Mathematics Test

Result

Mathematics Test - 3

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Weekly Quiz Competition

Question 1
4 / -1

A
1

B
0

C
2

D
None of these

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

An iso-profit line represents ______________.

A
an infinite number of solutions all of which yield the same profit

B
an infinite number of solution all of which yield the same cost

C
an infinite number of optimal solutions

D
a boundary of the feasible region

Solution

The graph of the profit function is called an iso profit line. It is called this because iso means same or equal and the profit anywhere on the line is the same.

So, an iso-profit lines represents an infinite number of solutions all of which yield the same profit.
Question 4
4 / -1

A
0

B
1

C
2

D
3

Solution
Question 5
4 / -1

A dice is rolled three times and the sum of three numbers appearing on the uppermost face is 15 . What is the chance that the first roll was four?

A
1/216

B
2/69

C
1/5

D
3/71

Solution
Question 6
4 / -1

Determine the maximum value of Z = 3 x + 4 y if the feasible region (shaded) for a LPP is shown in Figure.

A
(0, 38)

B
(0, 0)

C
(52, 0)

D
(44, 16)

Solution
Question 7
4 / -1

A

B

C

D

Solution
Question 8
4 / -1

A line makes angle α, β, y with x-axis, y -axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to:

A
2

B
1

C
-2

D
-1

Solution
Question 9
4 / -1

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella?

A

B

C

D

Solution

In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.
Question 10
4 / -1

Consider the following statements:

1. The null set is a subset of every set.

2. Every set is a subset of itself.

3. If a set has 10 elements, then its power set will have 1024 elements.

Which of the above statements are correct?

A
1 and 2 only

B
2 and 3 only

C
1 and 3 only

D
1, 2 and 3

Solution

1. The null set is a subset of every set - The intersection of two sets is a subset of each of the original sets.

So if {} is the empty set and A is any set then {} intersect A is {} which means {} is a subset of A and {} is a subset of {}.

You can prove it by contradiction. Let's say that you have the empty set {} and a set A.

2. Every set is a subset of itself.

When we say that a set A is a subset of B, we mean that every element in A is also in B. A Venn diagram shows this nicely:

This also means that every set, A, is a subset of itself because every element of A is obviously an element of A.