ECAT Mathematics MCQ's Test For Full Book With Answers

ECAT Mathematics MCQ's Test For Full Book

Sr. # Questions Answers Choice
1 A and B throw a dice. The probability that A's throw is not greater then B's is 5 / 12 7 / 12 1 / 6 1 / 2
2 Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is 0.28 0.13 0.12 0.42
3 For two events A and B if P(A) = P (A/B) = 1/4 and P(B/A) = 1/2, then A is sub-event of B A and B are mutually exclusive A and B are independent and P(A/B) = 3/4 None of these
4 A box containing 10 mangoes out of which 4 are rotter. Two mangoes are taken together from the box. If one of them is found to be good, the probability that the other is also good is 1 / 3 8 / 15 5 / 13 5 / 9
5 An experiment yields 3 mutually exclusive and exhaustive events A, B, C, if P(A) =2 and P(B) = 3. then P(C) = 1 / 11 2 / 11 3 / 11 6 / 11
6 A card is drawn from a pack of cards numbered 2 to 53. the probability that the number on the card is prime number less than 20 is 2 / 13 4 / 13 5 / 13 8 / 13
7 Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is 375 500 625 150
8 A combination lock on a suitcase has 3 wheels each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, the probability of a person guessing the right combination is 1 / 500 1 / 504 1 / 252 1 / 250
9 A machine operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. the probability that the machine will fail during the year is 0.2647 0.2692 0.3647 None of these
10 The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is 1 / 10 2 / 10 3 / 10 4 / 10
11 Five engineering, four mathematics, two chemistry books are placed on a table at random.The probability that the books of each kind are all together is
12 If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then the probability that the drawn balls are of different colours is 1 / 66 3 / 66 19 / 66 47 / 66
13 The probability of getting a number between 1 and 100 which is divisible by 1 and itself if only is 1 / 4 1 / 2 3 / 4 25 / 98
14 Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is 14 / 29 20 / 39 1 / 2 n
15 Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7 7 / 40 5 / 40 11 / 40 None of these
16 A committee consists of 9 experts taken from three institutions A, B, and C, of which 2 are from, A, 3 form B and 4 from C. If three experts resign, then the probability that they belong to different institutions is 1 / 729 1 / 24 1 / 21 2 / 7
17 A bag contains 5 white, 7 red and 5 black balls. If four balls are drawn one by one with replacement, the probability that none is white is (11/16)<sup>2</sup> (5/16)<sup>2</sup> (11/16)<sup>4</sup> (5/16)<sup>4</sup>
18 Two cards are drawn at random without replacement. the probability that the first is a king and second is not a king is 48 / 663 24 / 663 12 / 663 None of these
19 A bag contains 7 whit, 5 black and 4 rd balls. If two balls are drawn at random from the bag, the probability that they are not of the same color is 73 / 120 83 / 120 67 / 120 43 / 120
20 1 / 2 1 / 3 1 / 4 None of these
21
22 1.5 1.2 8 None of these
23 0.9 0.74 0.2016 None of these
24 An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is 3 / 10 5 / 10 7 / 10 9 / 10
25 Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement is <sup>6</sup>C<sub>3</sub>x <sup>4</sup>C<sub>2</sub> <sup>4</sup>C<sub>2</sub>x <sup>4</sup>P<sub>3</sub> <sup>4</sup>P<sub>2</sub>x <sup>6</sup>P<sub>3</sub> None of these
26 There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is <sup>n</sup>P<sub>m</sub> <sup>n</sup>C<sub>m</sub>x (m - 1) ! <sup>n-1</sup>P<sub>m</sub> None of these
27 Fifteen girls compete in a race. The first three places can be taken by them in 3! ways 12! ways 15 x 14 x 13 ways 42 ways
28 The number of ways of arranging the letter AAAAA BBB CCC D EE F in a row when no two C's are together is
29 Number of permutations of n distinct objects taken r(<n - 3) at a time which exclude 3(<n) particular objects is 3! P(n, r - 3) P(n, 3) P(n, r - 3) P(r, r)P(n, r - 3) P(n - 3, r)
30 The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is 260 356 410 96
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