Permutation Test

Result

Permutation Test - 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

A
3

B
36

C
66

D
108

Solution

Required no. of ways = ³C₂ × ⁹C₂ = 3 × 36 = 108.
Question 2
1 / -0

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.

Hence, option D is correct.
Question 3
1 / -0

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A
140

B
196

C
280

D
346

Solution

Number of choices = ⁵C₄ × ⁸C₆ + ⁵C₅ × ⁸C₅
= 140 + 56 = 196.
Question 4
1 / -0

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

A
Less than 500

B
At least 500 but less than 750

C
At least 750 but less than 1000

D
At least 1000

Solution

N₁N₂N₃ – N₆, D₁D₂D₃
The number of ways = 6c₄ × 3c₁ × 24 × 4
= 15 × 3 × 24 × 4 = 1080 × 4
Hence, option D is correct.
Question 5
1 / -0

Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃
Statement-2: The number of ways of choosing any 3 places from 9 different places is ⁹C₃.

A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

C
Statement-1 is true, Statement-2 is false

D
Statement-1 is false, Statement-2 is true.

Solution

∴ The number of ways of distributing n identical objects among r persons such that each person gets at least one object is same as the number of ways of selecting (r - 1) places out of (n-1) different places, that is n-1Cr-1. Therefore, statement 1 is true, and statement 2 is true but statement 2 is not the correct reason or explanation for statement 1. Hence, option B is correct.