CBSE Questions for Class 11 Engineering Maths Sets Quiz 9 - MCQExams.com

A set of $$n$$ numbers has the sum $$s$$. Each number of the set is increased by $$20$$, then multiplied by $$5$$, and then decreased by $$20$$. The sum of the numbers in the new set thus obtained is:
  • $$s+20n$$
  • $$5s+80n$$
  • $$s$$
  • $$5s$$
If $$A= \{x:x$$ is a multiple of $$2\}, \,\,B= \{x:x$$ is a multiple of $$5\}$$ and $$C = \{x:x$$ is a multiple of 10$$\}$$, then $$ A\cap (B\cap C)$$ is equal to 
  • $$A$$
  • $$B$$
  • $$C$$
  • $$\{x:x$$ is a multiple of $$100\}$$
If $$M = \left\{ {x:x \geqslant 7\,\,{\text{and}}\,x \in N} \right\}$$ for universal set of natural numbers, then $$M'$$ is
  • $$\left\{ {1,2,3,4,5} \right\}$$
  • $$\left\{ {1,2,3,4,5,6,7} \right\}$$
  • $$\left\{ {1,2,3,4,5,6} \right\}$$
  • $$\left\{ {0,1,2,3,4,5,6} \right\}$$
If $$X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $$ and $$Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $$, then $$X\cap Y=$$
  • $$X$$
  • $$Y$$
  • $$\phi $$
  • $$\left\{ 0 \right\} $$
In the equation $${ \left( x-m \right)  }^{ 2 }-{ \left( x-n \right)  }^{ 2 }={ \left( m-n \right)  }^{ 2 }$$, $$m$$ is a fixed positive number, and $$n$$ is a fixed negative number. The set of values $$x$$ satisfying the equation is:
  • $$x\ge 0$$
  • $$x\le n$$
  • $$x=0$$
  • the set of all real numbers
  • none of these
The number of binary operations on the set $$\{1, 2, 3\}$$ is _________.
  • $$3^9$$
  • $$9^3$$
  • $$27$$
  • $$3!$$
The relation $$S=\{(3, 3), (4, 4)\}$$ on the set $$A=\{3, 4, 5\}$$ is __________.
  • Not reflexive but symmetric and transitive
  • Reflexive only
  • Symmetric only
  • An equivalence relation
In order to draw a graph of $$f(x) = ax^{2} + bx + c$$, a table of values was constructed. These values of the function for a set of equally spaced increasing values of $$x$$ were $$3844, 4096, 4227, 4356, 4489, 4624$$, and $$4761$$. The one which is incorrect is
  • $$4096$$
  • $$4356$$
  • $$4489$$
  • $$4761$$
  • None of these
State true or false.
Let $$A = \{1, 2, 3\}, B = \{2, 4, 6, 8\}, C = \{3, 4, 5, 6\}$$ then 
$$n(A - B) = 2$$
  • True
  • False
If $$X$$ and $$Y$$ are two sets, then $$X\cap \left( X\cup Y \right)$$ equals
  • $$X$$
  • $$Y$$
  • $$\phi$$
  • $$None\ of\ these$$
If X = {$$4^n \,-\,3n\,-\,1\,:\,\epsilon N$$} and
 Y = {$$9(n\,-\,1) \,:\,\epsilon N$$}
then $$X\subset Y$$ 
  • True
  • False
Given : A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
Find : $$(A \, \times \, B) \, \cap \, (B \, \times \, C)$$.
  • {4,4}
  • {3,4}
  • {3,4}, {3,3}
  • {3,3}
Let $$A=\left\{ x:x\ \in\ R,\left| x \right| <1 \right\}$$
$$B=\left\{ x:x\ \in\ R,\left| x-1 \right| \ge 1 \right\}$$
and $$A\cup B=R-D$$, then set $$D$$ is
  • $$\left\{ x:1 < x \le 2 \right\}$$
  • $$\left\{ x:1\le x<2 \right\}$$
  • $$\left\{ x:1\le x\le 2 \right\}$$
  • None of these
If sets $$A$$ and $$B$$ are define as
$$A=\left\{ \left( x,y \right) :y={ e }^{ x },x\in R \right\}$$
$$B=\left\{ \left( x,y \right) :y=x,x\in R \right\}$$, then 
  • $$B\subset A$$
  • $$A\subset B$$
  • $$A\cap B=\phi$$
  • $$A\cup B=A$$
Let $$A=\left\{ \left( x,y \right) :y={ e }^{ x },x\in R \right\}$$
      $$B=\left\{ \left( x,y \right) :y={ e }^{ -x },x\in R \right\}$$. Then 
  • $$A\cap B=\phi$$
  • $$A\cap B\neq \phi$$
  • $$A\cup B={ R }^{ 2 }$$
  • $$none\ of\ these$$
If $$X$$ and $$Y$$ are two sets, then $$X\cap \left( Y\cup X \right)'$$ equals
  • $$X$$
  • $$Y$$
  • $$\phi$$
  • $$None\ of\ these$$
Suppose $${A_1},{A_2},...,{A_{30}}$$ are thirty sets each having 5 elements and $${B_1},{B_2},...,{B_n}$$ are $$n$$ sets each with 3 elements, let $$\bigcup\limits_{i = 1}^{30} {{A_i}}  = \bigcup\limits_{i = 1}^n {Bj}  = S$$ and each element of $$S$$ belongs to exactly 10 of the $${A_i}'s$$ and exactly 9 of the $$B,'s$$. Then $$n$$ is equal to 
  • $$15$$
  • $$3$$
  • $$45$$
  • $$35$$
Consider the word $$W=MISSISSIPPI$$.
If $$N$$ denotes the number of different selections of $$5$$ letters from the word $$W = MISSISSIPPI$$ then $$N$$ belongs to the set,
  • $$\{ 15,\ 16,\ 17,\ 18,\ 19\} $$
  • $$\{ 20,\ 21,\ 22,\ 23,\ 24\} $$
  • $$\{ 25,\ 26,\ 27,\ 28,\ 29\} $$
  • $$\{ 30,\ 31,\ 32,\ 33,\ 34\} $$
If $$A=\{1,2,3\}, B=\{3,4\}$$ and $$C=\{1,3,5\}$$, then $$A \times (B - C) =$$
  • $$(A \times B ) - (A \times C )$$
  • $$(A \times B ) + (A \times C )$$
  • $$(A \times B ) - (B \times C )$$
  • $$(A \times B ) - (C \times A )$$
If $$X =\{1,2,3,4,5,6,7,8,9, 10\}$$ is the universal set and$$ A= \{1, 2, 3,4\}, B= \{2,4,6,8\}, C= \{3,4,5,6\}$$  verify the following.
(a) $$A \cup (B\cup C) = (A \cup B) \cup C$$
(b)$$A \cap (B\cup C) = (A \cap B) \cup (A \cap C)$$
(c) $$(A')' =A$$
  • Only a is true
  • Only b and c are true
  • Only a and b are true
  • All three a,b and c are true.
Which is the simplified representation of $$(A' \cap B'\cap C)\cup(B\cap C) \cup (A\cap C)$$ where A,B,C are subsets of set X
  • $$A$$
  • $$B$$
  • $$C$$
  • $$X\cap(A \cup B\cup C)$$
In certain town, $$25\%$$ families own a cell phone, $$15\%$$ families own a scooter and $$65\%$$ families own neither a cell phone nor a scooter. If $$1500$$ families own both a cell phone and a scooter, then the total number of families in the town is:
  • $$10000$$
  • $$20000$$
  • $$30000$$
  • $$50000$$
If $$A \subset B$$, then
  •  $$C - B \subset C - A$$.
  • $$A \cup B = A$$
  • $$A \cap B = B$$
  • None
If two sets $$A$$ and $$B$$ are having $$99$$ elements in common, then the number of ordered pairs common to each of the sets $$AxB$$ and $$BxA$$ are
  • $$2^{99}$$
  • $$99^{2}$$
  • $$100$$
  • $$18$$
$$S_1:(p\Rightarrow q) V ( q \Rightarrow p )$$ is a tautology.
$$S_2: ((p\Rightarrow q) V ( q \Rightarrow p))$$ is a fallacy
  • $$S_1$$ is true, $$S_2$$ is false
  • $$S_1$$ false
  • $$S_1$$ is false, $$S_2$$ is false
  • $$S_1$$ is true
$$If\,A = \left\{ {\left( {x,y} \right)\,\left| {{x^2} + {y^2} \le \left. 4 \right\}\,and} \right.} \right.$$
$$B = \left\{ {\left( {x,y} \right)\,\left| {{{(x - 3)}^2} + {y^2}} \right. \le \left. 4 \right\}} \right.\,and\,the$$
$$po{\mathop{\rm int}} \,P\left( {a,\frac{1}{2}} \right)\,belongs\,to\,the\,set\,B - A$$ then the set of possible real values of $$a$$ is
  • $$\left( {\frac{{1 + \sqrt {3} }}{4},\frac{{7 + \sqrt 7 }}{4}} \right)$$
  • $$\left( {\frac{{7 - \sqrt 7 }}{4},\frac{{1 + \sqrt 7 }}{4}} \right)$$
  • $$\left( {\frac{{1 - \sqrt {31} }}{4},\frac{{7 - \sqrt 7 }}{4}} \right)$$
  • none of these
In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that $$20$$ candidates were good in GD and $$30$$ were good in PI. The number of candidates good in both GD and PI is expected to be about:
  • $$6$$
  • $$10$$
  • $$20$$
  • $$30$$
Let $$A=\{x:x\in R\  \&\ x^2+1=0\}$$ then $$A$$ is a null set.
  • True
  • False
Let $$A\subset B$$ then $$A'\cap B'=$$
  • $$A'$$
  • $$B'$$
  • $$B$$
  • none of these
Range of the function f(x) = cos (K sinx) is [-1, 1], then the positive integral value of K can be?
  • 1
  • 2
  • 5
  • 4
0:0:1


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Practice Class 11 Engineering Maths Quiz Questions and Answers