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1.  
In how many different arrangements of the letters of the word BANANA do the three A's come together?

Correct Answer: E [12]

Explanation:

Glue AAA into one unit: units AAA, B, N, N → 4!/2!

2.  
A committee of 4 is to be chosen from 5 men and 4 women so that it has at least 2 women. In how many ways can this be done?

Correct Answer: A [81]

Explanation:

²W ²M: 6 × 10 = 60; ³W ¹M: 4 × 5 = 20; ⁴W: 1 → 81.

3.  
In how many arrangements of the letters of the word DAUGHTER are the three vowels NOT all together?

Correct Answer: D [36000]

Explanation:

Total 8! = 40,320; all vowels together 6!

4.  
A bag has 4 red, 5 blue and 3 green balls. Three balls are drawn at random. The probability that all three are of different colours is:

Correct Answer: B [3/11]

Explanation:

4 × 5 × 3 = 60 favourable; ¹²C₃ = 220 → 60/220 = 3/11.

5.  
Two dice are thrown. The probability that the product of the numbers is even is:

Correct Answer: D [3/4]

Explanation:

Odd product only if both odd: 9/36 → even = 1 − 1/4 = 3/4.

6.  
In how many ways can 4 boys and 3 girls stand in a row so that no two girls are next to each other?

Correct Answer: A [1440]

Explanation:

Boys 4! = 24; 5 gaps → ⁵C₃ × 3!

7.  
Two cards are drawn together from a pack of 52. The probability that one is red and the other is black is:

Correct Answer: B [26/51]

Explanation:

26 × 26/1,326 = 676/1,326 = 26/51.

8.  
There are 10 points in a plane; 4 of them lie on one straight line and no other three are in a line. How many triangles can be formed with these points as vertices?

Correct Answer: E [116]

Explanation:

¹⁰C₃ − ⁴C₃ = 120 − 4 = 116 (the 4 collinear points give no triangle).

9.  
All arrangements of the letters of the word MANGO are written in dictionary order. What is the position of MANGO?

Correct Answer: C [51]

Explanation:

Letters A, G, M, N, O. Before M: A, G → 2 × 4!

10.  
Bag A has 4 white and 2 black balls; bag B has 3 white and 5 black balls. A die is thrown: if it shows 1 or 2, a ball is drawn from bag A, otherwise from bag B. The probability that the ball is white is:

Correct Answer: E [17/36]

Explanation:

1/3 × 4/6 + 2/3 × 3/8 = 2/9 + 1/4 = 17/36.

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