferred coffee. Each of  the guests liked one or the other beverage. How many guests liked both tea and coffee?
  • 15
  • 18
  • 19
  • 33
In a certain group of 75 students, 16  students are taking physics, geography  and English; 24 students are taking  physics and geography, 30 students are  taking physics and English; and 22 students are taking geography and  English. However, 7 students are taking only physics, 10 students are taking only geography and 5 students are taking only English. How many of these students are taking physics?
  • n(P) = 45
  • n(P) = 35
  • n(P) = 65
  • n(P) = 55
In a class of 80 children, 35% children can play only cricket, 45% children can play only table-tennis and the remaining children can play both the games. In all, how many children can play cricket?
  • $$55$$
  • $$44$$
  • $$36$$
  • $$28$$
In a certain group of 36 people, 18 are wearing hats and 24 are wearing sweaters. If six people are wearing neither a hat nor a sweater, then how many people are wearing both a hat and a sweater ?
  • $$30$$
  • $$22$$
  • $$12$$
  • $$8$$
While preparing the progress reports of the students, the class teacher found that 70% of the students passed in Hindi, 80% passed in English  and only 65% passed in both the subjects. Find out the percentage of students who failed in both the subjects.
  • $$15%$$
  • $$20%$$
  • $$30%$$
  • $$35%$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers