Q. 3 One can use three different transports which move
at 10, 20, and 30 kmph, respectively. To reach from
A to B, Amal took each mode of transport 1/3 of his
total journey time, while Bimal took each mode of
transport 1/3 of the total distance. The percentage by
which Bimal’s travel time exceeds Amal’s travel time
is nearest to

Q. 4 With rectangular axes of coordinates, the number of
paths from (1, 1) to (8, 10) via (4, 6), where each
step from any point (x, y) is either to (x, y + 1) or to
(x + 1, y), is

Q. 5 At their usual efficiency levels, A and B together finish
a task in 12 days. If A had worked half as efficiently
as she usually does, and B had worked thrice as
efficiently as he usually does, the task would have
been completed in 9 days. How many days would A
take to finish the task if she works alone at her usual
efficiency?

Q. 6 Meena scores 40% in an examination and after
review, even though her score is increased by 50%,
she fails by 35 marks. If her post-review score is
increased by 20%, she will have 7 marks more than
the passing score. The percentage score needed for
passing the examination is

Q. 7 In a race of three horses, the first beat the second
by 11 metres and the third by 90 metres. If the second
beat the third by 80 metres, what was the length, in
metres, of the racecourse?

Q. 8 Consider a function f satisfying f(x + y) = f(x) f(y)
where x, y are positive integers, and f(1) = 2.
If f(a + 1) + f(a + 2) + ... + f(a + n) = 16(2^{n} – 1) then a
is equal to

Q. 9 AB is a diameter of a circle of radius 5 cm. Let P and
Q be two points on the circle so that the length of
PB is 6 cm, and the length of AP is twice that of AQ.
Then the length, in cm, of QB is nearest to

Q. 10 A chemist mixes two liquids 1 and 2. One litre of
liquid 1 weighs 1 kg and one litre of liquid 2 weighs
800 gm. If half litre of the mixture weighs 480 gm,
then the percentage of liquid 1 in the mixture, in terms
of volume, is

Q. 11 Let T be the triangle formed by the straight line
3x + 5y – 45 = 0 and the coordinate axes. Let the
circumcircle of T have radius of length L, measured
in the same unit as the coordinate axes. Then, the
integer closest to L is

Q. 12 On selling a pen at 5% loss and a book at 15% gain,
Karim gains Rs. 7. If he sells the pen at
5% gain and the book at 10% gain, he gains
Rs. 13. What is the cost price of the book in Rupees?

Q. 13 The income of Amala is 20% more than that of Bimala
and 20% less than that of Kamala. If Kamala's
income goes down by 4% and Bimala's goes up by
10%, then the percentage by which Kamala's income
would exceed Bimala's is nearest to

Q. 15 Two cars travel the same distance starting at
10:00 am and 11:00 am, respectively, on the same
day. They reach their common destination at the
same point of time. If the first car travelled for at
least 6 hours, then the highest possible value of the
percentage by which the speed of the second car
could exceed that of the first car is

Q. 17 The wheels of bicycles A and B have radii 30 cm and
40 cm, respectively. While traveling a certain
distance, each wheel of A required 5000 more
revolutions than each wheel of B. If bicycle B traveled
this distance in 45 minutes, then its speed, in km
per hour, was

Q. 19 The product of two positive numbers is 616. If the
ratio of the difference of their cubes to the cube of
their difference is 157:3, then the sum of the two
numbers is

Q. 22 In a circle of radius 11 cm, CD is a diameter and AB
is a chord of length 20.5 cm. If AB and CD intersect
at a point E inside the circle and CE has length
7 cm, then the difference of the lengths of BE and
AE, in cm, is

Q. 23 A person invested a total amount of Rs 15 lakh. A
part of it was invested in a fixed deposit earning 6%
annual interest, and the remaining amount was
invested in two other deposits in the ratio 2 : 1, earning
annual interest at the rates of 4% and 3%,
respectively. If the total annual interest income is
Rs 76000 then the amount (in Rs lakh) invested in
the fixed deposit was

Q. 25 Let S be the set of all points (x, y) in the x-y plane
such that | x | + | y | ≤ 2 and | x | ≥ 1. Then, the area,
in square units, of the region represented by S equals

Q. 26 A club has 256 members of whom 144 can play
football, 123 can play tennis, and 132 can play
cricket. Moreover, 58 members can play both football
and tennis, 25 can play both cricket and tennis, while
63 can play both football and cricket. If every member
can play at least one game, then the number of
members who can play only tennis is

Q. 27 Three men and eight machines can finish a job in
half the time taken by three machines and eight men
to finish the same job. If two machines can finish the
job in 13 days, then how many men can finish the
job in 13 days?

Q. 28 Amala, Bina, and Gouri invest money in the ratio
3 : 4 : 5 in fixed deposits having respective annual
interest rates in the ratio 6 : 5 : 4. What is their total
interest income (in Rs) after a year, if Bina's interest
income exceeds Amala's by Rs 250?

Q. 30 Ramesh and Gautam are among 22 students who
write an examination. Ramesh scores 82.5. The
average score of the 21 students other than Gautam
is 62. The average score of all the 22 students is one
more than the average score of the 21 students other
than Ramesh. The score of Gautam is

Q. 32 In a class, 60% of the students are girls and the rest
are boys. There are 30 more girls than boys. If 68%
of the students, including 30 boys, pass an
examination, the percentage of the girls who do not
pass is

Q. 33 If the population of a town is p in the beginning of any
year then it becomes 3 + 2p in the beginning of the
next year. If the population in the beginning of 2019
is 1000, then the population in the beginning of 2034
will be