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Set-1 3. If
1. You should _________ when to say p:q=1:2
_________. q:r=4:3
A. no / no B. no / know r:s=4:5
C. know / know D. know / no and u is 50% more than s, what is the ratio p
Ans. D : u?
Sol. You should know when to say no. A. 2: 15 B. 16: 15
2. Two straight lines pass through the origin (x0, C. 1 : 5 D. 16 : 45
y0) = (0, 0). One of them passes through the Ans. D
point (x2, y2) = (1,3) and the other passes Sol. Given:
through the point (x2, y2) = (1, 2). p:q = 1:2, q:r = 4:3, r:s = 4:5
What is the area enclosed between the r 12 q 16 p 8
or, = , = and =
straight lines in the interval [0,1] on the x- s 15 r 12 q 16

axis? Let, p = 8k, q = 16k, r = 12 k and s = 15 k

A. 0.5 B. 1.0  50 
u = 1 + s
C. 1.5 D. 2 .0  100 

Ans. A = 1.5 s
Sol. = 1.5 × 15 k = 22.5 k
p:u = 8 k : 22.5 k
= 16 : 45
4. Given the statements:
• P is the sister of Q.
• Q is the husband of R.
• R is the mother of S.
• T is the husband of P.
Based on the above information, T is ______
of S.
Area enclosed = Area of the shaded region
A. the grandfather B. an uncle
= Area of ΔDAB
C. the father D. a brother
1
= × base × height Ans. B
2
Sol. The family tree is as shown below:
1
= × AB × OC
2
1
= ×1×1
2
= 0.5 sq. units
T is the uncle of S

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5. In the following diagram, the point R is the healthy? It turns out that it is never too early.
center of the circle. The lines PQ and ZV are For example, babies who start eating healthy
tangential to the circle. The relation among in the first year are more likely to have better
the areas of the squares, PXWR, RUVZ and overall health as they get older.
SPQT is Which one of the following is the CORRECT
logical inference based on the information in
the above passage?
A. Healthy eating is important for those
with good health conditions, but not for
others
B. Eating healthy can be started at any
age, earlier the better
C. Eating healthy and better overall health
A. Area of SPQT = Area of RUVZ = Area of are more correlated at a young age, but
PXWR not older age
B. Area of SPQT = Area of PXWR - Area of D. Healthy eating is more important for
RUVZ adults than kids
C. Area of PXWR = Area of SPQT - Area of Ans. B
RUVZ Sol. The conclusion is that eating healthy and
D. Area of PXWR = Area of RUVZ- Area of better overall health are more co-related at a
SPQT young age but not older age.
Ans. B 7. P invested ₹ 5000 per month for 6 months of
Sol. Area of square SPQT = PQ2 …(1) a year and Q invested ₹ x per month for 8
Area of square PXWR = PR2 …(2) months of the year in a partnership business.
Area of square RUVZ = RZ2 = QR2 [RZ = QR The profit is shared in proportion to the total
= radius] …(3) investment made in that year.
In ΔPQR, ∠PQR = 90° as PQ is tangent to the If at the end of that investment year, Q
circle
4
receives of the total profit, what is the
PR2 = PQ2 + QR2 …(4) 9
From (1), (2), (3) and (4) we can write. value of x (in ₹)?
Area of square PXWR = Area of square SPQT A. 2500 B. 3000
+ Area of square RUVZ C. 4687 D. 8437
⇒ Area of square SPQT = Area of square Ans. B
PXWR - Area of square RUVZ Sol. The ratio of the profits = 5000 × 6: 8x
6. Healthy eating is a critical component of 15000
=
healthy ageing. When should one start eating 4x

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4x Calculation of median:
% share of the profit of Q =
4x + 15000 No. of variates, N =  fi = 50 (even)
From the question th
Nth  N 
4x 4 Median = mean of &  + 1 variate
= 2  2 
4x + 15000 9
= mean of 25th & 26th variate
⇒ 9x = 4x + 15000
6+6
⇒ 5x = 15000 = =6
2
x = 3000
Mode = Marks corresponding to maximum
8. The above frequency chart shows the frequency = 7
frequency distribution of marks obtained by a Hence, mode > median > mean
set of students in an exam. 9. In the square grid shown on the left, a person
standing at P2 position is required to move to
P5 position.
The only movement allowed for a step
involves “two moves along one direction
followed by one move in a perpendicular
direction”. The permissible directions for
movement are shown as dotted arrows in the
right.
For example, a person at a given position Y
can move only to the positions marked X on
From the data presented above, which one of the right.
the following is CORRECT? Without occupying any of the shaded squares
A. mean > mode > median at the end of each step, the minimum number
B. mode > median > mean of steps required to go from P2 to P5 is
C. mode > mean > median
D. median > mode > mean
Ans. B
fixi
Sol. Mean =
fi

3  3 + 9  4 + 11  5 + 7  6 + 14  7 + 2  8 + 4  9
=
3 + 9 + 11 + 7 + 14 + 2 + 4 A. 4 B. 5
9 + 36 + 55 + 42 + 98 + 16 + 36 C. 6 D. 7
=
50
Ans. B
292 Sol. Moves will be A – B – C – D – E = F
= = 5.84
50

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Ans. D
Sol. On unfolding, the given alignment will always
be followed:

i.e., A to B, B to C, C to D, D to E and E to F Which is only shown in option D.

Minimum no. of steps = 5
10. Consider a cube made by folding a single Set-2
sheet of paper of appropriate shape.
The interior faces of the cube are all blank. 1. The movie was funny and I…….
However, the exterior faces that are not A. could help laughing
visible in the above view may not be blank. B. couldn’t help laughed
C. couldn’t help laughing
D. could helped laughed
Ans. C
Sol. The movie was funny and I couldn’t help
laughing.
1 1 1
Which one of the following represents a 2. x:y:z = : :
2 3 4
possible unfolding of the cube?
x+z−y
What is the value of ?
y

A. A. 0.75 B. 1.25
C. 2 .25 D. 3 .25
Ans. B
1 1 1
Sol. x : y : z = : :
2 3 4
B.
x 1/2 3
 = =
y 1/3 2

y 1/3 4
C.  = =
z 1/4 3

x+z−y x z
= + −1
y y y

D. 3 3 5
= + −1 = = 1.25
2 4 4

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3. Both the numerator and the denominator Sol. The given data can be shown in the venn
3 diagram as below:–
of are increased by a positive integer, x,
4
15
and those of are decreased by the same
17
integer. This operation results in the same
value for both the fractions. What is the value
of 𝑥?
A. 1 B. 2
C. 3 D. 4
Ans. C Total no. of students interested in physics,
3 + x 15 − x chemistry and maths all together
Sol. =
4 + x 17 − x
= 120+20+30+30+105+10+90 = 405.
⇒ (x + 3) (x – 17) = (x – 15) (x + 4) Total no. of students = 450
⇒ x2 – 14x – 51 = x2 – 11x – 60 ∴ No. of students interested in humanities
⇒ 3x – 9 = 0 = 450–405 = 45
x=3 5. For the picture shown above, which one of the
4. A survey of 450 students about their subjects following is the correct picture representing
of interest resulted in the following outcome: reflection with respect to the mirror shown as
• 150 students are interested in Mathematics. the dotted line?
• 200 students are interested in Physics.
• 175 students are interested in Chemistry.
• 50 students are interested in Mathematics
and Physics.
• 60 students are interested in Physics and
Chemistry.
• 40 students are interested in Mathematics
A. B.
and Chemistry.
• 30 students are interested in Mathematics,
Physics and Chemistry.
• Remaining students are interested in
Humanities. C. D.

Based on the above information, the number

of students interested in Humanities is Ans. A
A. 10 B. 30 Sol. The image will be symmetrical about the
C. 40 D. 45 dotted line so that on folding about the dotted
Ans. D line, both pictures overlap each other.

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year such that the share is proportional to
their individual total investment over the
year?
A. 22 : 23 : 24 B. 22 : 33 : 50
C. 33 : 46 : 60 D. 63 : 86 : 110
Ans. D
6. In the last few years, several new shopping
Sol. Let the initial investments be 3x, 4x and 5x,
malls were opened in the city. The total
respectively.
number of visitors in the malls is impressive.
Now, after increasing their monthly
However, the total revenue generated
investment by 10%, 15% and 20%,
through sales in the shops in these malls is
respectively, the monthly instalment will be:
generally low.
3.3x, 4.6x and 6x, respectively
Which one of the following is the CORRECT
Ratio of their profits at the end of year
logical inference based on the information in
= Ratio of their investments
the above passage?
= (3x + 3.3x) : (4x + 4.6x) : (5x + 6x)
A. Fewer people are visiting the malls but
= 6.3x : 8.6x : 11x
spending more
= 63 : 86 : 110
B. More people are visiting the malls but not
8. Consider the following equations of straight
spending enough
lines:
C. More people are visiting the malls and
Line L1: 2x – 3y = 5
spending more
Line L2: 3x + 2y = 8
D. Fewer people are visiting the malls and not
Line L3: 4x – 6y = 5
spending enough
Line L4: 6x – 9y = 6
Ans. B
Which one among the following is the correct
Sol. The inference drawn from the passage is that
statement?
more people are visiting the malls but not
A. L1 is parallel to L2 and L1 is perpendicular
spending enough.
to L3
7. In a partnership business the monthly
B. L2 is parallel to L4 and L2 is perpendicular
investment by three friends for the first six
to L1
months is in the ratio 3: 4: 5 . After six
C. L3 is perpendicular to L4 and L3 is parallel
months, they had to increase their monthly
to L2
investments by 10%, 15% and 20%,
D. L4 is perpendicular to L2 and L4 is parallel
respectively, of their initial monthly
to L3
investment. The new investment ratio was
Ans. D
kept constant for the next six months.
Sol.
What is the ratio of their shares in the total
L1 : 2x – 3y = 5 ⇒ slope = 2/3
profit (in the same order) at the end of the

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L2 : 3x + 2y = 8 ⇒ slope = – 3/2 The above two criteria are fulfilled in both the
L3 : 4x – 6y = 5 ⇒ slope = 4/6 = 2/3 diagrams, i.e. only conclusions I and III are
L4 : 6x – 9y = 6 ⇒ slope = 6/9 = 2/3 correct.
Slope of L1 = slope of L3 = slope of L4 10. An ant walks in a straight line on a plane
⇒ L1, L3 and L4 are parallel to each other leaving behind a trace of its movement. The

2  −3  initial position of the ant is at point P facing

slope of L4 × slope of L2 =  = −1
3  2  east.

⇒ L2 and L4 are perpendicular to each other The ant first turns 72° anticlockwise at P, and

9. Given below are two statements and four then does the following two steps in sequence

conclusions drawn based on the statements. exactly FIVE times before halting.

Statement 1: Some soaps are clean. 1. moves forward for 10 cm.

Statement 2: All clean objects are wet. 2. turns 144o clockwise.

Conclusion I: Some clean objects are soaps.

Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps. The pattern made by the trace left behind by

Which one of the following options can be the ant is

logically inferred?
A. Only conclusion I is correct
A. B.
B. Either conclusion I or conclusion II is
correct
C. Either conclusion III or conclusion IV is
correct
D. Only conclusion I and conclusion III are C. D.

correct
Ans. D
Sol. The possible representations are:– Ans. C
Sol. The path is shown below:

We can observe that:–

• Some clean objects are soaps
• Some wet objects are soaps
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