Question for UKPSC Assistant Professor (Mathematics) - Quiz / Questions / MCQ in English

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Latest UKPSC Assistant Professor (Mathematics) Exam Question (Objective Questions), MCQ in English

Subjects : Mathematics

Question Bank UKPSC Assistant Professor (Mathematics) Exam - English

Mathematics

Q 1 :

The elements of the set {x : x is an integer, x² : 4} can be represent as .....Z..... . Here, Z refers to

1. A.{–2, 2} 
2. B.{–1, 0, 1}
3. C.{–2, –1, 0, 1, 2}
4. D.{0, 1, 2}

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Q 2 :

1. D.None of these

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Q 3 :

If Y = {x : x is a positive factor of the number 2p – 1(2p – 1), where 2p – 1 is a prime number}, then Y can be represent in roster form as

1. A.{2}
2. B.{1, 2}  
3. C.{1, 2, 22, ....., 2p – 1}
4. D.{1, 2, 22, 23,.... 2p – 1, (2p – 1)}

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Q 4 :

The set {x : x is a positive integer less than 6 and 3x – 1 is an even number} in roster form is

1. A.{1, 2, 3, 4, 5}
2. B.{1, 2, 3, 4, 5, 6}  
3. C.{2, 4, 6}
4. D.{1, 3, 5}

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Q 5 :

If A B and A B, then

1. A.A is called a proper subset of B
2. B.A is called a super set of B
3. C.A is not a subset of B 
4. D.B is a subset of A

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Q 6 :

The number of non-empty subsets of the set{1, 2, 3, 4} is

1. A.15
2. B.14
3. C.16
4. D.17

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Q 7 :

The number of elements of the power set of a set containing m elements is

1. A.2^m – 1
2. B.m 
3. C.m²
4. D.2^m

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Q 8 :

If A = {x : x = n², n = 1, 2, 3}, then number of proper subsets is

1. A.3
2. B.8
3. C.7
4. D.None of these

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Q 9 :

If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is

1. A.16
2. B.15  
3. C.4 
4. D.None of these 

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Q 10 :

Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then

1. A.A is always a subset of the complement of B
2. B.B is always a subset of A  
3. C.A and B are always disjoint
4. D.A and the complement of B are always non-disjoint  

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Q 11 :

Which of the following is/are empty set? 
A = {x : x2 + x + 1 = 0 and x Î Z}   B = {x : x is a prime number and 19 < x < 23}

1. A.A
2. B.B  
3. C.Both A and B
4. D.None of the above 

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Q 12 :

The set {x : x⁴ = 1 and x R} is .....X.... set. Here, X refers to

1. A.empty
2. B.finite
3. C.infinite
4. D.singleton 

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Q 13 :

The universal set for the sets   
A = {x : x² – 5x + 6 = 0} and   
B = {x : x² – 3x + 2 = 0} having least number of elements is

1. A.{1, 2}
2. B.{1, 3}
3. C.{1, 2, 3}
4. D.{0, 1, 2, 3}

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Q 14 :

If A = {1, 2, 3}, B = {x € R : x2 – 2x + 1 = 0}, 

C = {1, 2, 2, 3} and 

D = {x € R : x3 – 6x2 + 11x – 6 = 0}, then the equal sets are

1. A.A and B
2. B.A and C  
3. C.A, B and C 
4. D.A, C and D

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Q 15 :

If A = (–3, 5) and  B = [–7, 9], then

1. A.A = B
2. B.A B 
3. C.B A
4. D.None of these 

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Q 16 :

Two finite sets have m and n elements, respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The value of m and n respectively are

1. A.7, 6
2. B.5, 1
3. C.6, 3
4. D.8, 7

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Q 17 :

Combine terms: 12a + 26b  - 4b – 16a .

1. A.4a + 22b
2. B.-28a + 30b
3. C.-4a + 22b
4. D.28a + 30b

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Q 18 :

The average of first 50 natural numbers is ………… .

1. A.25.30
2. B.25.5
3. C.25.00
4. D.12.25

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Q 19 :

60 Times of 8 Equals to

1. A.480
2. B.300
3. C.250
4. D.400

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Q 20 :

Consider the sets

A = {x : x is a real number and x² + 1 = 0}

B = {x : x is a real number and x² – 16 = 0}

C = {x : x is a real number and x² = x + 2}

Which of the following is are null set ?

1. A.A
2. B.A and B
3. C.A and C
4. D.A, B and C

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Q 21 :

If X = {4n – 3n – 1: n Î N} and Y = {9(n – 1): n Î N}; where N is the set of natural numbers, then X È Y is equal to

1. A.N
2. B.Y – X
3. C.X
4. D.Y

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Q 22 :

Which of the following is / are correct?

I. {2, 3, 4} {1, 2, 3, 4, 5}

II. {a, b, c} {b, c, d}

III. {x : x is an equilateral triangle in a plane} Ì {x : x is a triangle in the same plane}

IV. {x : x is an even natural number} {x : x is an integer}

1. A.I and III are correct
2. B.II and III are correct  
3. C.Only IV is correct 
4. D.All above are correct 

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Q 23 :

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Q 24 :

Consider the following statements :
1. The set of all irrational numbers between √2 and √5 is an infinite set .
2. The set of all odd integers less than 100 is a finite set .
Which of the statements given above is/are correct ?

1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2

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Q 25 :

What is the Next Prime Number after 7 ?

1. A.13
2. B.12
3. C.14
4. D.11

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Q 26 :

If A and B are two given sets, then A (A B)^C is equal to

1. A.A
2. B.B

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Q 27 :

121 Divided by 11 is

1. A.11
2. B.10
3. C.19
4. D.18

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Q 28 :

Let X be the universal set for sets A and B, if n(A) = 200, n(B) = 300 and n = 100, then n is equal to 300 provided n(X) is equal to

1. A.600
2. B.700
3. C.800
4. D.900

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Q 29 :

1. A.{3, 4, 10}
2. B.{2, 8, 10}
3. C.{4, 5, 6}
4. D.{3, 5, 14}

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Q 30 :

Let A = {x : x is a prime factor of 240} B = {x : x is the sum of any two prime factors of 240}, then

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Q 31 :

If A = {x : x is a multiple of 4 and x N} and B = {x : x is a multiple of 6 and x N}, then A B consists of all multiples of

1. A.16
2. B.12
3. C.8
4. D.4

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Q 32 :

1. A.A = B
2. B.B = C
3. C.A = C 
4. D.None of these

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Q 33 :

1. A.equal
2. B.disjoint
3. C.either equal or disjoint
4. D.none of the above

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Q 34 :

1. A.{–i, i}
2. B.{–1, 1}
3. C.{–1, 1, i, –i}
4. D.None of these

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Q 35 :

If A = {x : f(x)= 0} and 
B = {x : g(x) = 0}, then A B will be

1. A.[f(x)]2 + [g(x)]2 = 0
2. D.None of the above 

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Q 36 :

In a group of 400 people, 250 can speak Hindi and 200 can speak English. Then, people who can speak both Hindi and English are

1. A.60
2. B.80  
3. C.50
4. D.45

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Q 37 :

20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. The number of teacher teaching Physics only, is

1. A.12
2. B.8
3. C.16
4. D.20

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Q 38 :

In a class of 100 students, 70 have taken Science, 60 have taken Mathematics, 40 have taken both Science and Mathematics. The number of students who have not taken Science or Mathematics or both Science and Mathematics, is equal to

1. A.90
2. B.10
3. C.30
4. D.20

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Q 39 :

A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like the product B, then least number that must have like both products, is

1. A.730
2. B.170 
3. C.180 
4. D.1270

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Q 40 :

If there are three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is

1. A.42 
2. B.43 
3. C.45 
4. D.None of these

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Q 41 :

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, then number of men who received meal in exactly two of the three sports is

1. A.18 
2. B.15 
3. C.9 
4. D.24

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Q 42 :

In the class of 175 students, the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. Then, number of students opted Mathematics alone is

1. A.35
2. B.48
3. C.60
4. D.20

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Q 43 :

In a town of 10000 families it was found that 40% family buy newspaper A, 20% family buy newspaper B and 10% family buy newspaper C, 5% families buy and B, 3% families buy B and C and 4% families buy A and C. If 2% families buy all the three newspapers. Then, number of families which by A only is

1. A.3100
2. B.3300  
3. C.2900
4. D.1400

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Q 44 :

In a city, 20% of the population travles by car, 50% travles by bus and 10% travles by both car and bus. Then, person travelling by car or bus, is

1. A.80%
2. B.40% 
3. C.60% 
4. D.70%

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Q 45 :

Universal set,
U = {x | x⁵ – 6x⁴ + 11x³ – 6 x 2 = 0}
A = {x | x² – 5x + 6 = 0}
B = {x | x² – 3x + 2 = 0}
What is the value of (A B)?

1. A.{1, 3}
2. B.{1, 2, 3}
3. C.{0, 1, 3}
4. D.{0, 1, 2, 3}

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Q 46 :

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Q 47 :

If P(A) denotes the power set of A and A is the void set, then what is the number of elements in P{P{P{P(A)}}}?

1. A.Zero
2. B.1
3. C.4
4. D.16

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Q 48 :

If A = {1, 2, 3, 4, 5}, b = {x : x2 – 5x + 6 = 0} and C = {x : x2 = 4 or x = 1}, then

1. C.Both (a) and (b)
2. D.None of the above

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Q 49 :

In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak atleast one of two languages. The number of people who speak 'English', 'English but not Hindi' are respectively

1. A.40, 15 
2. B.15, 40
3. C.35, 15 
4. D.25, 15

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Q 50 :

If P = {1, 2}, then P × P × P = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}. The ordered triplet missing in P × P × P are

1. A.(1, 2), (2, 1)
2. B.(1, 2, 1), (2, 1, 1) 
3. C.(1, 2, 2), (2, 1, 2) 
4. D.(1, 2, 2), (2, 1, 1)

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