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
a.
(−4, 5)
Correct Answer
b.
(4, 5)
c.
(−3, 4)
d.
(0, 11)
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Q2nat
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
✓ Accepted Answer:84
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Q3mcq
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
a.
1 : 6
b.
1 : 4
c.
1 : 5
d.
1 : 7
Correct Answer
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Q4nat
For natural numbers $x, y$, and $z$, if $x y+y z=19$ and $y z+x z=51$, then the
minimum possible value of $x y z$ is
✓ Accepted Answer:34
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Q5mcq
Let $a, b, c$ be non-zero real numbers such that $b^2 \lt 4 a c$, and $f(x)=a x^2+b x+c$. If the set $S$ consists of al integers $m$ such that $f(m)\lt0$, then the
set $S$ must necessarily be
a.
the set of all integers
b.
either the empty set or the set of all integers
Correct Answer
c.
the empty set
d.
the set of all positive integers
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Q6mcq
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
a.
15
Correct Answer
b.
12
c.
6
d.
10
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Q7mcq
The average of three integers is 13 . When a natural number $n$ is included, the
average of these four integers remains an odd integer. The minimum possible value of
$n$ is
a.
3
b.
4
c.
5
Correct Answer
d.
1
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Q8nat
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
✓ Accepted Answer:111
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Q9mcq
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 ₹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 ₹744. Then the amount, in rupees, that she had spent in
buying almonds is
a.
1440
b.
1176
c.
1680
Correct Answer
d.
2520
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Q10mcq
The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite
number of solutions for $x$ is
a.
-1
b.
0
c.
1
Correct Answer
d.
2
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A trapezium $\text{ABCD}$ has side $\text{AD}$ parallel to $\text{BC}, \angle \text{BAD}=90^{\circ}, \text{BC}=3 \text{~cm}$ and $\text{AD}=8 \text{~cm}$. If the
perimeter of this trapezium is $36 \text{~cm}$, then its area, in sq. $\text{cm}$,
is
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For any real number $x$, let $[x]$ be the largest integer less than or equal to
$x$. If $\sum_{n=1}^N\left[\frac{1}{5}+\frac{n}{25}\right]=25$ then $N$ is
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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
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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 ₹ 308.32 per kg and makes an
overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
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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
a.
62.5%
b.
37.5%
c.
60%
d.
40%
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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
a.
48
b.
53
c.
47
d.
52
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For any natural number $n$, suppose the sum of the first $n$ terms of an arithmetic
progression is $\left(n+2 n^2\right)$. If the $n^{\text {th }}$ term of the
progression is divisible by 9 , then the smallest possible value of $n$ is
a.
4
b.
8
c.
7
d.
9
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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
a.
1 : 2
b.
3 : 1
c.
1 : 4
d.
4 : 1
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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 $4^k+3\left(4^k\right)+4^{k+2}$, where $k$ is any positive integer. Then
$(A+B)$ equals
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