R4RIN – MCQs, Mock Tests | Mathematics Mathematics MCQs Set-7

If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is?

1. 1024
2. 2048
3. 512
4. 4096

✅ Correct Answer: 4

If set A X B=B X A then which of the following sets may satisfy?

1. A={1, 2, 3}, B={1, 2, 3, 4}
2. A={1, 2}, B={2, 1}
3. A={1, 2, 3}, B={2, 3, 4}
4. None of the mentioned

✅ Correct Answer: 2

If set A has 10 elements, set B has 20 elements, 5 elements are common to both then find the number of elements in X∪Y.

1. 10
2. 15
3. 20
4. 25

✅ Correct Answer: 4

What is A ∪ B for two mutually exclusive sets A and B?

1. n (A) + n (B)
2. n (A) – n (B)
3. n (B) – n (A)
4. n (A) * n (B)

✅ Correct Answer: 1

In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like both tea and coffee?

1. 1
2. 2
3. 7
4. 9

✅ Correct Answer: 2

In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like neither tea nor coffee?

1. 1
2. 2
3. 3
4. 4

✅ Correct Answer: 3

In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like only tea?

1. 2
2. 3
3. 4
4. 5

✅ Correct Answer: 1

In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like only coffee?

1. 2
2. 3
3. 4
4. 5

✅ Correct Answer: 2

In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read both newspaper?

1. 100
2. 300
3. 1000
4. 1300

✅ Correct Answer: 2

In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read only Hindustan Times?

1. 100
2. 200
3. 300
4. 600

✅ Correct Answer: 3

In a city of 1000 population, all people read newspaper. 600 people read Hindustan Times and 700 people read Times of India. How many people read only Times of India?

1. 200
2. 400
3. 600
4. 700

✅ Correct Answer: 2

In a committee, if 50 people speak French, 20 people speak Spanish, 10 people speak both the languages, then how many people speak at least one of the two languages?

1. 10
2. 20
3. 50
4. 60

✅ Correct Answer: 4

A group conducted a survey of 100 consumers and reported that 72 consumers like apples and 45 consumers like oranges, what is the least number that must have liked both products?

1. 14
2. 15
3. 16
4. 17

✅ Correct Answer: 4

In a population of 1000 people, 700 people play football, 600 people play cricket, and 100 people play both. Is the data correct?

1. True
2. False
3.
4.

✅ Correct Answer: 2

In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the student knows either Hindi or English. How many students are there in the group?

1. 75
2. 100
3. 125
4. 175

✅ Correct Answer: 3

If 200 people like tea, 300 people like coffee and 250 people like both. Is the data correct?

1. True
2. False
3.
4.

✅ Correct Answer: 2

The cardinality of the set A = {1, 2, 3, 4, 6} is?

1. 5
2. 6
3. Integer
4. None of the mentioned

✅ Correct Answer: 1

For two equal sets there ___________

1. Cardinality is same
2. Cardinality is different
3. May be same or different
4. None of the mentioned

✅ Correct Answer: 1

If A is a subset of B then _______

1. The cardinality of A is greater than B
2. The cardinality of B is greater than A
3. Can’t say
4. None of the mentioned

✅ Correct Answer: 2

If there is a bijection between two sets A and B then _______

1. Cardinality of A is greater than B
2. Cardinality of B is greater than A
3. Cardinality of B is equal to A
4. None of the mentioned

✅ Correct Answer: 3

Let a set E ={0,2,4,6,8….} of non-negative even numbers and O = {1, 3, 5, 7, 9,…..} of non-negative odd numbers then?

1. Cardinality of set E is greater than that of O
2. Cardinality of set O is greater than that of E
3. Cardinality of set E is equal to that of O
4. None of the mentioned

✅ Correct Answer: 3

Cardinality of the set of lower letter english alphabets is 26.

1. True
2. False
3.
4.

✅ Correct Answer: 1

Cardinality of the set of even prime number under 10 is 4.

1. True
2. False
3.
4.

✅ Correct Answer: 2

If for sets A and B there exists an injective function but not bijective function from A to B then?

1. Cardinality of A is strictly greater than B
2. Cardinality of B is strictly greater than A
3. Cardinality of B is equal to A
4. None of the mentioned

✅ Correct Answer: 2

If cardinality of (A U B) = cardinality of A+ cardinality of B. This means ____________

1. A is a subset of B
2. B is a subset of A
3. A and B are disjoint
4. None of the mentioned

✅ Correct Answer: 3

If A is a subset of B and B is a subset of C, then cardinality of A U B U C is equal to ____________

1. Cardinality of C
2. Cardinality of B
3. Cardinality of A
4. None of the mentioned

✅ Correct Answer: 1

How to define a set?

1. A collection of well-defined objects or element
2. A collection of unordered objects or element
3. Any random elements
4. A collection of special characters

✅ Correct Answer: 1

How is a set denoted?

1. ()
2. {}
3. []
4. **

✅ Correct Answer: 2

How will you define a set of all real numbers?

1. {x: -1 < x < 1}
2. [x: -∞ < x < ∞]
3. {x: -∞ < x < ∞}
4. {x: -Z < x < +Z}

✅ Correct Answer: 3

How will you define Union of two sets A and B?

1. {x: x € A or x € B}
2. {x: x € A or x € B (or both)}
3. {x: x € A and B}
4. {x: x € A – B}

✅ Correct Answer: 2

What will be the set of the interval (a, b]?

1. {x: a < x < b}
2. {x: a ≤ x ≤ b}
3. {x: a < x ≤ b}
4. {x: a ≤ x < b}

✅ Correct Answer: 3

How to solve for x, if |x-1| ≥ 3?

1. (-∞, -2) ∪ (4, ∞)
2. (-∞, -2] ∪ [4, ∞)
3. (0, -2] ∪ (4, 0)
4. (-∞, ∞) – {-2, 4}

✅ Correct Answer: 2

What is the set of all x for which 1/(x – 1)(3 – x) ≤ 1?

1. (-∞, 1) ∪ (3, ∞)
2. (-∞, 1) ∪ (3, ∞) ∪ {2}
3. (-∞, 1) ∪ {2}
4. (3, ∞) ∪ {2}

✅ Correct Answer: 2

A set can be a collection but a collection cannot be a set.

1. True
2. False
3.
4.

✅ Correct Answer: 1

Which of the following holds true for a vector quantity?

1. It has only magnitude
2. It has only direction
3. A vector has both direction and magnitude
4. A vector can never be negative

✅ Correct Answer: 3

A scalar quantity has only magnitude and no direction.

1. True
2. False
3.
4.

✅ Correct Answer: 1

Which of the given qualities is a vector?

1. Speed
2. Time
3. Weight
4. Volume

✅ Correct Answer: 1

Which of the following is not a vector quantity?

1. Speed
2. Density
3. Force
4. Velocity

✅ Correct Answer: 2

Two vectors having the same initial points are called as ________________

1. collinear vectors
2. unit vectors
3. coinitial vectors
4. equal vectors

✅ Correct Answer: 3

A unit vector is a vector whose magnitude is unity.

1. True
2. False
3.
4.

✅ Correct Answer: 1

Which of the following condition is true for equal vectors?

1. They have the same direction but not same magnitude
2. They have the same magnitude and direction
3. They have the same initial point
4. They are parallel to the same line

✅ Correct Answer: 2

The vector whose initial and final points coincide is called ____________

1. unit vector
2. coinitial vectors
3. equal vectors
4. zero vector

✅ Correct Answer: 4

The vectors which start from the same initial point are called collinear vectors.

1. True
2. False
3.
4.

✅ Correct Answer: 2

Which of the following is the condition for two vectors to be Collinear?

1. The vectors should be parallel to the same line
2. The vectors should have the same initial point
3. The vectors should have the same magnitude
4. The vectors should have the magnitude 1 and 0 respectively

✅ Correct Answer: 1

Find the order of the differential equation y’-20y+2=0.

1. 2
2. 8
3. 0
4. 1

✅ Correct Answer: 4

Find the degree of the differential equation y”-12cosec y=0.

1. 1
2. 2
3. 4
4. Not defined

✅ Correct Answer: 1

Find the order and degree of the differential equation 7y’-3y=0.

1. Order -1, Degree-2
2. Order -2, Degree-3
3. Order -1, Degree-1
4. Order -3, Degree-2

✅ Correct Answer: 3

How many arbitrary constants will be there in the general solution of a second order differential equation?

1. 3
2. 4
3. 2
4. 1

✅ Correct Answer: 3

The number of arbitrary constants in a particular solution of a fourth order differential equation is __________________

1. 1
2. 0
3. 4
4. 3

✅ Correct Answer: 2

What is the order of the differential equation of the family of circles with one diameter along the line y = x axis?

1. 3
2. 2
3. 1
4. 0

✅ Correct Answer: 2