Two men are walking towards each other alongside a railway track, A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 secodns. Assume the velocities are constant throughout.
118. How long after the train has passed the second man will the two men meet?
a. 89.7 minutes
119. The ratio of the velocities of the first man to the second man is
a. 89.7 minutes
c. 90. 3 minutes
"bhai mere" and "sir" are running on a track AB of length 10 metres. They start running simultaneously
from the ends A and B respectively. The moment they reach either of the ends, they turn around and
continue running. bhai mere and sir run with constant speeds of 2m/s and 5m/s respectively. How far
from A (in metres) are they, when they meet for the 23rd time?
In how many ways can 6 letters A, B, C, D, E and F be arranged in a row such that D is always
somewhere between A and B?
A game consisting of 50 rounds is played among P, Q and R as follows:
Two players play in each round and the player who loses in that round is replaced by the third player
in the next round. If the only rounds in which P played against Q are the 3rd, 14th, 25th and 36th, then
what can be the maximum number of games won by R?
A is the set of the first 100 natural numbers. What is the minimum number of elements that should
be picked from A to ensure that atleast one pair of numbers whose difference is 10 is picked?
The lengths of the three edges of a cuboid are increased by a%, b% and c%. The volume increases
by V%, where V is an integer. How many values can V take if a, b, c are real numbers and
10 ≤ a, b, c ≤ 20?
677 has exactly 5 digits when converted into base 'n' from the decimal system. What is the minimum
possible value of 'n'?
Three boys A, B and C start running at constant speeds from the same point P along the circumference
of a circular track. The speeds of A, B and C are in the ratio 5:1:1. A and B run clockwise while
C runs in the anticlockwise direction. Each time A meets B or C on the track he gives them a card.
What is the difference in the number of cards received by B and C if A distributes 33 cards in all?
M' and 'N' are natural numbers such that by M = (5N – 4) (5N + 1). If 1≤ N ≤ 200,what is the
harmonic mean of all the possible values of M?
x^2 – 3y^2 = 1376
How many integer solutions exist for the given equation?
In a Table Tennis tournament, the number of male participants was twice the number of female
participants. Each player played a match with each of the rest of the players exactly once. Each
match involved exactly two players. No match ended in a draw. The number of matches won by the
female players was equal to the number of matches won by the male players. wt
can be the total number of matches in which a male player defeated a female player?
A and B are the two opposite ends of a swimming pool and the distance between them is
420 metres. Ankur and Manu start swimming towards each other at the same time from A and B,
with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns back
and starts swimming towards the other end. At what distance (in metres) from A will they meet when
Manu is in his 13th round?
A large cube is formed by bringing together 729 smaller identical cubes. Each face of the larger
cube is painted with red colour. How many smaller cubes are there none of whose faces is painted?
In how many ways can 18 identical balls be distributed among 3 identical boxes?
What is the total number of ways of selecting twenty balls from an infinite number of blue, green and
yellow balls?
What is the number of common tangents of the circles x2 + y2 – 2x – 2y – 23 = 0 – 26y + 141 = 0?
There are two Arithmetic Progressions A and B such that their nth terms are given by
An = 101 + 3(n – 1) and Bn = 150 + (n – 1), where n is the set of natural numbers. The first 50 terms
of A and B are written alternately i.e. A1B1A2B2…..A50B50.
so formed is divided by 11?
A = {3, 23, 43 ………..603} and S is a subset of A. If the sum of no two elements of S is more than
606, then what can be the maximum possible number of elements in S?
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Q. A drum of 20 litres is filled with milk.A milkman has only two measuring vessels of 3 litres and 5 litres without any calibration.He has to measure four lts of milk for a customer without using any other vessel.Minimum how many operations are req. for this work,where an operation is counted if the milk is transferred from one vessel to another vessel? a. 5 b. 6 c. 8 d. 11
