Sets Test

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Sets Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is an empty set?

A
{x | x is a real number and x² – 1 = 0}

B
{x | x is a real number and x² + 1 = 0}

C
{x | x is a real number and x² – 9 = 0}

D
{x | x is a real number and x² = x + 2}

Solution

As x² + 1 = 0 ⇒ x²= -1 = i²

x = ±i , will not give a real number, so option (2) represents an empty set.
Question 2
1 / -0

If A = {letters of the word xerox} and B = {x, y, z, w}, then find A ∪ B.

A
{x, y, z, w}

B
{x, y, z, e, r, o, w}

C
{letters of the word xerox}

D
{x, y, z, z}

Solution

A = {x, e, r, o} and B = {x, y, z, w}
A ∪ B = {x, y, z, e, r, o, w}
Question 3
1 / -0

If X = {4ⁿ – 3n – 1 : n ∈ N} and Y = {9 (n – 1) : n ∈ N}, then which of the following is equal to X U Y?

A
X

B
Y

C
N

D
None of these

Solution

Putting the values of n = 1, 2, 3, 4, ………, we will get X = {0, 9, 54…} and Y = {0, 9, 18, 27, 36, 45, 54, ….}
Hence, X U Y will be a set equal to the value of Y.

i.e. X U Y = {0, 9, 18, 27, 36, 45, 54, ….}
So, X U Y = Y
Question 4
1 / -0

Given that aN = {ax : x ∈ N} and bN ∩ cN = dN, where b, c ∈ N and b, c are co-prime to each other.

Which of the following conditions is true according to the statement given above?

A
d = bb

B
c = bd

C
b = cc

D
d = bc

Solution

We have,

bN = {bx | x ∈ N} = Set of positive integral multiples of b
cN = {cx | x ∈ N} = Set of positive integral multiples of c

bN ∩ cN = Set of positive integral multiples of b and c both
As they are co-primes, LCM(b, c) = bc.

Therefore, if d = LCM of b and c, then d = bc.
Question 5
1 / -0

If N_a = {an : n ∈ N}, find the value of N₆∩ N₈.

A
N₂

B
N₄₈

C
N₈

D
N₂₄

Solution

N₆ contains all the multiples of 6 and N₈ contains those of 8. So, N_6∈ N₈ contains all those numbers, which are common multiples of 6 and 8 both, i.e. multiples of 24 (LCM of 6 and 8 is 24).

So, N_{6 ∈} N ₈ = N₂₄
Question 6
1 / -0

In a meeting of 100 people, there were 23 Indian men and 29 Indian women. Of these Indian people, 4 were dentists and 24 were either men or dentists. Assuming that there were no foreign dentists, find the number of female dentists who attended the meeting.

A
1

B
4

C
2

D
3

Solution

Since there were no foreign dentists, there could be no foreign female dentists.
Hence, in order to find out the number of female dentists, we will simply find the number of Indian female dentists, i.e. n(W ∩ D).

At first, we will find n(M ∩ D), using n(M ∪ D) = n(M) + n(D) – n(M ∩ D).
24 = 23 + 4 – n(M ∩ D)

⇒ n(M ∩ D) = 3
Thus, number of male Indian dentists = 3

As there were 4 Indian dentists in all,
Number of Indian female dentists = 4 – 3 = 1, i.e. n(W ∩ D) = 1

Therefore, only 1 female dentist attended the meeting.
Question 7
1 / -0

In a group of 50 persons, everyone takes either tea or coffee. If 35 persons take tea and 25 persons take coffee, then the number of persons who take tea only (and not coffee) is

A
10

B
25

C
35

D
None of these

Solution

Total number of persons = 50
Number of persons who take tea = 35
Number of persons who take coffee = 25
Number of persons who take both tea and coffee = 35 + 25 - 50 = 10
Now, number of persons who take tea only = 35 - 10 = 25

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Re-Attempt Weekly Quiz Competition

Sets Test - 3

Result

Sets Test - 3

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Rank

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SHARING IS CARING

Question 1

{x | x is a real number and x2 – 1 = 0}

{x | x is a real number and x2 + 1 = 0}

{x | x is a real number and x2 – 9 = 0}

{x | x is a real number and x2 = x + 2}

Solution

Question 2

{x, y, z, w}

{x, y, z, e, r, o, w}

{letters of the word xerox}

{x, y, z, z}

Solution

Question 3

X

Y

N

None of these

Solution

Question 4

d = bb

c = bd

b = cc

d = bc

Solution

Question 5

N2

N48

N8

N24

Solution

Question 6

1

4

2

3

Solution

Question 7

10

25

35

None of these

Solution

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{x | x is a real number and x² – 1 = 0}

{x | x is a real number and x² + 1 = 0}

{x | x is a real number and x² – 9 = 0}

{x | x is a real number and x² = x + 2}

N₂

N₄₈

N₈

N₂₄