ECAT Pre Engineering Entry Test With Answers

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ECAT Pre Engineering Entry Test

Sr. # Questions Answers Choice
1 Digit in the unit place of the number 183! + 3183 7 6 3 0
2 If the expansion of (1 + x)20, then co-efficient of rth ad (r + 4)th term are equal, then r is 7 8 9 10
3 If the sum of co-efficient in the expansion of (a+b)nis 4096, then the greatest co-efficient in the expansion is 1594 792 924 2924
4 If the sum of co-efficient in the expansion of (a+b)nis 4096, then the greatest co-efficient in the expansion is 1594 792 924 2924
5 The positive integer just greater than (1+0.0001)10000is 4 5 2 3
6
7 2 and 9 3 and 2 2/3 and 9 3/2 and 6
8 28 / 81 28 / 243 81 / 28 243 / 82
9 405 / 256 504 / 259 450 / 263 None
10 <sup>10</sup>C<sub>6</sub> <sup>10</sup>C<sub>5</sub> <sup>10</sup>C<sub>4</sub> None
11 If in the expansion of (1+x)n, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x= 4 5 6 7
12 Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is 9028 9208 9802 9820
13 Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is 2 / 19 3 / 29 17 / 19 4 / 19
14 5 / 12 3 / 8 5 / 8 7 / 4
15 A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is 50 25 10 100
16 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
17 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
18 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
19 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
20 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
21 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
22 Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is 375 500 625 150
23 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
24 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
25 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
26 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
27 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
28 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
29 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
30 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
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