Mathematics MCQ Quiz Hub

1. What is the circumference of a circle if the radius is 7 m?
8 m
2 m
44 m
22 m

2. Find the area of a semicircle if the radius is 6 cm.
1.35 m
6.54 m
18.00 m
8.05 m

3. Find the radius of the circle if the circumference is 12 m.
1.90 m
1.09 m
7.90 m
1.40 m

4. Find the radius of a circle if 2 m is the area of the circle.
√0.83 m
5 m
√0.63 m
√38 m

5. Find the radius of the circle if the area of the circle is 22 cm.
1521.14 m
1511.14 m
1021.14 m
1520.14 m

6. What is the circumference of the circle if the radius is 121 cm?
760.00 cm
765.57 cm
750.57 cm
760.57 cm

7. Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.
0.07 m
0.47 cm
0.79 m
0.57 cm

8. The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.
3.07 cm
0.37 cm
2.33 cm
4.57 cm

9. Find the diameter of the circle if the area of the circle is 6 m.
3.07 m
2.74 m
2.33 m
4.57 m

10. Which graph represents relation between whole and its parts?
Histogram
Pie graph
Line graph
Stacked bar graph

11. What is the nature of function f(x) = 7x-4 on R?
Increasing
Decreasing
Strictly Increasing
Increasing and Decreasing

12. Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.
(π/4, 5π/4)
(-π/4, 5π/4)
(π/4, -5π/4)
(-π/4, π/4)

13. Find the interval in which function f(x) = sinx+cosx is increasing.
(5π/4, 2π)
[0, π/4) and (5π/4, 2π]
(π/4, -5π/4)
(-π/4, π/4)

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

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

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

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

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

19. Which of these is not a type of relation?
Reflexive
Surjective
Symmetric
Transitive

20. Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.
R = {(1, 2), (1, 3), (1, 4)}
R = {(1, 2), (2, 1)}
R = {(1, 1), (2, 2), (3, 3)}
R = {(1, 1), (1, 2), (2, 3)}

21. Which of the following relations is transitive but not reflexive for the set S={3, 4, 6}?
R = {(3, 4), (4, 6), (3, 6)}
R = {(1, 2), (1, 3), (1, 4)}
R = {(3, 3), (4, 4), (6, 6)}
R = {(3, 4), (4, 3)}

22. 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?
(2,3) ∈ R
(4,2) ∈ R
(2,1) ∈ R
(5,0) ∈ R

23. Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?
R = {(7, 7), (8, 8), (9, 9)}
R = {(7, 8), (8, 7), (8, 9)}
R = {0}
R = {(7, 8), (8, 8), (8, 9)}

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

25. (a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?
Reflexive relation
Symmetric relation
Equivalence relation
Transitive relation

26. 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 ______
6
5
9
4

27. The less-than relation, <, on a set of real numbers is ______
not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
a partial ordering since it is asymmetric and reflexive
a partial ordering since it is antisymmetric and reflexive
not a partial ordering because it is not antisymmetric and reflexive

28. 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 ______
(145, 265) and (0, 153)
(22, 101) and (0, 153)
(101, 22) and (145, 265)
(101, 22) and (0, 153)

29. 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}, {2, 4}
{1}, {1, 2, 3}
{1}
{1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}

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

31. 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?
Every non-empty subset of has a greatest lower bound
It is uncountable
Every non-empty finite subset of has a least upper bound
Every non-empty subset of has a least upper bound

32. 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?
P(x) = True for all x S such that x ≠ b
P(x) = False for all x ∈ S such that b ≤ x and x ≠ c
P(x) = False for all x ∈ S such that x ≠ a and x ≠ c
P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

33. Hasse diagrams are first made by ______
A.R. Hasse
Helmut Hasse
Dennis Hasse
T.P. Hasse

34. If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______
upward planar
downward planar
lattice
biconnected components

35. Which of the following relation is a partial order as well as an equivalence relation?
equal to(=)
less than(<)
greater than(>)
not equal to(!=)

36. The relation ≤ is a partial order if it is ___________
reflexive, antisymmetric and transitive
reflexive, symmetric
asymmetric, transitive
irreflexive and transitive

37. In which of the following relations every pair of elements is comparable?
≤
!=
>=
==

38. In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?
an element n exists for which m=n
An element m is maximal in the poset
A set with the same subset of the poset
An element m is minimal in the poset

39. In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element?
{v, x, y, z}
1
∅
{vx, xy, yz}

40. 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?
43722
2359296
6487535
131963

41. The maximum number of edges in a bipartite graph on 14 vertices is ___________
56
14
49
87

42. In a ______ the degree of each and every vertex is equal.
regular graph
point graph
star graph
euler graph

43. What is the maximum number of edges in a bipartite graph on 14 vertices?
78
15
214
49

44. Bipartite graphs are used in ________
modern coding theory
colouring graphs
neural networks
chemical bonds

45. All closed walks are of ______ length in a bipartite graph.
infinite
even
odd
odd prime

46. Every complete bipartite graph must not be _______
planar graph
line graph
complete graph
subgraph

47. The spectrum of a graph is _______ if and only if it is _______ graph.
symmetry, bipartite
transitive, bipartite
cyclic, Euler
reflexive, planar

48. n undirected graph G which is connected and acyclic is called ____________
bipartite graph
cyclic graph
tree
forest