LOD 1
Q1. Find the units digit of 34563^20359 + 2358^784.
a) 3 b) 9 c) 5 d) 1
A
Q2. Find the remainder of 2^133 divided by 133.
a) 1 b) 2 c) 128 d) 131
C
Q3. Three bells toll regularly at intervals of 8 minutes, 12 minutes and 18 minutes respectively. Find the time gap between two successive instances of all 3 bells tolling together.
a) 1 hour 6 minutes b) 1 hour 12 minutes c) 2 hours 24 minutes d) 1 hour 18 minutes
B
Q4. There are 8375 raisin chocolates, 5025 almond chocolates and 20100 cashew nut chocolates available. The chocolates have to be arranged in boxes such that the combination of chocolates in each box is the same i.e., each box contains the same number of chocolates of each kind and no chocolates of any kind are left over. Find the number of boxes required if minimum number of chocolates are put in each box.
a) 1675 b) 1785 c) 1895 d) 1681
A
Q5. From a place P, buses to A leave once every 30 minutes, buses to B leave once every 35 minutes, buses to C leave once every 45 minutes. If buses left for A, B and C simultaneously at 10:00 a.m, from P, when is the next occasion when buses leave together for each of the 3 destinations?
a) 12:30 p.m. b) 8:50 p.m. c) 10:30 p.m. d) 8:30 p.m.
D
Q6. Find the number of divisors of 2280.
a) 16 b) 28 c) 32 d) 30
C
LOD 2
Q1. A four-digit number has the sum of its digits in the odd positions equal to the sum of its digits in the even positions. If it is subtracted from the number formed by reversing it, the result will always be divisible by
a) 9 b) 11 c) 13 d) Both (A) and (B)
D
Q2. Find the sum of the remainders obtained when a number n is divided by 9 and 7 successively, if n is the smallest number that leaves respective remainders of 4, 6 and 9 when divided successively by 13, 11 and 15.
a) 4 b) 5 c) 9 d) 6
D
Q3. The sets Qp are defined as {p, p + 1, p + 2, p + 3, p + 4, p + 5, p + 6}, where p = 1, 2, 3 .100. How many of these sets contain a multiple of 11?
a) 63 b) 64 c) 62 d) 65
A
Q4. How many three-digit positive integers have their hundreds, tens and units digits in ascending order?
a) 70 b) 77 c) 84 d) 504
C
Q5. How many ordered pairs (a, b) exist such that LCM of a and b is 23 57 1113 (a, b Î N)?
a) 2460 b) 2835 c) 2645 d) 2840
B
Q6. How many times should the keys of a typewriter be pressed in order to type the first 299 natural numbers by pressing space bar once between any two successive natural numbers?
a) 1087 b) 749 c) 789 d) 1088
A
LOD 3
Q1. Rahul had some chocolates with him. He had just enough chocolates to distribute them among two groups of children A and B in the following manner. He distributed the chocolates among the children in group A such that each child got as many chocolates as the number of children in it. He distributed the chocolates among the children in group B such that each child got as many chocolates as the square of the number of children in it. He distributed 9 more chocolates to children in group A than in group B. If he had less than 600 chocolates, how many possibilities exist for the number of chocolates with him?
a) 2 b) 1 c) 3 d) 4
A
Q2. A certain number of chocolates which is a perfect square are distributed among 2156 students of a school equally. Find the minimum number of chocolates distributed given that it is greater than 90,000.
a) 94864 b) 98464 c) 99864 d) 96864
A
Q3. Find the highest common factor of the numbers
(1331)4, (1001)5, (2453)6, (3126)7 and (1456)8.
a) 5 b) 25 c) 1 d) None of these
C
Q4. The number of ways of expressing 44100 as a product of two co-primes is ______.
a) 8 b) 7 c) 16 d) 17
A
Q5. Find the smallest four-digit number which leaves remainders 2, 3 and 4 when divided by 5, 6 and 7 respectively.
a) 1003 b) 1047 c) 1053 d) 1060
B
Q6. Find the last two digits of 7^14 × 3^43 .
a) 21 b) 23 c) 27 d) 43
B