Here, we have two sections A and B. Section A has 3 question and B has 5 question and one question from each section is compulsory according to the given condition.
∴ Number of ways selecting one or more than one question from section A
= 2³ - 1 = 7
Similarly, from section B = 2⁵ - 1 = 31

Correct Option: B

Here, we have two sections A and B. Section A has 3 question and B has 5 question and one question from each section is compulsory according to the given condition.
∴ Number of ways selecting one or more than one question from section A
= 2³ - 1 = 7
Similarly, from section B = 2⁵ - 1 = 31
According to the rule of multiplication, the required number of ways in which a candidate can select the question
= 7 x 31 = 217

There are 10 station on railway line.
So, the number of different journey tickets between two station from given 10 stations from one side = ¹⁰C₂ = 10 x 9/2 = 45.

Correct Option: B

There are 10 station on railway line.
So, the number of different journey tickets between two station from given 10 stations from one side = ¹⁰C₂ = 10 x 9/2 = 45.

Similarly, number of different journey tickets from other side = 45
∴ Total number of tickets to be generated by authorities. = 45 + 45 = 90

If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or if Mrs. X is not selected then Mr. Y can be there in the committee...
So, required number of ways
= ⁸C₃ x ⁶C₄ + ⁷C₃ x ⁷C₄

Correct Option: D

If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or if Mrs. X is not selected then Mr. Y can be there in the committee...
So, required number of ways
= ⁸C₃ x ⁶C₄ + ⁷C₃ x ⁷C₄
= [(8 x 7 x 6)/(3 x 2)] x [(6 x 5)/(2 x 1)] + [(7 x 6 x 5)/(3 x 2)] x [(7 x 6 x 5)/(3 x 2)]
= 840 + 1225
= 2065

A five-digit number, which is divisible by 3, is formed when sum of digits is also divisible by 3.

So, combination formed using six-digits, which are divisible by 3
= 5 + 4 + 3 + 2 + 1 = 15
= 5 + 4 + 2 + 1 + 0 = 12

So, set of number are (5, 4, 3, 2, 1) and (5, 4, 2, 1, 0).

Number formed by using 1st set = 5 x 4 x 3 x 2 x 1 = 120
Similarly, using 2nd set = 4 x 4 x 3 x 2 x 1 = 96

Correct Option: C

A five-digit number, which is divisible by 3, is formed when sum of digits is also divisible by 3.

So, combination formed using six-digits, which are divisible by 3
= 5 + 4 + 3 + 2 + 1 = 15
= 5 + 4 + 2 + 1 + 0 = 12

So, set of number are (5, 4, 3, 2, 1) and (5, 4, 2, 1, 0).

Number formed by using 1st set = 5 x 4 x 3 x 2 x 1 = 120
Similarly, using 2nd set = 4 x 4 x 3 x 2 x 1 = 96

Hence, using 2nd set, underlined place cannot be filled by 0, otherwise it will become a four-digit number.
∴ Total number = 120 + 96 = 216

Any of the 4 colour can be chosen for the first stripe. Any of the remaining 3 colours can be used for the second stripe. The third stripe can again be coloured in 3 ways (we can repeat the colour of the first stripe but not use the colours of the second stripe).
Similarly, There are 3 ways to colour each of the remaining stripes.
∴ The number of ways the flag can be coloured is 4(3)⁵ = (12) (3)⁴ = 12 x 81

Correct Option: A

Any of the 4 colour can be chosen for the first stripe. Any of the remaining 3 colours can be used for the second stripe. The third stripe can again be coloured in 3 ways (we can repeat the colour of the first stripe but not use the colours of the second stripe).
Similarly, There are 3 ways to colour each of the remaining stripes.
∴ The number of ways the flag can be coloured is 4(3)⁵ = (12) (3)⁴ = 12 x 81