CBSE Questions for Class 11 Engineering Maths Sets Quiz 7 - MCQExams.com

The sets $$\displaystyle S_{x}$$ are defined to be $$(x, x + 1, x + 2, x + 3, x + 4)$$ where $$x=1, 2, 3,.....80$$. How many of these sets contain $$6$$ or its multiple? 
  • $$65$$
  • $$66$$
  • $$59$$
  • $$60$$
If $$A=\{\dots,-6,-4,-2,0,2,4,6,\dots\}$$, then
  • $$10\notin A$$
  • $$-10\notin A$$
  • $$5\in A$$
  • $$50\in A$$
If $$\displaystyle Q=\left((x|x=\frac{1}{y}\:\ \text{wher} \ e\:y\in N\right)$$, then
  • $$0\notin Q$$
  • $$1\in Q$$
  • $$2\in Q$$
  • $$\displaystyle\frac{2}{3}\in Q$$
If A and B are disjoint then $$\displaystyle \left ( A\cap B \right ){}'=$$_______
  • $$A$$
  • $$B$$
  • $$\displaystyle \phi $$
  • $$\displaystyle \mu $$
For any two sets $$A$$ and $$B$$, $$A-\left( A-B \right) $$ equals
  • $$B$$
  • $$A-B$$
  • $$A\cap B$$
  • $${ A }^{ C }\cap { B }^{ C }$$
Three sets $$A, B, C$$ are such that $$\displaystyle A=B\cap C$$ and $$\displaystyle B=C\cap A$$, then
  • $$\displaystyle A\subset B$$
  • $$\displaystyle A\supset B$$
  • $$\displaystyle A\equiv B$$
  • $$\displaystyle A\subset { B }^{ \prime }$$
If X is a finite set. Let $$P(X)$$ denote the set of all subsets of X and let $$n(X)$$ denote the number of elements in X. If for two finite subsets $$A, B, n(P(A)) = n(P(B)) + 15$$ then $$n(B) = $$ ____, $$n(A) =$$ _____
  • $$n(A) = 4, n(B) = 0$$
  • $$n(A) = 5, n(B) = 0$$
  • $$n(A) = 4, n(B) = 2$$
  • $$n(A) = 6, n(B) = 0$$
P, Q and R are three sets and $$\xi = P\cup Q\cup R$$. Given that $$n(\xi) = 60, n (P\cap Q) = 5, n(Q\cap R) = 10, n(P) = 20$$ and $$n(Q) = 23$$, find $$n(P\cup R)$$
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  • $$37$$
  • $$38$$
  • $$45$$
  • $$52$$
If n is a member of both set A$$=\left\{\displaystyle\frac{4}{7}, 1, \frac{5}{2}, 4, \frac{1}{2}, 7\right\}$$ and set B$$=\left\{\displaystyle\frac{4}{7}, \frac{7}{4}, 4, 7\right\}$$, which of the following must be true?
I. n is an integer.
II. $$4n$$ is an integer.
III. $$n=4$$
  • None
  • II only
  • I and II only
  • I and III only
  • I, II, and III
$$A - B =$$ _____
  • $$A \cup (A\cap B)$$
  • $$B - A$$
  • $$A - (A\cap B)$$
  • $$A'\cap B$$
$$(P\cap Q)' \cup R$$
  • $$\left \{a, c, e, f, g, h, i, j\right \}$$
  • $$\left \{a, c, d, e, f, h, i, j\right \}$$
  • $$\left \{a, c, d, e, f, g, h, j\right \}$$
  • $$\left \{a, c, d, e, f, g, h, i, j\right \}$$
If $$A$$ and $$B$$ are any two sets, then state the following statement is true/false 
$$A - (A - B) = A\cap B$$
  • True
  • False
In a class, $$20$$ opted for Physics, $$17$$ for Maths, $$5$$ for both and $$10$$ for other subjects. The class contains how many students?
  • $$35$$
  • $$42$$
  • $$52$$
  • $$60$$
If $$A = \{ a, b, p, d\}  B = \{ p, d, e\}  C = \{p, e, f, g\}$$ then find 

$$A \times (B \cap C ) $$ is equal to 
  • $$ (A \times B) \cup (A \times C)$$
  • $$ (A \times B) \cap (A \times C)$$
  • $$ (A \times B) \cap (A \times C)\cap (B\times C)$$
  • none
In a class of 250 students, 175 take mathematics and 142 take science. How many take both mathematics

and science? (All take math and/or science.)
  • 67
  • 75
  • 33
  • 184
  • cannot be determined from information given
Let $$S = \left \{(a, b, c)\epsilon N\times N\times N : a + b + c =a \leq b\leq c\right \}$$ and $$T = \left \{a, b, c)\epsilon N\times N\times N : a, b, c,\ are\ in\ A.P.\right \}$$, where $$N$$ is the set of all natural numbers. Then the number of elements in the set $$S\cap T$$ is
  • $$6$$
  • $$7$$
  • $$13$$
  • $$14$$
If $$A=\left \{ 5,\left \{ 5,6 \right \},7 \right \}$$, which of the following is correct? 
  • $$\left \{ 5,6 \right \}\in A$$
  • $$\left \{ 5 \right \}\in A$$
  • $$\left \{ 7 \right \}\in A$$
  • $$\left \{ 6 \right \}\in A$$
If A and B are two sets, where A has more elements than B. Calculate the least possible value of n(A) + n(B), where n(A) is the number of elements in A and n(B) is the number of elements in B.
  • $$n(A)$$
  • $$n(B)$$
  • $$n(A+B)$$
  • None of these
Solve the following inequalities: $$\displaystyle\frac{1}{2-|x|}\geq 1$$.
  • $$x\epsilon (-8, -1]\cup [1,2)$$
  • $$x\epsilon (-2, -1]\cup [1,2)$$
  • $$x\epsilon (-2, -1]\cup [1,6)$$
  • $$x\epsilon (-2, 0]\cup [1,2)$$
If $$X=\left \{ a,\left \{ b,c \right \},d \right \}$$, which of the following is a subset of $$X$$?
  • $$\left \{ a,b \right \}$$
  • $$\left \{ b,c \right \}$$
  • $$\left \{ c,d \right \}$$
  • $$\left \{ a,d \right \}$$
Which one of the following is a finite set?
  • $$\left \{ x:x\in Z,x< 5 \right \}$$
  • $$\left \{ x:x\in W,x\geq 5 \right \}$$
  • $$\left \{ x:x\in N,x> 10 \right \}$$
  • { $$x:x$$ is an even prime number }
Which one of the following is correct?
  • $$\left \{ x:x^{2}=-1,x\in Z \right \}=\phi$$
  • $$\phi=0$$
  • $$\phi=\left \{ 0 \right \}$$
  • $$\phi=\left \{ \phi \right \}$$
The number of subsets of the set $$\left \{ 10,11,12 \right \}$$ is
  • $$3$$
  • $$8$$
  • $$6$$
  • $$7$$
If $$n(A) = 20, n(B) = 30$$ and $$n(A \cup B)= 40$$, then $$n(A \cap B)$$ is equal to: 
  • $$50$$
  • $$10$$
  • $$40$$
  • $$70$$
For any three sets , A B and C, $$B\setminus (A \cup C)$$ is:
  • $$(A\setminus B)\cap (A\setminus C)$$
  • $$(B\setminus A)\cap (B \setminus C)$$
  • $$(B \setminus A)\cap (A\setminus C)$$
  • $$(A\setminus B)\cap (B \setminus C)$$
Let U = { $$x \in N : 1 \le x \le 10 $$ } be the universal set, $$N$$ being the set of natural numbers. If $$A = \{1, 2, 3, 4\}$$ and $$B = \{2, 3, 6, 10\} $$ then what is the complement of $$(A - B)$$ ?
  • $$\{6, 10\}$$
  • $$\{1, 4\}$$
  • $$\{2, 3, 5, 6, 7, 8, 9, 10\}$$
  • $$\{5, 6, 7, 8, 9, 10\}$$
If $$A= \{ p, q, r, s \}$$, $$B = \{ r, s, t, u \}$$, then $$A /B$$ is:
  • { p, q }
  • { r, s }
  • { t, u }
  • {p, q, t, u }
Out of 500 first year students, 260 passed in the first semester and 21 0 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters ?
  • $$30$$
  • $$40$$
  • $$70$$
  • $$140$$
If $$A : \left \{x : x \text { is a multiple of } 3\right \}$$ and $$B = \left \{x : x \text { is a multiple of } 4\right \}$$ and $$C = \left \{x : x \text { is a multiple of } 12\right \}$$, then which one of the following is a null set?
  • $$(A / B) \cup C$$
  • $$(A / B) / C$$
  • $$(A \cap B)\cap C$$
  • $$(A \cap B)/ C$$
Which  one of the following is not true? 
  • $$A\setminus B=A\cap B'$$
  • $$A\setminus B=A\cap B$$
  • $$A\setminus B=(A\cup B)\cap B'$$
  • $$A\setminus B=(A\cup B)\setminus B$$
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