CBSE Questions for Class 11 Engineering Maths Sets Quiz 12 - MCQExams.com

State whether the following statements are true(T) or false(F):
A collection of books is a set.
  • True
  • False
State true or false for each of the following. Correct the wrong statement If $$A = \{0\}$$, then $$n (A) = 0$$
  • True
  • False
State true or false for each of the following. Correct the wrong statement 

  • True
  • False
In $$n(P)= n(M)$$, then $$P \rightarrow M$$
  • True
  • False
M $$\cup$$ N = {1, 2, 3, 4, 5, 6} and M = {1, 2, 4} then which of the following represent set N?
  • {1, 2, 3}
  • {3, 4, 5, 6}
  • {2, 5, 6}
  • {4, 5, 6}
If $$P \ \subseteq \  M$$, then Which of the following set represent $$P \ \cap \ (P \ \cup \ M)$$ ?
  • P
  • M
  • P $$\cup$$ M
  • P' $$\cap$$ M
Find the correct option for the given question.
Which of the following collections is a set?
  • Colours of the rainbow
  • Tall trees in the school campus
  • Rich people in the village
  • Easy examples in the book
Examine whether the following statements are true or false:
$$\left\{a,e \right\}  \subset \left\{x : x \ is\ a\ vowel\ in\ the\ English\ alphabet \right\}$$
  • True
  • False
Examine whether the following statements are true or false:$$\left\{x : x\ is\ an\ even\ natural\ number\ less\ than\ 6 \right\}  \subset \left\{x : x is\ a\ natural\ number\ which\ divides\ 36 \right\}$$
  • True
  • False
Examine whether the following statements are true or false:$$\left\{1,2,3 \right\}  \subset \left\{1,3,5 \right\}$$
  • True
  • False
Examine whether the following statements are true or false:
$$\left\{a,b \right\} \not \subset \left\{b,c,a \right\}$$
  • True
  • False
In each of the following, determine whether the statements is true or false if it is true prove it if it false given an example.
If $$A \subset B$$ and $$B \subset C$$, then $$A \subset C$$
  • True
  • False
Examine the following statements: 
{x : x is an even natural number less then 6} $$\subset  $$ { x : x is natural number which divide 36 } 
  • True
  • False
If $$ \cap = \left \{ 1, 2, 3, 4, 5, 6   \right \}, A = \left \{ 2, 3 \right \} $$ and $$B = \left \{ 3, 4, 5  \right \}$$ then :
  • $$ (A \cap B )' = \left \{ 2, 3, 4, 5 \right \}$$
  • $$B - A = \left \{ 4, 5 \right \}$$
  • $$A - B = \left \{ 2, 4, 5 \right \}$$
  • $$( A \cap B ) = \left \{ 3 \right \}$$
If $$A=\left [ \frac{5}{111} \frac{-3}{336}\right ]$$ and det $$(-3A^{2013}+A^{2014})=\alpha ^{\alpha }\beta ^{2}(1+\gamma +\gamma ^{2})$$ then, where $$\alpha ,\beta ,\gamma $$ are integers
  • $$\alpha = 2013$$
  • $$\beta = 3$$
  • $$\gamma = 10$$
  • none of these
If A = {1, 2, 3}, B = {3, 4, 5}, C = {4, 6}, then A x $$( B \cup C)$$ =
  • {(1, 3) (1, 4) (1, 5) (1, 6) (2, 3) (2, 4) (2, 5) (2, 6) (3,3) (3, 4) (3,5) (3, 6)}
  • A x $$(B \cap C)$$
  • B x $$(A \cap C)$$
  • all the above
$$A - (B \cup C)= $$
  • $$(A - B) \cap (A - C)$$
  • $$(A - B) \cup (A - C)$$
  • $$(A - B) \cup C$$
  • $$(A - B) \cap C$$
Which of the following statements is true (if N, W and I are sets of Natural, Whole and Integer numbers respectively ?
  • $$N\, \subset \, W\, \subset \, I$$
  • $$I\, \subset \, N\, \subset \, W$$
  • $$W\, \subset \, N\, \subset \, I$$
  • $$I\, \subset \, W\, \subset \, N$$
S = {1, 2, 3, 5, 8, 13, 21, 34 }. Find $$\displaystyle \sum $$ max (A), where the sum is taken over all 28 elements subsets A to S.
  • 844
  • 480
  • 484
  • 488
There are 6 boxes numbered 1, 2, ...Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
  • 5
  • 21
  • 33
  • 60
The set $$\{x/| x L|< K\}$$ is the same for all $$K > 0$$ and for all L, as
  • $$\{x/0 < x < L + K\}$$
  • $$\{x/L K < x < L + K\}$$
  • $$\{x/|L K| < x <|L + K|\}$$
  • $$\{x/|L x| > K\}$$
  • $$\{x/ K < x < L\}$$
The dual of $$-p\wedge (q\vee \sim r)$$ is
  • $$p\vee (\sim q \wedge r)$$
  • $$\sim p\vee (q\wedge r)$$
  • $$p\wedge (q\wedge r)$$
  • $$\sim q\vee(q\wedge \sim r)$$
If $$S$$ represents the set of all real numbers $$x$$ such that $$1\le x \le 3$$ and $$T$$ represents the set of all real numbers $$x$$ such that $$2 \le x \le 5$$, the set represented by $$S \cap T$$ is
  • $$2 \le x \le 3$$
  • $$1 \le x \le 5$$
  • $$x \le 5 $$
  • $$x\ge 5$$
  • none of these
In a town of $$10,000$$ families it was found that $$40\%$$ families buy newspaper $$A$$, $$20\%$$ families buy newspaper $$B$$ and $$10\%$$ families buy newspaper $$C$$. $$5\%$$ families buy $$A$$ and $$B$$, $$3\%$$ buy $$B$$ and $$C$$ and $$4\%$$ buy $$A$$ and $$C$$. If $$2\%$$ families buy all the three newspaper, find the number of families which buy (i) $$A$$ only (ii) $$B$$ only (iii) none of $$A, B$$ and $$C$$
  • (i) $$3000$$ (ii) $$1800$$ (iii) $$4600$$
  • (i) $$3300$$ (ii) $$1400$$ (iii) $$4000$$
  • (i) $$3500$$ (ii) $$1600$$ (iii) $$3800$$
  • none
Union set is defined as 
  • a collection of sets is the set of all elements in the collection
  •  It is one of the fundamental operations through which sets can be combined and related to each other.
  • Set whole each element is an element of all the present set
  • None of these
Sets $$A$$ and $$B$$ have $$5$$ and $$6$$ elements respectively and $$\left( A\triangle B \right) =C$$ then the number of elements in set $$\left( A-\left( B\triangle C \right)  \right)$$ is 
  • $$5$$
  • $$6$$$
  • $$0$$
  • $$4$$
If $$20$$% of three subsets (i.e., subsets containing exactly three elements) of the set $$A = \left \{a_{1}, a_{2}, ...., a_{n}\right \}$$ contain $$a_{2}$$, then the value of $$n$$ is
  • $$15$$
  • $$16$$
  • $$17$$
  • $$18$$
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 $$\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ j=1 }^{ n }{ { B }_{ j } =S}$$ and each element of $$S$$ belongs to exactly $$10$$ of the $${A}_{i}s$$ and exactly $$9$$ of the $${B}_{j}s.$$ Then $$n$$ is equal to
  • $$15$$
  • $$3$$
  • $$45$$
  • $$None\ of\ these$$
All the permissible values of $$b$$, if $$a=0$$ and $${S}_{2}$$ is a subset of $$\left( 0,\pi  \right) $$
  • $$b\in \left( -n\pi ,2n\pi \right) ;\in Z$$
  • $$b\in \left( -n\pi ,2\pi -n\pi \right) ;\in Z$$
  • $$b\in \left( -n\pi ,n\pi \right) ;\in Z$$
  • none of these
An investigator interviewed $$100$$ students to determine their preferences for the three drinks: milk (M), coffee(C) and tea (T). He reported the following: $$10$$ students had all the three drinks M, C, T; $$20$$ had M and C only; $$30$$ had C and T; $$25$$ had M and T; $$12$$ had M only; $$5$$ had C only; $$8$$ had T only. Then how many did not take any of the three drinks is?
  • $$20$$
  • $$30$$
  • $$36$$
  • $$42$$
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