21. A basket contains x white, 6 red and 4 yellow colour balls. If one ball is taken randomly from the basket and the probability of getting a red colour ball is 2/5, then find the total number of balls in the basket.

A. 12
B. 18
C. 16
D. 15
E. None of these

Option “D” is correct.

Total number of balls = 10 + x

Required probability

= > 6/(10 + x) = 2/5

= > 10 + x = 15

= > x = 5

Total number of balls in the basket = 10 + 5 = 15 balls
22. In a class,35% of students offered Maths and 25% offered Biology and 5% offered both. If a student is selected at random, then find the probability that he has offered Maths or Biology only.

A. 50%
B. 60%
C. 55%
D. 45%
E. Can’t be determined

Option “C” is correct.

Let the total number of students be 100,

Maths students = 35

Biology students = 25

Both = 5

Required probability = 35/100 + 25/100 – 5/100=55/100=55%
23. A box contains red and green balls and the total number of balls in the box is 15. If the probability of picking a green ball is 0.4, find the number of red balls from the box.

A. 8
B. 7
C. 9
D. 6
E. 12

Option “C” is correct.

Total number of balls = 15

Number of green balls =x

Number of red balls = 15 – x

xC1 / 15C1 = 0.4

x = 6

Number of red balls = 15 – 6 = 9
24. A bag contains (x – 1) red balls, 3 blue balls and 4 green balls. If one ball is taken out randomly and the probability of getting a green ball is 2/5, find the value of x.

A. 4
B. 6
C. 2
D. 3
E. 1

Option “A” is correct.

Total number of balls = x – 1 + 4 + 3 = x + 6

2/5 = 4C1/(x + 6)C1

2/5 = 4/(x + 6)

20 = 2x + 12

2x = 8

x = 4
25. There are 50 balls and they marked the number from 1 to 50. If a ball is randomly chosen, what is the probability that the number is not divisible by 6 or 9?

A. 33/50
B. 1/10
C. 37/50
D. 39/50
E. None of these

Option “D” is correct.

Divisible by 6 = 6, 12, 18, 24, 30, 36, 42, 48

Divisible by 9 = 9, 18, 27, 36, 45

Total number of balls divisible by 6 or 9 = 11

Number of balls not divisible by 6 or 9 = 50 – 11 = 39

Required probability = 39/50
26. In a class has 3 boys and 2 girls, two students were selected. In how many different ways can they be selected such that at least one girl should be there?

A. 5
B. 8
C. 7
D. 6
E. None of these

Option “C” is correct.

Total number of ways=5C2

No girls selected =3C2

Required ways=5C2 – 3C2 =10 – 3=7
27. In how many ways word “BANKING” can be arranged in such a way that all vowels and consonants comes together?

A. 120
B. 280
C. 360
D. 240
E. None of these

Option “D” is correct.

Vowels=A, I=2!

Consonant=B, N, K, N, G=5!

Required ways=2! * 5!/2! * 2!

=240
28. How many three digit numbers can be formed with the digits 2, 3, 5, 6, 9, if repetition of digits is allowed?

A. 120
B. 240
C. 144
D. 720
E. None of these

Option “E” is correct.

Options for hundred’s place = 5 (all digits)

Options for ten’s place = 5 (all digits)

Options for unit’s place = 5 (all digits)

Total number of ways = 5 * 5 * 5 = 125 ways
29. In how many ways word “NEPAL” is arranged in that all vowels and consonants come together?

A. 12
B. 27
C. 24
D. 7
E. None of these

Option “C” is correct.

Number of vowels = E, A = 2

Remaining letters = N, P, L = 3

Number of ways = 2! * 3! * 2!

= 24
30. In how many ways word “NEPAL” is arranged in that all vowels and consonants come together?

A. 120
B. 270
C. 246
D. 120
E. 185

Option “E” is correct.

Number of ways = 6C2 * 4C2 + 6C3 * 4C1 + 6C4

= 3 * 5 * 2 * 3 + 20 * 4 + 3 * 5

= 15 * 6 + 20 * 4 + 15

= 185
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