Question Paper ESE - General Studies & Engineer Aptitute
1. An Egyptian fraction has a numerator equal to 1, and its denominator is a positive integer. What is the maximum number of different Egyptian fraction such that their sum is equal to 1, and their denominators are equal to 10 or less?
(a) 3
(b) 5
(c) 7
(d) 9
Answer: (a)
2. What is the least number which must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?
(a) 32
(b) 53
(c) 46
(d) 39
Answer: (b)
3. What is the greatest number consisting of six digits which on being divided by 6, 7, 8, 9, 10 leaves 4, 5, 6, 7, 8 as remainders respectively?
(a) 997920
(b) 997918
(c) 999999
(d) 997922
Answer: (d)
4. What is the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder?
(a) 2987
(b) 3601
(c) 3600
(d) 2986
Answer: (b)
5. A group of four numbers has only one prime number amongst them. Which of the following must be true about the group?
I. HCF of the four numbers of the group is either 1 or equal to that prime number.
II. LCM of the fur numbers of the group is same as product of the prime number and LCM of the remaining three numbers.
III. Product of the four numbers is equal to product of the prime number × HCF of the group × LCM of the group
(a) I only
(b) II only
(c) I and II only
(d) All of these
Answer: (a)
6. If (a, n)! is defined as product of n consecutive numbers starting from a, where a and n are both natural numbers, and if H is the HCF of (a, n)! and n!, then what can be said about H?
(a) H = a!
(b) H = n!
(c) H >
n!(d) H
> a × n Answer: (b)
7. A ball is dropped from a height of 12 m and it rebounds ½ of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?
(a) 36 m
(b) 30 m
(c) 48 m
(d) 60 m
Answer: (a)
8. Two new charity organizations C1 and C2 were formed, with x members each, on January 1, 2003. On first day of each, subsequent month, in C1, number of members increase by a certain number a, while in C2, number of members increase in such a way that ratio of the number of members in a month to the preceding month bear a ratio equal to b. On May 1, 2003, both organizations had the same number of members. If a = 20x, then b will be
(a) 2
(b) 3
(c) 2.5
(d) 3.5
Answer: (b)
9. What is the ratio of common differences d1 and d2 of two arithmetic progressions of respective nth terms are in the ratio of 2n + 3 : n - 11?
(a) 1 : 2
(b) 2 : 3
(c) 2 : 1
(d) 1 : 3
Answer: (c)
10. A school has 5 divisions in a class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is the overall average of the marks per students?
(a) 56.8
(b) 58.2
(c) 62.4
(d) 60.8
Answer: (d)