JEE Main Sets Relations And Functions: Quiz!

1) If A = {p, q, r, s} and B = {7, 8, 9}, find which of the following is a set of ordered pair, are relations from A to B?

R = {(7, p), (9, p)}

R = {(p, 7), (r, 8), (s, 7)}

R = {(7, s), (8, q), (r, 9)}

R = {(8, s), (9, q)}

In part (b), the given relation r is a subset of A × B and hence, it is a relation but in all other options, no other relation is a subset of A × B and hence only option (b) is correct.

Explanation

In part (b), the given relation r is a subset of A × B and hence, it is a relation but in all other options, no other relation is a subset of A × B and hence only option (b) is correct.

2) In an international conference of 200 people, there are 53 Indian women and 39 Indian men. Of these Indian people, 7 are doctors and 42 are either men or doctors. There are no foreign doctors. How many women doctors are attending the conference?

1

2

3

4

Given n (M ∪ D) = 42;
n (M) + n (D) – n (M ∩ D) = n (M ∪ D); 39 + 7 – n (M ∩ D) = 46
n (M ∩ D) = 4;
Amongst the men there are only 4 doctors and as there are no foreign doctors so there are total three Indian women doctors because the total no of doctors is 7.

Explanation

Given n (M ∪ D) = 42;
n (M) + n (D) – n (M ∩ D) = n (M ∪ D); 39 + 7 – n (M ∩ D) = 46
n (M ∩ D) = 4;
Amongst the men there are only 4 doctors and as there are no foreign doctors so there are total three Indian women doctors because the total no of doctors is 7.

3)

{ α∶ π/2≤α≤5π/6}

{ α∶ π≤α≤3π/2}

{α∶π/2≤α≤3π/2}

Both a & b

Explanation

4)

Explanation

5)

Which of the following is correct about the above functions?

F is a one-one onto function

Z = r (cotθ + tanθ), so |z| = r

F is a one-one but not onto function

None of these

clearly f is a one-one function but not onto function f will always be a real number and even numbers do not have any pre-image.

Explanation

clearly f is a one-one function but not onto function f will always be a real number and even numbers do not have any pre-image.

6) Which of the following is the empty set?

From the question it is clearly evident that option (b) is correct as x ∈ R but in the given condition the x belongs to the imaginary values as x = ± 3i.

Explanation

From the question it is clearly evident that option (b) is correct as x ∈ R but in the given condition the x belongs to the imaginary values as x = ± 3i.

7)

S = qr

R = qs

Q = rs

None of these

Given that q and r are relatively prime, therefore the given relation: qN ∩ rN = sN can be written as (qr) N = sN which implies that:
s = qr.

Explanation

Given that q and r are relatively prime, therefore the given relation: qN ∩ rN = sN can be written as (qr) N = sN which implies that:
s = qr.

8) Two finite sets have 'x' & 'y' elements. The total number of subsets of the first set is 56 more than the total number of the second set. Which of the following are the values of 'x' & 'y'?

7, 6

5, 1

8, 7

6, 3

Explanation

9) In a sports hostel, 21 are on the baseball team, 26 are on the hockey team and 29 are on the football team. 14 play hockey and baseball, 15 play hockey and football, and 8 play all three games. How many total noes of players are there?

43

37

44

52

n (B) = 21, n (H) = 26, n (F) = 29;
n (H ∩ B) = 14, n (H ∩ F) = 15, n (F ∩ B) = 12, n (B ∩ H ∩ F) = 8;
Total no of players = n (B ∪ H ∪ F);
n (B ∪ H ∪ F) = n (B) + n (H) + n (F) – n (H ∩ B) – n (H ∩ F) – n (F ∩ B) + n (B ∩ H ∩ F);
n (B ∪ H ∪ F) = 21 +26 +29 – 14 – 15 – 12 + 8 = 76 – 41 + 8;
n (B ∪ H ∪ F) = 43

Explanation

n (B) = 21, n (H) = 26, n (F) = 29;
n (H ∩ B) = 14, n (H ∩ F) = 15, n (F ∩ B) = 12, n (B ∩ H ∩ F) = 8;
Total no of players = n (B ∪ H ∪ F);
n (B ∪ H ∪ F) = n (B) + n (H) + n (F) – n (H ∩ B) – n (H ∩ F) – n (F ∩ B) + n (B ∩ H ∩ F);
n (B ∪ H ∪ F) = 21 +26 +29 – 14 – 15 – 12 + 8 = 76 – 41 + 8;
n (B ∪ H ∪ F) = 43

10)

{x : 2 ≤ x < 4 }

{x : 2 < x ≤4 }

{x : 2 ≤ x ≤ 4 }

{x : 2 > x < 4 }

Explanation