The elements of the set {x : x is an integer, x2 : 4} can be represent as .....Z..... . Here, Z refers to
A
{–2, 2}
B
{–1, 0, 1}
C
{–2, –1, 0, 1, 2}
D
{0, 1, 2}
Question 2Single Answer
A
B
C
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
A
{2}
B
{1, 2}
C
{1, 2, 22, ....., 2p – 1}
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
A
{1, 2, 3, 4, 5}
B
{1, 2, 3, 4, 5, 6}
C
{2, 4, 6}
D
{1, 3, 5}
Question 5Single Answer
If A B and A B, then
A
A is called a proper subset of B
B
A is called a super set of B
C
A is not a subset of B
D
B is a subset of A
Question 6Single Answer
The number of non-empty subsets of the set{1, 2, 3, 4} is
A
15
B
14
C
16
D
17
Question 7Single Answer
The number of elements of the power set of a set containing m elements is
A
2m – 1
B
m
C
m2
D
2m
Question 8Single Answer
If A = {x : x = n2, n = 1, 2, 3}, then number of proper subsets is
A
3
B
8
C
7
D
None of these
Question 9Single Answer
If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is
A
16
B
15
C
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
A
A is always a subset of the complement of B
B
B is always a subset of A
C
A and B are always disjoint
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}
A
A
B
B
C
Both A and B
D
None of the above
Question 12Single Answer
The set {x : x4 = 1 and x R} is .....X.... set. Here, X refers to
A
empty
B
finite
C
infinite
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
A
{1, 2}
B
{1, 3}
C
{1, 2, 3}
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
A
A and B
B
A and C
C
A, B and C
D
A, C and D
Question 15Single Answer
If A = (–3, 5) and B = [–7, 9], then
A
A = B
B
A B
C
B A
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
A
7, 6
B
5, 1
C
6, 3
D
8, 7
Question 17Single Answer
Combine terms: 12a + 26b - 4b – 16a .
A
4a + 22b
B
-28a + 30b
C
-4a + 22b
D
28a + 30b
Question 18Single Answer
The average of first 50 natural numbers is ………… .
A
25.30
B
25.5
C
25.00
D
12.25
Question 19Single Answer
60 Times of 8 Equals to
A
480
B
300
C
250
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 ?
A
A
B
A and B
C
A and C
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
A
N
B
Y – X
C
X
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}
A
I and III are correct
B
II and III are correct
C
Only IV is correct
D
All above are correct
Question 23Single Answer
A
B
C
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 ?
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
Question 25Single Answer
What is the Next Prime Number after 7 ?
A
13
B
12
C
14
D
11
Question 26Single Answer
If A and B are two given sets, then A (A B)C is equal to
A
A
B
B
C
D
Question 27Single Answer
121 Divided by 11 is
A
11
B
10
C
19
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
A
600
B
700
C
800
D
900
Question 29Single Answer
A
{3, 4, 10}
B
{2, 8, 10}
C
{4, 5, 6}
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
A
B
C
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
A
16
B
12
C
8
D
4
Question 32Single Answer
A
A = B
B
B = C
C
A = C
D
None of these
Question 33Single Answer
A
equal
B
disjoint
C
either equal or disjoint
D
none of the above
Question 34Single Answer
A
{–i, i}
B
{–1, 1}
C
{–1, 1, i, –i}
D
None of these
Question 35Single Answer
If A = {x : f(x)= 0} and
B = {x : g(x) = 0}, then A B will be
A
[f(x)]2 + [g(x)]2 = 0
B
C
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
A
60
B
80
C
50
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
A
12
B
8
C
16
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
A
90
B
10
C
30
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
A
730
B
170
C
180
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
A
42
B
43
C
45
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
A
18
B
15
C
9
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
A
35
B
48
C
60
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
A
3100
B
3300
C
2900
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
A
80%
B
40%
C
60%
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)?
A
{1, 3}
B
{1, 2, 3}
C
{0, 1, 3}
D
{0, 1, 2, 3}
Question 46Single Answer
A
B
C
D
Question 47Single Answer
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)}}}?
A
Zero
B
1
C
4
D
16
Question 48Single Answer
If A = {1, 2, 3, 4, 5}, b = {x : x2 – 5x + 6 = 0} and C = {x : x2 = 4 or x = 1}, then
A
B
C
Both (a) and (b)
D
None of the above
Question 49Single Answer
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
A
40, 15
B
15, 40
C
35, 15
D
25, 15
Question 50Single Answer
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
A
(1, 2), (2, 1)
B
(1, 2, 1), (2, 1, 1)
C
(1, 2, 2), (2, 1, 2)
D
(1, 2, 2), (2, 1, 1)
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Concerned Subject (Mathematics)
Question 51Single Answer
If A = {1, 2, 3, 4} and B = {5, 7, 9} then
A
A × B = B × A
B
n(A × B) =n(B × A)
C
Both (a) and (b)
D
None of the above
Question 52Single Answer
Let A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, then n[(A × B) (B × A)] is equal to
A
20
B
25
C
16
D
9
Question 53Single Answer
If n(A) = 3, n(B) = 4 then, n(A × A × B) is equal to
A
36
B
12
C
108
D
None of these
Question 54Single Answer
If A = {1, 2, 3}, B = {3, 8}, then (A B) × (A B) is equal to
A
{(8, 3), (8, 2), (8, 1), (8, 8)}
B
{(1, 2), (2, 2), (3, 3), (8, 8)}
C
{(3, 1), (3, 2), (3, 3), (3, 8)}
D
{(1, 3), (2, 3), (3, 3), (8, 3)}
Question 55Single Answer
The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Then, the remaining elements of A × A are
Which of the following functions is inverse of itself?
A
B
C
D
None of the above
Question 69Single Answer
If f(x) = ex and g(x) = logex, then which of the following is true?
A
f{g(x)} g{f(x)}
B
f{g(x)} = g{f(x)}
C
f{g(x)} + g{f(x)} = 0
D
f{g(x)} – g{f(x)} = 1
Question 70Single Answer
The value of parameter a, for which the function f : R → R given by f(x) = 1 + ax, a 0 is the inverse of itself, is
A
–2
B
–1
C
1
D
2
Question 71Single Answer
Let f: (2, 3) → (0, 1) be defined by f(x) = x – [x]. Then, f–1(x) equals to
A
x – 2
B
x + 1
C
x – 1
D
x + 2
Question 72Single Answer
The greatest integer function f: R → R, given by f(x) = [x] is
A
one-one
B
onto
C
both one-one and onto
D
neither one-one nor onto
Question 73Single Answer
The number of all one-one functions from set
A = {1, 2, 3} to itself is
A
2
B
6
C
3
D
1
Question 74Single Answer
A
B
C
D
Question 75Single Answer
A
B
C
D
Question 76Single Answer
In a college part girls and part boys attended a social camp. How many parts in the collegs students attended the camp ?
A
B
C
D
E
None of the above
Question 77Single Answer
The sum of two number is 16 and their difference is 2. What is the product to both numbers ?
A
35
B
56
C
56
D
72
Question 78Single Answer
What are the positive factors of 160 .
A
6
B
8
C
5
D
12
Question 79Single Answer
What is the value of (51 + 52 + 53 ........100) ?
A
1325
B
5050
C
3775
D
3325
Question 80Single Answer
What is the sum of all natural numbers that come in the between 1 to 100, which a multiple of 7 ?
A
735
B
745
C
675
D
705
Question 81Single Answer
What is the unit digit of 279 + 167 × 342 ?
A
1
B
3
C
5
D
8
Question 82Single Answer
Which of the given values is completely divisible by 15 ?
A
2365
B
1375
C
4365
D
2275
Question 83Single Answer
For which value of M, the divisor 34M fully divisible by 12 ?
A
2
B
0
C
8
D
6
Question 84Single Answer
If 432p1 is completely divisiable 34M fully divisiable by 12 ?
A
1
B
8
C
7
D
2
Question 85Single Answer
Which is the smallest number to be added to 100, so that the resulting number is completely divisible by 6 ?
A
2
B
3
C
5
D
4
Question 86Single Answer
When a number is divided by 80, the remainded is 20. When the same number is divided by 16, what will be the remainder ?
A
2
B
4
C
6
D
8
Question 87Single Answer
Which of the fractions is the largest among and ?
A
B
C
D
All are equal
Question 88Single Answer
What is the two digits largest prime number ?
A
91
B
93
C
97
D
99
Question 89Single Answer
What is the sum of first 15 odd natural numbers ?
A
255
B
225
C
235
D
215
Question 90Single Answer
What will be the sum of all natural numbers from 75 to 97 ?
A
1598
B
1978
C
1798
D
1958
Question 91Single Answer
If the quotient of is positive, which of the following would be true ?
A
a > 0
B
b > 0
C
ab > 0
D
a + b > 0
Question 92Single Answer
If the last two digits of a three-digit number is multiple of 6, then the original integer will always be divisible by ?
A
6
B
3
C
2
D
12
Question 93Single Answer
Find three consecutive numbers, in which sum of the two times of the first, three of second and four time of the third number os 191 ?
A
19, 20, 21
B
21, 22, 23
C
20, 21, 22
D
22, 23, 24
Question 94Single Answer
An office has 108 table and 132 chairs. If tables and of the chairs are broken, then how many people can work in the office, if required 1 table and 1 chair ?
A
86
B
90
C
90
D
99
Question 95Single Answer
If the sum of two numbers is a and the product is b, then what will be the sum of their reciprocal ?
A
B
C
D
Question 96Single Answer
The sum of all prime numbers not greater than 17 is ?
A
59
B
58
C
41
D
42
Question 97Single Answer
What is the decimal fraction of 2.349 ?
A
B
C
D
Question 98Single Answer
Which of the following number is divisible by 9 ?
A
45699
B
12381
C
45696
D
12348
Question 99Single Answer
The largest 4 - digit number is X, which is divisible by 18, 15 and 12 . Then the value of X will be ?
A
9989
B
9980
C
9999
D
9900
Question 100Single Answer
The sum of two numbers is 20 and the product is 91 . What should be the sum of their reciprocal ?
A
B
C
D
Question 101Single Answer
Find the smallest 6 digit number which is multiple of 18 ?
A
100000
B
999900
C
100008
D
100006
Question 102Single Answer
The sum of a fraction and its reciprocal is the fractions is ?
A
B
C
D
4
Question 103Single Answer
The sum of digits of a twodigit number is 9 . By subtracting 27 from number, the digits of the number are interchanged, so what is that number ?
A
72
B
63
C
45
D
None of these
Question 104Single Answer
The product of two positive numbers is 2500. If one of these numbers is four times more than the other, then what will be the sum of these two numbers ?
A
25
B
125
C
225
D
None of these
Question 105Single Answer
A studednt were asked to divide a number by 3, but instead of dividing it, multiplied that number by 3, so that he got 29.7 as the result, what would be the correct result ?
A
3.3
B
3.9
C
9.9
D
None of these
Question 106Single Answer
The sum of two times of a number and three times its reciprocal is What is that number ?
A
7
B
6
C
5
D
4
Question 107Single Answer
A number is greater than three times of its reciprocal by What is that number ?
A
10
B
11
C
9
D
8
Question 108Single Answer
Which of the following numbers is completely divisible by 99 ?
A
57717
B
57625
C
55162
D
56982
Question 109Single Answer
One dividing a number by 38, we get 90 as the quotient and 19 as the remainder . What is that number ?
A
3401
B
3382
C
3458
D
3439
Question 110Single Answer
If the number 583_437 is completely divisible by 9, what will be the minimum integer in the blank space ?
A
4
B
5
C
3
D
6
Question 111Single Answer
How many such numbers are there between 1 and 200, which are divisible by 3 but not by 7 ?
A
38
B
45
C
57
D
66
Question 112Single Answer
When 2143 is divided by 38, what will be the quotient value ?
A
56
B
55
C
57
D
54
Question 113Single Answer
What is the sum of all indivisible numbers between 58 and 68 ?
A
179
B
178
C
187
D
183
Question 114Single Answer
The sum of the bouble of a fraction and its reciprocal is What is the fraction ?
A
B
C
D
Question 115Single Answer
What is the value of ?
A
B
C
D
Question 116Single Answer
A mechnic builds a wall in 70 hours. Taking breaks after 7 hours . How much of the wall is still to be built ?
A
0.9
B
0.8
C
0.5
D
0.75
Question 117Single Answer
If the sum of two numbers is 75 and their difference is 25, what will be the product of both the numbers ?
A
1350
B
1250
C
125
D
100
Question 118Single Answer
The sum of marks of A and B in a test is 120, B and C is 130 and C and A are 140 . How many marks are obtained by C ?
A
65
B
75
C
70
D
60
Question 119Single Answer
A number x is divisible by 7 . When this number is divided by 8, 12 and 16, the remainder is 3 in each case . The minimum value of x is ?
A
148
B
149
C
150
D
147
Question 120Single Answer
The greatst and smallest prime numbers are less than 100, what will be the difference between then ?
A
96
B
97
C
94
D
95
Question 121Single Answer
How to write following in ascending order ?
A
B
C
D
Question 122Single Answer
The simple fraction of is ?
A
B
C
D
Question 123Single Answer
The two positive integers are such that the sum of the first number and the double of the second number is 8 and their difference is 2, What are the numbers ?
A
7 and 5
B
6 and 4
C
4 and 2
D
3 and 5
Question 124Single Answer
Which of the following statements are not correct ?
A
Every natural number is an integer
B
Every natural number is a real number
C
Every real number is a rational number
D
Every integer is a rational number
Question 125Single Answer
After his death, Ram left part of his property in the name of his widowed wife and part of the remaining property in the name of his daughter and gave the remaining property to the son . If the songets Rs. 6,400 then what was Ram's original property ?
A
Rs. 16,000
B
Rs. 32,000
C
Rs. 24,000
D
Rs. 1,600
Question 126Single Answer
The product of all prime number between 80 and 90 is ?
A
83
B
89
C
7387
D
598347
Question 127Single Answer
5349 is added to 3957. 7062 is subtracted from the amount received . The resulting number will not be divisible by ?
A
4
B
3
C
7
D
11
Question 128Single Answer
Divide 50 in to two parts such that their sum of reciprocal is ?
A
35, 15
B
20, 30
C
24, 36
D
28, 22
Question 129Single Answer
When n is divided by 6, the remainder become 4 . Accordingly, when 2n is divided by 6, what will be the remainder ?
A
2
B
0
C
4
D
1
Question 130Single Answer
'a', dibides 228 and 18 is as remainder. 'a', has the largest twodigit value ?
A
70
B
21
C
35
D
30
Question 131Single Answer
The two numbers 11284 and 7655, when divided by a threedigit number, leave equal remainder Accordingly, what is the sum of the digits of the number (SSC CHSL 2013)
A
8
B
9
C
10
D
11
Question 132Single Answer
In a division question, the divisor is 3 times the quotient and 6 times remainder . According, if the remainder is 2, then what is the divident ?
A
50
B
48
C
36
D
28
Question 133Single Answer
If a number is greater than 31 as is smaller than 75 . So, that the number is ?
A
106
B
44
C
74
D
53
Question 134Single Answer
If what will be the be the value of ?
A
10x
B
100x
C
D
Question 135Single Answer
The temperature has increased from to at a unifrorm rate from 9 : 00 and to 2 : 00 am. Accordingly, exactly what was the temperature at 12 pm ?
A
27oC
B
30oC
C
32oC
D
28.5oC
Question 136Single Answer
In a match of 20 overs, the rate of runs required to win is 7 . 2 . If the rate of runs remains 6 by the end of the 15th over, how many runs will be required to win the match in the remaining overs ?
A
1.2
B
13.2
C
10.8
D
12
Question 137Single Answer
The tens digit in a twodigit number is 5 more than the unit digit . If 5 times the sum of both these digits is subtracted from that number, the digits of that number are reversed . Accordingly, what is the sum of the digits of that number ?
A
11
B
7
C
9
D
13
Question 138Single Answer
A new number is obtained by adding 47 to the product of 71 and an unknown number . 98 quotient can be obtained by dividing that new number by 7 . Accordingly, that unknown number is a multiplier of which of the following ?
A
2
B
5
C
7
D
3
Question 139Single Answer
Find the minimum value of * for which the number 82178342*52, is divided by 11 .
A
7
B
2
C
0
D
5
Question 140Single Answer
The product of three consecutive natural number is always divisiable by which of the following digit ?
A
6
B
7
C
5
D
4
Question 141Single Answer
The product of two numbers is 0.432 . If one number is 106, what is the other number ?
A
2.7
B
0.027
C
27
D
0.27
Question 142Single Answer
If an 8 digit number 136P5785 is completely divisible by 15, find the minimum value of P .
A
1
B
4
C
2
D
3
Question 143Single Answer
Which of the following is a rational number ?
A
B
C
D
Question 144Single Answer
If the number x4441 is divided by 11, what is the value of x ?
A
2
B
5
C
4
D
3
Question 145Single Answer
The number 428693745 has a difference of local value of 9 and 5 .
A
90995
B
99995
C
89995
D
8995
Question 146Single Answer
To get number 40, the number must be multiplied by ?
A
B
C
D
Question 147Single Answer
If the number x3451 is divisible by3, where x is a digit, then the sum of all possible value of x ?
A
15
B
16
C
11
D
14
Question 148Single Answer
Which of the following number is divisible by 9 ?
A
12321
B
12345
C
45656
D
45678
Question 149Single Answer
Which of the following number is a prime number ?
A
997
B
1147
C
45654
D
45678
Question 150Single Answer
Which of the following number is divisible by 12 ?