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)
(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
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)
All closed walks are of ______ length in a bipartite graph.
1.infinite
2.even
3.odd
4.odd prime
Bipartite graphs are used in ________
1.modern coding theory
2.colouring graphs
3.neural networks
4.chemical bonds
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
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
Every complete bipartite graph must not be _______
1.planar graph
2.line graph
3.complete graph
4.subgraph
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
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
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)
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
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
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
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
Hasse diagrams are first made by ______
1.A.R. Hasse
2.Helmut Hasse
3.Dennis Hasse
4.T.P. Hasse
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
In a ______ the degree of each and every vertex is equal.
1.regular graph
2.point graph
3.star graph
4.euler graph
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
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}
In which of the following relations every pair of elements is comparable?
1.≤
2.!=
3.>=
4.==
Is the function f(x) = 3x+10 is increasing on R?
1.True
2.False
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
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
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)}
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
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)}
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)}
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
n undirected graph G which is connected and acyclic is called ____________
1.bipartite graph
2.cyclic graph
3.tree
4.forest
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
The function f:R→R defined as f(x)=7x+4 is both one-one and onto.
1.True
2.False
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}
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
The maximum number of edges in a bipartite graph on 14 vertices is ___________
1.56
2.14
3.49
4.87
The relation ≤ is a partial order if it is ___________
1.reflexive, antisymmetric and transitive
2.reflexive, symmetric
3.asymmetric, transitive
4.irreflexive and transitive
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
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
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
What is the maximum number of edges in a bipartite graph on 14 vertices?
1.78
2.15
3.214
4.49
What is the nature of function f(x) = 7x-4 on R?
1.Increasing
2.Decreasing
3.Strictly Increasing
4.Increasing and Decreasing
Which graph represents relation between whole and its parts?
1.Histogram
2.Pie graph
3.Line graph
4.Stacked bar graph
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(!=)
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)}
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)}
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)}
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)}
Which of these is not a type of relation?
1.Reflexive
2.Surjective
3.Symmetric
4.Transitive