R4RIN – MCQs, Mock Tests | Mathematics Mathematics MCQs Set-2

What is the circumference of a circle if the radius is 7 m?

1. 8 m
2. 2 m
3. 44 m
4. 22 m

✅ Correct Answer: 3

Find the area of a semicircle if the radius is 6 cm.

1. 1.35 m
2. 6.54 m
3. 18.00 m
4. 8.05 m

✅ Correct Answer: 2

Find the radius of the circle if the circumference is 12 m.

1. 1.90 m
2. 1.09 m
3. 7.90 m
4. 1.40 m

✅ Correct Answer: 1

Find the radius of a circle if 2 m is the area of the circle.

1. √0.83 m
2. 5 m
3. √0.63 m
4. √38 m

✅ Correct Answer: 3

Find the radius of the circle if the area of the circle is 22 cm.

1. 1521.14 m
2. 1511.14 m
3. 1021.14 m
4. 1520.14 m

✅ Correct Answer: 1

What is the circumference of the circle if the radius is 121 cm?

1. 760.00 cm
2. 765.57 cm
3. 750.57 cm
4. 760.57 cm

✅ Correct Answer: 4

Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.

1. 0.07 m
2. 0.47 cm
3. 0.79 m
4. 0.57 cm

✅ Correct Answer: 3

The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.

1. 3.07 cm
2. 0.37 cm
3. 2.33 cm
4. 4.57 cm

✅ Correct Answer: 3

Find the diameter of the circle if the area of the circle is 6 m.

1. 3.07 m
2. 2.74 m
3. 2.33 m
4. 4.57 m

✅ Correct Answer: 2

Which graph represents relation between whole and its parts?

1. Histogram
2. Pie graph
3. Line graph
4. Stacked bar graph

✅ Correct Answer: 2

What is the nature of function f(x) = 7x-4 on R?

1. Increasing
2. Decreasing
3. Strictly Increasing
4. Increasing and Decreasing

✅ Correct Answer: 3

Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.

1. (π/4, 5π/4)
2. (-π/4, 5π/4)
3. (π/4, -5π/4)
4. (-π/4, π/4)

✅ Correct Answer: 1

Find the interval in which function f(x) = sinx+cosx is increasing.

1. (5π/4, 2π)
2. [0, π/4) and (5π/4, 2π]
3. (π/4, -5π/4)
4. (-π/4, π/4)

✅ Correct Answer: 2

Is the function f(x) = 3x+10 is increasing on R?

1. True
2. False
3.
4.

✅ Correct Answer: 1

The function f:R→R defined as f(x)=7x+4 is both one-one and onto.

1. True
2. False
3.
4.

✅ Correct Answer: 1

Let A={1,2,3} and B={4,5,6}. Which one of the following functions is bijective?

1. f={(2,4),(2,5),(2,6)}
2. f={(1,5),(2,4),(3,4)}
3. f={(1,4),(1,5),(1,6)}
4. f={(1,4),(2,5),(3,6)}

✅ Correct Answer: 4

Let P={10,20,30} and Q={5,10,15,20}. Which one of the following functions is one – one and not onto?

1. f={(10,5),(10,10),(10,15),(10,20)}
2. f={(10,5),(20,10),(30,15)}
3. f={(20,5),(20,10),(30,10)}
4. f={(10,5),(10,10),(20,15),(30,20)}

✅ Correct Answer: 2

Let M={5,6,7,8} and N={3,4,9,10}. Which one of the following functions is neither one-one nor onto?

1. f={(5,3),(5,4),(6,4),(8,9)}
2. f={(5,3),(6,4),(7,9),(8,10)}
3. f={(5,4),(5,9),(6,3),(7,10),(8,10)}
4. f={(6,4),(7,3),(7,9),(8,10)}

✅ Correct Answer: 1

Which of these is not a type of relation?

1. Reflexive
2. Surjective
3. Symmetric
4. Transitive

✅ Correct Answer: 2

Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.

1. R = {(1, 2), (1, 3), (1, 4)}
2. R = {(1, 2), (2, 1)}
3. R = {(1, 1), (2, 2), (3, 3)}
4. R = {(1, 1), (1, 2), (2, 3)}

✅ Correct Answer: 2

Which of the following relations is transitive but not reflexive for the set S={3, 4, 6}?

1. R = {(3, 4), (4, 6), (3, 6)}
2. R = {(1, 2), (1, 3), (1, 4)}
3. R = {(3, 3), (4, 4), (6, 6)}
4. R = {(3, 4), (4, 3)}

✅ Correct Answer: 1

Let R be a relation in the set N given by R={(a,b): a+b=5, b>1}. Which of the following will satisfy the given relation?

1. (2,3) ∈ R
2. (4,2) ∈ R
3. (2,1) ∈ R
4. (5,0) ∈ R

✅ Correct Answer: 1

Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?

1. R = {(7, 7), (8, 8), (9, 9)}
2. R = {(7, 8), (8, 7), (8, 9)}
3. R = {0}
4. R = {(7, 8), (8, 8), (8, 9)}

✅ Correct Answer: 1

Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?

1. R = {(4, 4), (5, 4), (5, 5)}
2. R = {(4, 4), (5, 5)}
3. R = {(4, 5), (5, 4)}
4. R = {(4, 5), (5, 4), (4, 4)}

✅ Correct Answer: 4

(a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?

1. Reflexive relation
2. Symmetric relation
3. Equivalence relation
4. Transitive relation

✅ Correct Answer: 1

Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______

1. 6
2. 5
3. 9
4. 4

✅ Correct Answer: 2

The less-than relation, <, on a set of real numbers is ______

1. not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
2. a partial ordering since it is asymmetric and reflexive
3. a partial ordering since it is antisymmetric and reflexive
4. not a partial ordering because it is not antisymmetric and reflexive

✅ Correct Answer: 1

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) ∊ P. ii)(a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153) The ordered pairs of natural numbers are contained in P are ______ and ______

1. (145, 265) and (0, 153)
2. (22, 101) and (0, 153)
3. (101, 22) and (145, 265)
4. (101, 22) and (0, 153)

✅ Correct Answer: 4

The inclusion of ______ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.

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

✅ Correct Answer: 3

Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________

1. | is an equivalence relation
2. It is a total order
3. Every subset of N has an upper bound under |
4. (N,|) is a lattice but not a complete lattice

✅ Correct Answer: 4

Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?

1. Every non-empty subset of has a greatest lower bound
2. It is uncountable
3. Every non-empty finite subset of has a least upper bound
4. Every non-empty subset of has a least upper bound

✅ Correct Answer: 1

Let (A, ≤) be a partial order with two minimal elements a, b and a maximum element c. Let P:A –> {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) ⇒ P(b) for all satisfying a ≤ b, where ⇒ stands for logical implication. Which of the following statements cannot be true?

1. P(x) = True for all x S such that x ≠ b
2. P(x) = False for all x ∈ S such that b ≤ x and x ≠ c
3. P(x) = False for all x ∈ S such that x ≠ a and x ≠ c
4. P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

✅ Correct Answer: 4

Hasse diagrams are first made by ______

1. A.R. Hasse
2. Helmut Hasse
3. Dennis Hasse
4. T.P. Hasse

✅ Correct Answer: 2

If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______

1. upward planar
2. downward planar
3. lattice
4. biconnected components

✅ Correct Answer: 1

Which of the following relation is a partial order as well as an equivalence relation?

1. equal to(=)
2. less than(<)
3. greater than(>)
4. not equal to(!=)

✅ Correct Answer: 1

The relation ≤ is a partial order if it is ___________

1. reflexive, antisymmetric and transitive
2. reflexive, symmetric
3. asymmetric, transitive
4. irreflexive and transitive

✅ Correct Answer: 1

In which of the following relations every pair of elements is comparable?

1. ≤
2. !=
3. >=
4. ==

✅ Correct Answer: 1

In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?

1. an element n exists for which m=n
2. An element m is maximal in the poset
3. A set with the same subset of the poset
4. An element m is minimal in the poset

✅ Correct Answer: 2

In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element?

1. {v, x, y, z}
2. 1
3. ∅
4. {vx, xy, yz}

✅ Correct Answer: 1

Let G be the graph defined as the Hasse diagram for the ⊆ relation on the set S{1, 2,…, 18}. How many edges are there in G?

1. 43722
2. 2359296
3. 6487535
4. 131963

✅ Correct Answer: 2

The maximum number of edges in a bipartite graph on 14 vertices is ___________

1. 56
2. 14
3. 49
4. 87

✅ Correct Answer: 3

In a ______ the degree of each and every vertex is equal.

1. regular graph
2. point graph
3. star graph
4. euler graph

✅ Correct Answer: 3

What is the maximum number of edges in a bipartite graph on 14 vertices?

1. 78
2. 15
3. 214
4. 49

✅ Correct Answer: 4

Bipartite graphs are used in ________

1. modern coding theory
2. colouring graphs
3. neural networks
4. chemical bonds

✅ Correct Answer: 1

All closed walks are of ______ length in a bipartite graph.

1. infinite
2. even
3. odd
4. odd prime

✅ Correct Answer: 2

Every complete bipartite graph must not be _______

1. planar graph
2. line graph
3. complete graph
4. subgraph

✅ Correct Answer: 3

The spectrum of a graph is _______ if and only if it is _______ graph.

1. symmetry, bipartite
2. transitive, bipartite
3. cyclic, Euler
4. reflexive, planar

✅ Correct Answer: 1

n undirected graph G which is connected and acyclic is called ____________

1. bipartite graph
2. cyclic graph
3. tree
4. forest

✅ Correct Answer: 3