ECAT — Engineering College Admission Test (UET)
Take the ECAT Mathematics — Permutations, Combinations and Probability (Set 3): 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 number of arrangements of all the letters of ASSASSINATION is:
Answer: C. 10810800
Explanation: 13 letters with A ×3, S ×4, I ×2, N ×2: 13!/(3!·4!·2!·2!) = 10810800.
Q2. The number of arrangements of the letters of the word COMMITTEE is:
Answer: C. 45360
Explanation: 9 letters with M, T, E each repeated twice: 9!/(2!·2!·2!) = 362880/8 = 45360.
Q3. The number of different 4-letter arrangements of the letters of BOOK is:
Answer: C. 12
Explanation: 4!/2! = 12, since the letter O repeats.
Q4. From 5 men and 4 women a committee of 3 is chosen with at least one woman. The number of ways is:
Answer: A. 74
Explanation: Total C(9,3) = 84 less all-men C(5,3) = 10 gives 74.
Q5. Five people are seated in a row. The number of arrangements in which two particular people are NOT seated together is:
Answer: B. 72
Explanation: Total 5! = 120; with the two together: 2 × 4! = 48. So 120 − 48 = 72.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. Six persons sit around a circular table. The number of arrangements in which two particular persons sit next to each other is:
Q7. How many 4-digit numbers with no repeated digit can be formed from the digits 1, 2, 3, 4, 5 that are even?
Q8. The number of 3-digit numbers divisible by 5 with all digits different is:
Q9. If ⁿP₂ = 72, then n equals:
Q10. If ⁿC₇ = ⁿC₉, then ⁿC₂ equals:
Q11. The number of diagonals of a polygon with 12 sides is:
Q12. Eight points lie in a plane, of which exactly 4 are collinear and no other three are collinear. The number of distinct straight lines they determine is:
Q13. Ten points lie in a plane, 4 of them being collinear and no other three collinear. The number of triangles with vertices at these points is:
Q14. Two fair dice are thrown. The probability that the sum of the numbers is divisible by 4 is:
Q15. One card is drawn from a well-shuffled deck of 52. The probability that it is a king or a heart is:
Q16. Two cards are drawn without replacement from a deck of 52. The probability that both are aces is:
Q17. A bag has 5 red and 3 blue balls. Two balls are drawn together at random. The probability that they have the same colour is:
Q18. If P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3, then P(A ∪ B) is:
Q19. Three people are chosen at random. Assuming each is equally likely to be born on any day of the week, the probability that all three were born on different days of the week is:
Q20. The odds in favour of an event are 3 : 5. The probability that the event occurs is:
Q21. A fair die is rolled three times. The probability of getting at least one six is:
Q22. The number of arrangements of the letters of EQUATION in which all five vowels are together is:
Q23. A committee of 4 is to be chosen from 6 men and 4 women with exactly 2 women. The number of ways is:
Q24. The number of ways in which 5 different prizes can be given to 3 students, a student being allowed to receive any number of prizes, is:
Q25. At a party every one of 12 guests shakes hands exactly once with every other guest. The total number of handshakes is:
Q26. The number of ways to choose 3 different numbers from 1, 2, …, 20 so that their sum is even is:
Q27. If P(B) = 0.5 and P(A | B) = 0.4, then P(A ∩ B) equals:
Q28. Three fair dice are thrown. The probability that the total is 10 is:
Q29. A coin is tossed and a die is rolled together. The probability of getting a head and an even number is:
Q30. A cricket team of 5 players is chosen from 11 players so that the captain is always included. The number of possible teams is: