Mathematics Test 17

Result

Mathematics Test 17

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is

A
reflexive and transitive only

B
reflexive only

C
an equivalence relation

D
reflexive and symmetric only

Solution

Reflexive and transitive only.
e.g. (3, 3), (6, 6), (9, 9), (12, 12) [Reflexive]
(3, 6), (6, 12), (3, 12) [Transitive]
Question 2
4 / -1

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

A
880

B
629

C
630

D
879

Solution

First, one can select from 0 to 10 white balls in (10+1) ways.

Then, you can select from 0 to 9 green balls in (9+1) ways.

Finally, you can select from 0 to 7 red balls in (7+1) ways.

Hence the total number of choices = (10+1)(9+1)(7+1)

Now, this also includes 1 situation in which none of the balls is selected. Since we need to select atleast 1 ball, we will need to subtract that.

Therefore, number of ways of selecting one or more balls from 10 white, 9 green, and 7 black balls = (10 + 1) (9 + 1) (7 + 1) – 1 = 11×10 × 8 – 1 = 879.

Therefore, number of ways of selecting one or more balls from 10 white, 9 green, and 7 black balls = (10 + 1) (9 + 1) (7 + 1) – 1 = 11×10 × 8 – 1 = 879.