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question_answer1)
If \[U=\left\{ 1,\text{ }7,\text{ }11,\text{ }13,\text{ }15,\text{ }18,\text{ }21,\text{ }32,\text{ }35,\text{ }39 \right\},\]then which of the following is not a subset of U.
A)
\[A=\left\{ 1,\text{ }18,\text{ }7,\text{ }35 \right\}\] done
clear
B)
\[B=\left\{ 21,\text{ }11,\text{ }35,\text{ }7,\text{ }13 \right\}\] done
clear
C)
\[C=\left\{ 7,\text{ }18,\text{ }32,\text{ }11 \right\}\] done
clear
D)
\[D=\left\{ 1,\text{ }7,\text{ }18,\text{ }15,\text{ }13,\text{ }2 \right\}\] done
clear
E)
None of these done
clear
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question_answer2)
Let \[M=\left\{ 3,\text{ }5,\text{ }7,\text{ }8,\text{ }10,\text{ }12 \right\},\text{ }N=\left\{ 2,\text{ }4,\text{ }7,\text{ }8 \right\}\]and \[P=\left\{ 5,\text{ }10 \right\},\]then which among the following statements is incorrect?
A)
\[P~\subseteq M\] done
clear
B)
\[M\not\subset ~P\] done
clear
C)
\[\phi \subset P\] done
clear
D)
\[N\subset M\] done
clear
E)
None of these done
clear
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question_answer3)
Which among the following is a universal set for the other three sets?
A)
The set of natural numbers. done
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B)
The set of whole numbers. done
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C)
The set of integers. done
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D)
The set of negative of natural numbers. done
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E)
None of these done
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question_answer4)
Which among the following is not a proper subset of\[\left\{ a,\text{ }b,\text{ }c \right\}\]?
A)
\[\left\{ a,\text{ }b \right\}\] done
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B)
\[\left\{ a,\text{ }b,\text{ }c \right\}\] done
clear
C)
{b, c} done
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D)
\[\left\{ a \right\}\] done
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E)
None of these done
clear
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question_answer5)
If M is a proper subset of N, then M \[\bigcap \] N =
A)
\[\phi \] done
clear
B)
M done
clear
C)
N done
clear
D)
M\[\bigcup \]N done
clear
E)
None of these done
clear
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question_answer6)
If M is a subset of N, then M \[\bigcup \] N =
A)
M done
clear
B)
N done
clear
C)
M\[\bigcap \]N done
clear
D)
\[\phi \] done
clear
E)
None of these done
clear
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question_answer7)
Which among the following is an example of disjoint sets? |
P = {The set of odd numbers} |
Q = {The set of even numbers} |
R = {The set of prime numbers} |
A)
P and R done
clear
B)
P and Q done
clear
C)
Q and R done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer8)
If \[P=\left\{ 1,\text{ }2,\text{ }3 \right\}\]and \[Q=\left\{ 3,\text{ }4,\text{ }5 \right\},\]then \[(P\bigcup ~Q)\text{ }=\text{ }\_\_\_\_\]
A)
\[\left\{ 1,\text{ }2,\text{ }3 \right\}\] done
clear
B)
\[\left\{ 1,\text{ }2,\text{ }4,\text{ }5 \right\}\] done
clear
C)
\[\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\}\] done
clear
D)
\[\left\{ 3 \right\}\] done
clear
E)
None of these done
clear
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question_answer9)
If \[U=\left\{ 1,\text{ }3,\text{ }5,\text{ }7,\text{ }9,\text{ }a,\text{ }b,\text{ }c,\text{ }d \right\}\]and \[A=\left\{ 1,\text{ }3,\text{ }5 \right\}\]and \[B=\left\{ a,\text{ }b,\text{ }c \right\}\]then \[\left( A\bigcup B \right)'\]
A)
\[\left\{ 3,\text{ }3,\text{ }5,\text{ }a,\text{ }b,\text{ }c \right\}\] done
clear
B)
1, 3, 5 done
clear
C)
\[\left\{ a,\text{ }b,\text{ }c \right\}\] done
clear
D)
\[\left\{ 7,\text{ }9,\text{ }d \right\}\] done
clear
E)
None of these done
clear
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question_answer10)
lf \[P=\{x:x\in ,x\le 2\}\]and \[Q\text{ }=\left\{ x:x\in N,x<20 \right\}\]then \[n\text{ }(P\bigcup Q)=\_\_\_\_\]
A)
13 done
clear
B)
12 done
clear
C)
11 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer11)
Which among the following venn diagram represents
'?
A)
B)
C)
D)
E)
None of these done
clear
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question_answer12)
If \[P\bigcap Q=Q\]and \[P\bigcap Q=P\] then which among the following cannot be true?
A)
\[P=\left\{ \text{1, }2,\text{ }3 \right\}\]and\[Q=\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\}\] done
clear
B)
\[P=\left\{ a,\text{ }b \right\}\]and \[Q=\left\{ a,\text{ }b,\text{ }c \right\}\] done
clear
C)
\[P=\left\{ s \right\}\]and \[Q=\left\{ m,\text{ }n,\text{ }s \right\}\] done
clear
D)
\[P=\left\{ I,\text{ }m,\text{ }n \right\}\]and \[Q=\left\{ I,\text{ }m,\text{ }1,\text{ }2,\text{ }3 \right\}\] done
clear
E)
None of these done
clear
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question_answer13)
If M' = N, then \[(M\bigcap ~N)'\]is ____
A)
M done
clear
B)
N done
clear
C)
\[\phi \] done
clear
D)
\[\bigcup \] done
clear
E)
None of these done
clear
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question_answer14)
If \[P=Q',\]then \[(P\bigcup ~Q)'\]is ____
A)
P done
clear
B)
Q done
clear
C)
\[\bigcup \] done
clear
D)
\[\phi \] done
clear
E)
None of these done
clear
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question_answer15)
If \[A=\left\{ a,\text{ }b,\text{ }e,\text{ }g,\text{ }k,\text{ }I,\text{ }m,\text{ }n \right\},\]\[B=\left\{ c,\text{ }d,\text{ }s,\text{ }t,\text{ v}, \right\}\] and \[\bigcup \] is the set of all the letters of English alphabet, the\[A'~\bigcup ((A~\bigcap B)~\bigcup B')\]is equal to ____
A)
\[A~\bigcup B\] done
clear
B)
\[A'~\bigcap B'\] done
clear
C)
\[\bigcup \] done
clear
D)
B done
clear
E)
None of these done
clear
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question_answer16)
Which one among the following is incorrect?
A)
\[P-(Q~\bigcup R)=\left( P-Q \right)~\bigcap \left( P-R \right)\] done
clear
B)
\[(P\Delta Q)\Delta R=P\Delta (Q\Delta ~R)\] done
clear
C)
\[(P~\bigcup Q\bigcup ~R)'=P'\bigcap Q'\bigcap ~R'\] done
clear
D)
P - (Q - R) = (P - Q) ? R done
clear
E)
None of these done
clear
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question_answer17)
For any two non empty sets P and Q, if \[P-Q=P\]and \[Q-P=Q,\]then ______
A)
\[(P\bigcup Q)'=\phi \] done
clear
B)
\[P\bigcap Q=\phi \] done
clear
C)
\[P\subset Q\] done
clear
D)
\[Q\subset P\] done
clear
E)
None of these done
clear
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question_answer18)
If n(P) = 18 - x, n (Q) = 24 + x and n (P\[\bigcup \]Q) = 34, then n(P\[\Delta \]Q) = _____
A)
x+20 done
clear
B)
26 done
clear
C)
34-x done
clear
D)
30 done
clear
E)
None of these done
clear
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question_answer19)
If \[P=\left\{ a,\text{ }b,\text{ }c,\text{ }d \right\}\]and \[Q=\left\{ a,\text{ }c,\text{ }e \right\}\]then \[P\Delta Q=?\]
A)
\[\left\{ a,\text{ }b,\text{ }c,\text{ }d,\text{ }e \right\}\] done
clear
B)
\[\left\{ b,\text{ }d,\text{ }e \right\}\] done
clear
C)
\[\left\{ b,\text{ }d \right\}\] done
clear
D)
\[\left\{ a,\text{ }c \right\}\] done
clear
E)
None of these done
clear
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question_answer20)
If P and Q are two non-empty sets and P - Q is a null set, then ____
A)
P\[\subset \]Q done
clear
B)
Q\[\subset \]P done
clear
C)
P=Q done
clear
D)
P\[\in \]Q done
clear
E)
None of these done
clear
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question_answer21)
If n(P - Q) = 28, n(P\[\bigcup \]Q) = 80 and n(P\[\bigcap \]Q) = 35, then the value of n (Q) is
A)
17 done
clear
B)
52 done
clear
C)
42 done
clear
D)
38 done
clear
E)
None of these done
clear
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question_answer22)
Which of the following number can represent the subset of a non empty set?
A)
343 done
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B)
2048 done
clear
C)
68 done
clear
D)
743 done
clear
E)
None of these done
clear
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question_answer23)
In a class 40% of the student enrolled for maths and 60% enrolled for English. If 25% of the student enrolled for both maths and English, what % of the student of the class did not enroll for either of the two subject?
A)
5 done
clear
B)
10 done
clear
C)
15 done
clear
D)
25 done
clear
E)
None of these done
clear
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question_answer24)
In a laboratory, there are 48 students, in which 22 are enrolled in physics and chemistry, 26 are enrolled in chemistry. If the students in the laboratory are of atleast one of the two subjects, then how many students are enrolled in only physics and not of chemistry?
A)
18 done
clear
B)
26 done
clear
C)
22 done
clear
D)
30 done
clear
E)
None of these done
clear
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question_answer25)
If n\[\left( A\text{ }\times \text{ }B \right)\text{ }=\text{ }48\], n \[(B\,\,\times \,\,C)=\,\,64\] and n (B) =4, then n \[\left( A\text{ }\times \text{ }C \right)\] =?
A)
180 done
clear
B)
192 done
clear
C)
178 done
clear
D)
208 done
clear
E)
None of these done
clear
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question_answer26)
If (P \[\bigcup \] Q) \[\bigcap \] (P \[\bigcap \] Q) = P, then which one among the following is true?
A)
Q\[\subset \]P done
clear
B)
\[\phi \] done
clear
C)
P\[\subset \]Q done
clear
D)
both A and B done
clear
E)
None of these done
clear
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question_answer27)
If n (a) = 28, then which one among the following value of n (b) may result in n (A\[\bigcap \]B) being maximum?
A)
24 done
clear
B)
29 done
clear
C)
26 done
clear
D)
25 done
clear
E)
None of these done
clear
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question_answer28)
If P and Q are two non-empty equivalent sets, then which one among the following is a possible value of n\[\left( P\text{ }\times \text{ }Q \right)\]?
A)
8 done
clear
B)
2 done
clear
C)
1 done
clear
D)
6 done
clear
E)
None of these done
clear
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question_answer29)
Which one among the following statements is true for two given sets P and Q where n(P) = 26 and n(Q) = 5
A)
The minimum possible value of n \[(P\Delta Q)\]is 31. done
clear
B)
The maximum possible value of n \[(P\Delta Q)\]is 31. done
clear
C)
The minimum possible value of n \[(P\Delta Q)\]is 26. done
clear
D)
The maximum possible value of n \[(P\Delta Q)\]is 26. done
clear
E)
None of these done
clear
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question_answer30)
The set of intelligent students in a class is ______
A)
A null set done
clear
B)
A singleton set done
clear
C)
A finite set done
clear
D)
not a well-defined collection done
clear
E)
None of these done
clear
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question_answer31)
Which of the following is the empty set
A)
{x: x is a natural number and \[{{x}^{2}}-1=0\]} done
clear
B)
{x: x is a natural number and \[{{x}^{2}}+1=0\]} done
clear
C)
{x: x is a an integer number and \[{{x}^{2}}-9=0\]} done
clear
D)
{x: x is a an integer number and \[{{x}^{2}}=x+2\]} done
clear
E)
None of these done
clear
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question_answer32)
Let n (\[\bigcup \]) =700, n A = 200, n B = 300 and n (A \[\bigcap \] B) = 100, then n(A' \[\bigcap \] B')
A)
400 done
clear
B)
600 done
clear
C)
300 done
clear
D)
200 done
clear
E)
None of these done
clear
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question_answer33)
If A and B are any two sets, then A \[\cup \] (A \[\cup \] B) is equal to ______
A)
A done
clear
B)
B done
clear
C)
A' done
clear
D)
B' done
clear
E)
None of these done
clear
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question_answer34)
If A = {2, 4, 5}, B = {7, 8, 9}, then n \[\left( A\text{ }\times \text{ }B \right)\] is equal to
A)
6 done
clear
B)
9 done
clear
C)
3 done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer35)
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 5}, B = {6, 7}, then A n B' is
A)
B? done
clear
B)
A done
clear
C)
A' done
clear
D)
B done
clear
E)
None of these done
clear
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question_answer36)
If A and B are disjoint, then n(A \[\cup \] B) is equal to
A)
\[n(A)\] done
clear
B)
\[n(B)\] done
clear
C)
\[n\left( A \right)+n\left( B \right)\] done
clear
D)
\[n\left( A \right).n\left( B \right)\] done
clear
E)
None of these done
clear
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question_answer37)
30 teachers of a school either teach mathematics or physics. 22 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is _____
A)
12 done
clear
B)
8 done
clear
C)
16 done
clear
D)
15 done
clear
E)
None of these done
clear
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question_answer38)
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is _____
A)
22 done
clear
B)
33 done
clear
C)
10 done
clear
D)
45 done
clear
E)
None of these done
clear
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question_answer39)
If \[A=\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\},\text{ }B=\left\{ 2,\text{ }4,\text{ }6 \right\},\text{ }C=\left\{ 3,\text{ }4,\text{ }6 \right\},\]then (A\[\cup \]B) \[\cap \] C is ?___
A)
\[\left\{ 3,\text{ }4,\text{ }6 \right\}\] done
clear
B)
\[\left\{ 1,\text{ }2,\text{ }3 \right\}\] done
clear
C)
\[\left\{ 1,\text{ }4,\text{ }3 \right\}\] done
clear
D)
\[\left\{ 1,~2 \right\}\] done
clear
E)
None of these done
clear
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question_answer40)
If W is the set of all whole numbers and P is the set of all prime numbers and C is the set of all composite numbers, then W - (CUP) is equal to?.........
A)
\[\left\{ 0 \right\}\] done
clear
B)
\[\left\{ 1 \right\}\] done
clear
C)
\[\left\{ 0,\text{ }1 \right\}\] done
clear
D)
\[\{\phi \}\] done
clear
E)
None of these done
clear
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