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Objective Questions

Latest HPRCA Teachers Exam Question (Objective Questions), MCQ in English

Subjects : Mathematics, General Knowledge, Everyday Science, Logical Reasoning, Social Science, General English & General Hindi

Question Bank HPRCA Mathematics Teachers Exam - English
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Mathematics

Question 1Single Answer
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}
Question 2Single Answer
 
  1. A
  2. B
  3. C
  4. D
    None of these
Question 3Single Answer
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)}
Question 4Single Answer
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}
Question 5Single Answer
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
Question 6Single Answer
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
Question 7Single Answer
The number of elements of the power set of a set containing m elements is
  1. A
    2m – 1
  2. B
    m 
  3. C
    m2
  4. D
    2m
Question 8Single Answer
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
Question 9Single Answer
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 
Question 10Single Answer
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  
Question 11Single Answer
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 
Question 12Single Answer
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 
Question 13Single Answer
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}
Question 14Single Answer
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
Question 15Single Answer
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 
Question 16Single Answer
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
Question 17Single Answer
Combine terms: 12a + 26b  - 4b – 16a .
  1. A
    4a + 22b
  2. B
    -28a + 30b
  3. C
    -4a + 22b
  4. D
    28a + 30b
Question 18Single Answer
The average of first 50 natural numbers is ………… .
  1. A
    25.30
  2. B
    25.5
  3. C
    25.00
  4. D
    12.25
Question 19Single Answer
60 Times of 8 Equals to
  1. A
    480
  2. B
    300
  3. C
    250
  4. D
    400
Question 20Single Answer
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
Question 21Single Answer
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
Question 22Single Answer
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 
Question 23Single Answer
  1. A
  2. B
  3. C
  4. D
Question 24Single Answer
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
Question 25Single Answer
What is the Next Prime Number after 7 ?
  1. A
    13
  2. B
    12
  3. C
    14
  4. D
    11
Question 26Single Answer
If A and B are two given sets, then A (A B)C is equal to
  1. A
    A
  2. B
    B
  3. C
  4. D
Question 27Single Answer
121 Divided by 11 is
  1. A
    11
  2. B
    10
  3. C
    19
  4. D
    18
Question 28Single Answer
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
Question 29Single Answer
  1. A
    {3, 4, 10}
  2. B
    {2, 8, 10}
  3. C
    {4, 5, 6}
  4. D
    {3, 5, 14}
Question 30Single Answer
Let A = {x : x is a prime factor of 240} B = {x : x is the sum of any two prime factors of 240}, then
  1. A
  2. B
  3. C
  4. D
Question 31Single Answer
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
Question 32Single Answer
  1. A
    A = B
  2. B
    B = C
  3. C
    A = C 
  4. D
    None of these
Question 33Single Answer
  1. A
    equal
  2. B
    disjoint
  3. C
    either equal or disjoint
  4. D
    none of the above
Question 34Single Answer
  1. A
    {–i, i}
  2. B
    {–1, 1}
  3. C
    {–1, 1, i, –i}
  4. D
    None of these
Question 35Single Answer
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. B
  3. C
  4. D
    None of the above 
Question 36Single Answer
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
Question 37Single Answer
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
Question 38Single Answer
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
Question 39Single Answer
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
Question 40Single Answer
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
Question 41Single Answer
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
Question 42Single Answer
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
Question 43Single Answer
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
Question 44Single Answer
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%
Question 45Single Answer
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}
Question 46Single Answer
In a college  part girls and  part boys attended a social camp. How many parts in the collegs students attended the camp ?
  1. A
  2. B
  3. C
  4. D
  5. E
    None of the above
Question 47Single Answer
The sum of two number is 16 and their difference is 2. What is the product to both numbers ?
  1. A
    35
  2. B
    56
  3. C
    56
  4. D
    72
Question 48Single Answer
What are the positive factors of 160 .
  1. A
    6
  2. B
    8
  3. C
    5
  4. D
    12
Question 49Single Answer
What is the value of (51 + 52 + 53 ........100) ?
  1. A
    1325
  2. B
    5050
  3. C
    3775
  4. D
    3325
Question 50Single Answer
What is the sum of all natural numbers that come in the between 1 to 100, which a multiple of 7 ?
  1. A
    735
  2. B
    745
  3. C
    675
  4. D
    705
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