Q. 3 Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg
almonds when the cost of 7 kg cashews is the same
as that of 30 kg peanuts or 9 kg almonds. She mixes
all the three nuts and marks a price for the mixture
in order to make a profit of Rs. 1752. She sells 4 kg
of the mixture at this marked price and the remaining
at a 20% discount on the marked price, thus making
a total profit of Rs. 744. Then the amount, in rupees,
that she had spent in buying almonds is

Q. 4 Amal buys 110 kg of syrup and 120 kg of juice, syrup
being 20% less costly than juice, per kg. He sells
10 kg of syrup at 10% profit and 20 kg of juice at
20% profit. Mixing the remaining juice and syrup,
Amal sells the mixture at Rs. 308.32 per kg and
makes an overall profit of 64%. Then, Amal's cost
price for syrup, in rupees per kg, is

Q. 5 A mixture contains lemon juice and sugar syrup in
equal proportion. If a new mixture is created by
adding this mixture and sugar syrup in the ratio
1 : 3, then the ratio of lemon juice and sugar syrup in
the new mixture is

Q. 6 In a class of 100 students, 73 like coffee, 80 like tea
and 52 like lemonade. It may be possible that some
students do not like any of these three drinks. Then
the difference between the maximum and minimum
possible number of students who like all the three
drinks is

Q. 7 In a village, the ratio of number of males to females
is 5 : 4. The ratio of number of literate males to literate
females is 2 : 3. The ratio of the number of illiterate
males to illiterate females is 4 : 3. If 3600 males in
the village are literate, then the total number of
females in the village is

Q. 9 The average of three integers is 13. When a natural
number n is included, the average of these four
integers remains and odd integer. The minimum
possible value of n is

Q. 10 Trains A and B start traveling at the same time
towards each other with constant speeds from
stations X and Y, respectively. Train A reaches station
Y in 10 minutes while train B takes 9 minutes to
reach station X after meeting train A. Then the total
time taken, in minutes, by train B to travel from
station Y to station X is

Q. 12 Let ABCD be a parallelogram such that the
coordinates of its three vertices A, B, C are (1, 1),
(3, 4) and (–2, 8), respectively. Then, the coordinates
of the vertex D are

Q. 15 Let A be the largest positive integer that divides all
the numbers of the form 3^{k} + 4^{k} + 5^{k}, and B be the
largest positive integer that divides all the numbers
of the form 4^{k} + 3(4^{k}) + 4^{k+2}, where k is any positive
integer. Then (A + B) equals

Q. 16 The average weight of students in a class increases
by 600 gm when some new students join the class.
If the average weight of the new students is 3 kg
more than the average weight of the original students,
then the ratio of the number of original students to
the number of new students is

Q. 17 Let a, b, c be non-zero real numbers such that
b^{2} < 4ac, and f(x) = ax^{2} + bx + c. If the set S consists
of all integers m such that f(m) < 0, then the set S
must necessarily be

Q. 18 Alex invested his savings in two parts. The simple
interest earned on the first part at 15% per annum
for 4 years is the same as the simple interest earned
on the second part at 12% per annum for 3 years.
Then, the percentage of his savings invested in the
first part is

Q. 19 Pinky is standing in a queue at a ticket counter.
Suppose the ratio of the number of persons standing
ahead of Pinky to the number of persons standing
behind her in the queue is 3 : 5. If the total number of
persons in the queue is less than 300, then the
maximum possible number of persons standing
ahead of Pinky is

Q. 20 The number of ways of distributing 20 identical
balloons among 4 children such that each child gets
some balloons but no child gets an odd number of
balloons, is

Q. 21 A trapezium ABCD has side AD parallel to BC,
∠BAD = 90°, BC = 3 cm and AD = 8 cm. If the
perimeter of this trapezium is 36 cm, then its area,
in sq. cm, is

Q. 22 For any natural number n, suppose the sum of the
first n terms of an arithmetic progression is (n + 2n^{2}).
If the nth term of the progression is divisible by 9,
then the smallest possible value of n is