ECAT — Engineering College Admission Test (UET)
Take the ECAT Mathematics — Permutations, Combinations and Probability (Set 1): 30 multiple-choice questions (40 minutes) with instant scoring and a full…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. The value of 7!/5! is:
Answer: A. 42
Explanation: 7!/5! = 7 × 6 × 5!/5! = 42.
Q2. The value of ⁸P₃ is:
Answer: A. 336
Explanation: ⁸P₃ = 8!/5! = 8 × 7 × 6 = 336. (⁸C₃ = 56.)
Q3. The value of ¹⁰C₃ is:
Answer: B. 120
Explanation: ¹⁰C₃ = (10 × 9 × 8)/(3 × 2 × 1) = 120.
Q4. If ⁿC₂ = 45, then n equals:
Answer: B. 10
Explanation: n(n − 1)/2 = 45 ⇒ n(n − 1) = 90 = 10 × 9 ⇒ n = 10.
Q5. The number of distinct arrangements of all the letters of the word PAKISTAN is:
Answer: C. 20160
Explanation: 8 letters with A repeated twice: 8!/2! = 40320/2 = 20160.
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Q6. The number of distinct arrangements of the letters of the word LETTER is:
Q7. In how many ways can 6 people be seated around a circular table?
Q8. The number of different necklaces that can be made from 7 beads of different colours is:
Q9. A committee of 3 men and 2 women is to be chosen from 5 men and 4 women. The number of ways is:
Q10. The number of diagonals of a decagon (10-sided polygon) is:
Q11. How many triangles can be formed by joining 8 points in a plane, no three of which are collinear?
Q12. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if no digit is repeated?
Q13. If ⁿC₅ = ⁿC₇, then n equals:
Q14. The correct relation between ⁿPᵣ and ⁿCᵣ is:
Q15. If P(A ∩ B) = 0.2 and P(B) = 0.5, then the conditional probability P(A | B) is:
Q16. A fair die is rolled once. The probability of getting a prime number is:
Q17. Two fair dice are thrown. The probability that the sum of the numbers is 7 is:
Q18. Two fair dice are thrown. The probability that the sum is 9 is:
Q19. A card is drawn from a well-shuffled pack of 52. The probability that it is a king or a heart is:
Q20. Three fair coins are tossed together. The probability that they do not all show tails is:
Q21. If P(A) = 0.3, P(B) = 0.4 and P(A ∩ B) = 0.1, then P(A ∪ B) is:
Q22. A and B are independent events with P(A) = 1/2 and P(B) = 1/3. Then P(A ∪ B) is:
Q23. From a box of 5 red and 3 blue marbles, two marbles are taken out one after the other, the first not being put back. The probability that both marbles are red is:
Q24. If the probability of an event is 3/8, the odds in favour of the event are:
Q25. Which of the following can NOT be the probability of an event?
Q26. A student must answer 4 out of 7 questions, and question 1 is compulsory. The number of ways of choosing the questions is:
Q27. In how many ways can the letters of the word ECAT be arranged so that the two vowels are always together?
Q28. The probability that a leap year selected at random contains 53 Sundays is:
Q29. At a meeting, each of 12 people shakes hands once with every other person. The total number of handshakes is:
Q30. In how many ways can 5 different books be arranged on a shelf if two particular books must always be together?