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

1.regular graph

2.point graph

3.star graph

4.euler graph

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

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