CBSE Questions for Class 11 Engineering Maths Sets Quiz 5 - MCQExams.com

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 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 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
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 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.
  • $$15%$$
  • $$20%$$
  • $$30%$$
  • $$35%$$
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?
  • $$137$$
  • $$80$$
  • $$57$$
  • $$23$$

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 $$\left\{ 2,3,4,9 \right\} $$
How many students in this group are not taking any of the three subjects?
  • 8
  • 9
  • 10
  • 11
State true or false:
A set of rational number is a subset of a set of real numbers.
  • True
  • False
If two intersecting circles with two points in common are drawn then how many common chords can be drawn? Draw the figure and write the answer
  • Only one.
  • Many.
  • Three.
  • None of the options.
Which of the following sets is/are empty?
  • $$\displaystyle \left \{ x : x \in R ,x^{2} -4=0\right \}$$
  • $$\displaystyle \left \{ x : x \in R ,x^{4} +4=0\right \}$$
  • $$\displaystyle \left \{ x : x \in R ,x^{3} =1\right \}$$
  • $$\displaystyle \left \{ x : x \in R ,x^{8}+x^{4}+1=0 \right \}$$
The set of natural number is subset of set of real numbers.
State true or false:
  • True
  • False
  • Ambiguous
  • Data insufficient
Let $$\displaystyle A= \left \{ 7,8,9,a,b,c \right \} $$ and $$\displaystyle B= \left \{ 1,2,3,4 \right \} $$ then number of universal relation from the set $$A$$ to set $$B$$ and set $$B$$ to set $$A$$ are
  • equal in counting
  • can not be equal in counting
  • $$24$$
  • $$\displaystyle 2^{6}\times 2^{4} $$
$$\displaystyle \left \{ \left ( 1, 2 \right ) \right \}, and B=\left \{ 1, 3 \right \}, then\left ( A\times B \right )\cup \left ( B\times A \right )$$ $$\displaystyle =\left \{ \left ( 1, 3 \right ), \left ( 2, 3 \right ), \left ( 3, 1 \right ), \left ( 3, 2 \right ), \left ( 1, 1 \right ), \left ( 1, 2 \right ), \left ( 2, 1 \right ),\right \}$$
  • True
  • False
True or false :
$$\displaystyle A\times \left ( B\cap C \right )=\left ( A\times B \right )\cap \left ( A\times C \right )$$
  • True
  • False
Given the universal set $$B = \{-7,-3,-1,0,5,6,8,9\}$$, find :
$$B = \{x : -4 < x < 6\}$$
  • $$\{ -7, 0, 5,6\}$$
  • $$\{5,6,8,9\}$$
  • $$\{-3, -1, 0, 5\}$$
  • $$\{0,5\}$$
If universal set $$\xi = \{a, b, c, d, e, f,  g, h\}, A = \{b, c, d, e, f\},  B =\{a, b, c, g, h\}$$ and $$C = \{c, d, e, f, g\}$$, then find $$B - A$$
  • $$\{b,c,e,f\}$$
  • $$\{a, b, f, h\}$$
  • $$\{a, g, h\}$$
  • $$\{a,c,e,g\}$$
If universal set $$\xi = \{a, b, c, d, e, f,  g, h\}, A = \{b, c, d, e, f\},  B =\{a, b, c, g, h\}$$ and $$C = \{c, d, e, f, g\}$$ find $$(B - C)'$$
  • $$\{d, e, f, g\}$$
  • $$\{c, d, e, f, g\}$$
  • $$\{c, d, f, g\}$$
  • $$\{a, c, d, e, f, g\}$$
If A = (6, 7, 8, 9), B = (4, 6, 8, 10) and C = {$$x$$ : $$x \,\,\epsilon\,\,N$$ : $$2 < x \leq 7$$} ; find :
A - B
  • $$\{6,8\}$$
  • $$\{7,9\}$$
  • $$\{6,9\}$$
  • $$\{6,7,9,10\}$$
If $$A = (6, 7, 8, 9), B = (4, 6, 8, 10)$$ and $$C = \{x : x \,\,\epsilon\,\,N : 2 < x \leq 7\}$$ ; find :$$B - C$$
  • $$\{4, 6\}$$
  • $$\{4,6,8\}$$
  • $$\{6, 8, 10\}$$
  • $$\{8, 10\}$$
If $$A = (6, 7, 8, 9), B = (4, 6, 8, 10)$$ and $$C = \{x : x \,\,\epsilon\,\,N : 2 < x \leq 7\}$$ ; find : $$B - B$$
  • $$\phi$$
  • $$\{0\}$$
  • $$\{6,7\}$$
  • $$\{4\}$$
Verify: $$A'\cap  B = B - (A \cap B)$$.
  • True
  • False
$$A=\left\{ x:x\neq x \right\} $$ represents-
  • $$\left\{ 0 \right\} $$
  • $$\left\{ \right\} $$
  • $$\left\{ 1 \right\} $$
  • $$\left\{ x \right\} $$
Which of the following statements is false?
  • $$2$$ $$\in$$ {first five counting numbers.}
  • $$f$$ $${\notin }  $$ {consonants}
  • Rose $${\notin }$$ {the set of all fruits.}
  • Asia $${\in }$$ {Continents}
Let $$A = \{2,3,5,7,8,11\}$$ then which among the following is true?
  • $${7\notin A}$$
  • $$\{2,3\} \not\subset \ of \  A$$
  • $$ 2 \in A$$
  • None of the above
Which of the following statements is true
  • $$3\subseteq \left\{ 1,3,5 \right\} $$
  • $$3\in \left\{ 1,3,5 \right\} $$
  • $$\left\{ 3 \right\} \in \left\{ 1,3,5 \right\} $$
  • $$\left\{ 3,5 \right\} \in \left\{ 1,3,5 \right\} $$
Let $$P = \{ x | x$$ is a multiple of $$3$$ and less than $$100 $$ ,$$x$$ $$\displaystyle \in $$ $$N \}$$
$$Q = \{ x | x$$ is a multiple of $$10$$ and less than $$100$$, $$x$$ $$\displaystyle \in$$ $$N\}$$
  • $$\displaystyle Q\subset P$$
  • $$\displaystyle P\cup Q=$$ $$\{ x | x$$ is multiple of 30$$ ;$$ $$\displaystyle x \in N$$$$\}$$
  • $$\displaystyle P\cap Q=\phi $$
  • $$\displaystyle P\cap Q= $$ $$\{ x | x$$ is a multiple of 30$$ ; $$ $$\displaystyle x\in N$$$$\}$$
Find the set of all solutions of the equation $$2^{\left | y \right |}-\left | 2^{y-1}-1 \right |=2^{y-1}+1$$, the solution includes
  • $$y =-1$$
  • $$y>1$$
  • $$y=1$$
  • $$y<1$$
If $$Q=\{ x:x=\cfrac { 1 }{ y },$$ where $$ y\in N \} $$, then
  • $$0\in Q$$
  • $$1\in Q$$
  • $$2\in Q$$
  • $$\cfrac{2}{3} \in Q$$
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