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1.  
The value of 5! is:

Correct Answer: D [120]

Explanation:

5! = 5 × 4 × 3 × 2 × 1 = 120.

2.  
The value of ⁸C₃ is:

Correct Answer: A [56]

Explanation:

8 × 7 × 6/(3 × 2 × 1) = 56.

3.  
In how many ways can the letters of the word LOAN be arranged?

Correct Answer: C [24]

Explanation:

4 different letters → 4! = 24.

4.  
A coin is tossed four times. The probability of getting exactly three heads is:

Correct Answer: B [1/4]

Explanation:

⁴C₃/2⁴ = 4/16 = 1/4 (HHHT, HHTH, HTHH, THHH).

5.  
A die is thrown once. The probability of getting a prime number is:

Correct Answer: D [1/2]

Explanation:

Primes 2, 3, 5 → 3/6 = 1/2.

6.  
True or false? "ⁿCᵣ = ⁿCₙ₋ᵣ for every n and r (0 ≤ r ≤ n)."

Correct Answer: A [True]

Explanation:

Choosing r items is the same as choosing the n − r items left out.

7.  
Fill in the blank: A hexagon has ____ diagonals.

Correct Answer: B [9]

Explanation:

⁶C₂ − 6 = 15 − 6 = 9.

8.  
Odd one out – which of these is NOT equal to 10?

Correct Answer: C [⁴C₂]

Explanation:

⁴C₂ = 6; the others are 10.

9.  
Match: (i) 4! (ii) ⁶C₂ (iii) ⁵P₂ (iv) ⁷C₁ ; (p) 24 (q) 15 (r) 20 (s) 7

Correct Answer: A [i-p, ii-q, iii-r, iv-s]

Explanation:

4! = 24, ⁶C₂ = 15, ⁵P₂ = 20, ⁷C₁ = 7.

10.  
A card is drawn at random from a pack of 52 cards. The probability that it is a king is:

Correct Answer: B [1/13]

Explanation:

4 kings out of 52 → 1/13.

11.  
Two dice are thrown. The probability that the sum is 7 is:

Correct Answer: C [1/6]

Explanation:

6 ways out of 36 → 1/6.

12.  
A bag has 4 red and 6 blue balls. One ball is drawn at random. The probability that it is red is:

Correct Answer: D [2/5]

Explanation:

4 out of 10 → 2/5.

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