C

_ _ 5
first two places can be filled in 5 and 4 ways respectively so, total number of 3 digit number = 5 × 4 × 1 = 20

B

Vowels = E, E and A. They can be arranged in [latex](\frac {3!}{2!})[/latex] Ways
so total ways = 6![latex] \times (\frac {3!}{2!})[/latex] = 2160

C

Zero or more bananas can be selected in 4 + 1 = 5 ways (0 orange, 1 orange, 2 orange, 3 orange and 4 orange)
Similarly apples can be selected in 7 + 1 = 8 ways
And mangoes in 6 + 1 = 7 ways
So total number of ways = 5 × 8 × 7 = 280
But we included a case of 0 orange, 0 apple and 0 mangoes, so we have to subtract this, so 280 – 1 = 279 ways

C

From 15 points number of lines formed = [latex]^{15}{C}_{2}[/latex]
6 points are collinear, number of lines formed by these = [latex]^{6}{C}_{2}[/latex]
So total lines = [latex]^{15}{C}_{2} – ^{15}{C}_{2}[/latex] + 1 = 91

A

4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!