17 MENSURATION 2D

Triangles:

Equilateral Triangle: Scalene Triangle: Area of Triangle:

(i) when base and height

given

Area of equilateral triangle

Area of scalene triangle =
=
3 2
a s s  a s  b s  c 
4
semi perimeter =
Perimeter = 3a abc
s
Length of median or height 2 1
Area of triangle = bh
3 Perimeter = a + b + c 2
= a
2

Isosceles Triangle: (ii) when adjacent sides

Right angled Triangle:
and included angle given

Area of isosceles triangle =

1
b
4a 2  b 2 Area of triangle =  ab sin
Area of right angled triangle 2
4
1
Perimeter = 2a + b
= bh
2
b2 Perimeter = b  h  b 2  h 2
Height = a 2 
4
Hypotenuse = b 2  h 2

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Rectangle: Rhombus: Circle:

Area of rectangle = l x b
Perimeter = 2(l + b)
Area of rhombus =
Length of rectangle = Area of circle = r 2
1
l 2  b2  d1  d 2
2 Perimeter of circle = 2r

Length of side = a = Semi circle:

Square: d  d2
1
2 2

2
Perimeter = 4a

1 2
Area of semicircle = r
Trapezium:
2
Perimeter of semicircle =
Area of square = a2
r  2r
Perimeter = 4a
Sector:
Length of rectangle = 2a

Area of trapezium =
Parallelogram:
 a  c   h
1
(i) when base and height 2
given

Arc length = r (when

angle is given in radian)

Arc length=
r (when
Regular Hexagon:
180
Area of parallelogram = angle is given in degree)
bh
Area of Sector =
r 2 (when
2
(ii) when adjacent sides angle is given in radian)
and included angle given
Area of hexagon = 6 x Area Area of Sector =
r 2
of equilateral triangles 360
(when angle is given in
3 2 degree)
= 6 a
4
Area of parallelogram =
lb sin

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 PRACTICE SHEET-1
1. The diagonal of a square is 4√2 cm. The (1) 6 (2) 3
diagonal of another square whose area is (3) 3/2 (4) 3/4
double that of the first square is:
(1) 8 √2 cm (2) 16 cm 9. From a point in the interior of an equilateral
(3) √32 cm (4) 8 cm triangle, the length of the perpendiculars to
the three sides are 6 cm, 8 cm and 10 cm
2. The breadth of a rectangular hall is three- respectively. The area of the triangle is
fourth of its length. If the area of the floor is (1) 48 cm2 (2) 16√3 cm2
768 sq. m., then the difference between the (3) 192√3 cm2 (4) 192 cm2
length and breadth of the hall is:
(1) 8 metres (2) 12 metres 10. The area of an isosceles triangle is 4 square
(3) 24 metres (4) 32 metres unit. If the length of the third side is 2 unit,
the length of each equal side is
3. The length of a plot is five times its breadth. (1) 4 units (2) 2√ 3 units
A playground measuring 245 square metres (3) √17 units (4) 3 √2 units
occupies half of the total area of the plot.
What is the length of the plot? 11. 360 sq. cm and 250 sq. cm are the area of
(1) 35√2 metres (2)175√ 2 metres two similar triangles. If the length of one of
(3) 490 metres (4) 5 √2 metres the sides of the first triangle be 8 cm, then
the length of the corresponding side of the
4. The difference between the length and second triangle is
breadth of a rectangle is 23 m. If its 1 1
perimeter is 206 m, then its area is (1) 6 cm (2) 6 cm
(1) 1520 m 2 (2) 2420 m 2 5 3
(3) 2480 m2 (4) 2520 m2 2
(3) 6 (4) 6 cm
3
5. A path of uniform width runs round the
inside of a rectangular field 38 m long and 12. The perimeter of an isosceles triangle is 544
32 m wide. If the path occupies 600m2, then 5
the width of the path is cm and each of the equal sides is times
(1) 30 m (2) 5 m 6
(3) 18.75 m (4) 10 m the base. What is the area (in cm2) of the
triangle?
6. The length and breadth of a rectangle are (1) 38172 (2) 18372
increased by 20% and 25% respectively. The (3) 31872 (4) 13872
increase in the area of the resulting
rectangle will be: 13. The perimeter of a rhombus is 100 cm. If
(1) 60% (2) 50% one of its diagonals is 14 cm, then the area
(3) 40% (4) 30% of the rhombus is
(1) 144 cm2 (2) 225 cm2
7. The length of a room floor exceeds its (3) 336 cm 2 (4) 400 cm2
breadth by 20 m. The area of the floor
remains unaltered when the length is 14. If the measure of one side and one diagonal
decreased by 10 m but the breadth is of a rhombus are 10 cm and 16 cm
increased by 5 m. The area of the floor (in respectively, then its area (in cm2) is :
square metres) is : (1) 60 (2) 64
(1) 280 (2) 325 (3) 96 (4) 100
(3) 300 (4) 420
15. The ratio of the length of the parallel sides of
8. The sides of a triangle are 3 cm, 4 cm and 5 a trapezium is 3:2. The shortest distance
cm. The area (in cm2) of the triangle formed between them is 15 cm. If the area of the
by joining the mid points of this triangle is:

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 trapezium is 450 cm2, the sum of the length 23. If ∆ABC is similar to ∆DEF such that BC = 3
of the parallel sides is cm, EF = 4 cm and area of ∆ABC = 54 cm2,
(1) 15 cm (2) 36 cm then the area of ∆DEF is :
(3) 42 cm (4) 60 cm (1) 66 cm2 (2) 78 cm2
(3) 96 cm 2 (4) 54 cm2
16. A parallelogram has sides 15 cm and 7 cm
long. The length of one of the diagonals is 20 24. In ∆ABC, O is the centroid and AD, BE, CF
cm. The area of the parallelogram is are three medians and the area of ∆AOE =
(1) 42 cm2 (2) 60 cm2 15 cm2, then area of quadrilateral BDOF is
(3) 84 cm2 (4) 96 cm2 (1) 20 cm2 (2) 30 cm2
(3) 40 cm2 (4) 25 cm2
17. In ∆ABC, D and E are the points of sides AB
and BC respectively such that DE || AC and 25. A straight line parallel to the base BC of the
AD : DB = 3 : 2. The ratio of area of triangle ABC intersects AB and AC at the
trapezium ACED to that of ∆BED is points D and E respectively. If the area of
(1) 4 : 15 (2) 15 : 4 the ∆ABE be 36 sq.cm, then the area of the
(3) 4 : 21 (4) 21 : 4 ∆ACD is
(1) 18 sq.cm (2) 36 sq.cm
18. ABCD is a trapezium in which AB||DC and (3) 18 cm (4) 36 cm
AB = 2 CD. The diagonals AC and BD meet
at O. The ratio of area of triangles AOB and 26. ABC is a right angled triangle, B being the
COD is right angle. Mid-points of BC and AC are
(1) 1 : 1 (2) 1 : √2 respectively B' and A'. The ratio of the area
(3) 4 : 1 (4) 1 : 4 of the quadrilateral AA'BB' to the area of the
triangle ABC is
19. The areas of a square and a rectangle are (1) 1 : 2 (2) 2 : 3
equal. The length of the rectangle is greater (3) 3 : 4 (4) N. A.
than the length of any side of the square by
5 cm and the breadth is less by 3 cm. Find 27. Two triangles ABC and PQR are congruent.
the perimeter of the rectangle. If the area of ∆ABC is 60 sq. cm, then area of
(1) 17 cm (2) 26 cm ∆PQR will be
(3) 30 cm (4) 34 cm (1) 60 sq.cm (2) 30 sq.cm
(3) 15 sq.cm (4) 120 sq.cm
20. If the side of a square is increased by 25%,
then its area is increased by: 28. Two sides of a parallelogram are 20 cm and
(1) 25% (2) 55% 25 cm. If the altitude corresponding to the
(3) 40.5% (4) 56.25% side of length 25 cm is 10 cm, then the
altitude corresponding to the other pair of
21. ABC is an isosceles right angled triangle sides is
with ∠B = 90°. On the sides AC and AB, two (1) 10.5 cm (2) 12 cm
equilateral triangles ACD and ABE have (3) 12.5 cm (4) 10 cm
been constructed. The ratio of area of ∆ABE
and ∆ACD is 29. The diagonal of a quadrilateral shaped field
(1) 1 : 3 (2) 2 : 3 is 24m and the perpendiculars dropped on it
(3) 1 : 2 (4) 1 : 2 from the remaining opposite vertices are 8m
and 13m. The area of the field is
22. Two triangles ABC and DEF are similar to (1) 252 m2 (2) 156 m2
each other in which AB = 10 cm, DE = 8 cm. (3) 96 m 2 (4) 1152 m2
Then the ratio of the area of triangles ABC
and DEF is 30. Two isosceles triangles have equal vertical
(1) 4 : 5 (2) 25 : 16 angles and their areas are in the ratio 9:16.
(3) 64 : 125 (4) 4 : 7 Then the ratio of their corresponding heights
is-
(1) 4.5 : 8 (2) 4 : 3
(3) 8 : 4.5 (4) 3 : 4

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 ANSWER KEY
1. (4) 2. (1) 3. (1) 4. (4) 5. (2) 6. (2) 7. (3) 8. (3) 9. (3) 10. (3)
11. (3) 12. (4) 13. (3) 14. (3) 15. (4) 16. (3) 17. (4) 18. (3) 19. (4) 20. (4)
21. (3) 22. (2) 23. (3) 24. (2) 25. (2) 26. (3) 27. (1) 28. (3) 29. (1) 30. (4)

PRACTICE SHEET-2
1. The area of the ring between two concentric between the area of the larger circle and that
circles, whose circumference are 88 cm and of the smaller circle).
132 cm, is: (1) 9 : 16 (2) 9 : 25
(1) 780 cm2 (2) 770 cm2 (3) 16 : 25 (4) 16 : 27
(3) 715 cm2 (4) 660 cm2
7. The diameter of two circles are the side of a
2. Four equal circles each of radius ‘a’ units square and the diagonal of the square. The
touch one another. The area enclosed ratio of the area of the smaller circle and the
between them (π = 22/7), in square units, is larger circle is
6 2 (1) 1 : 2 (2) 1 : 4
(1) 3a2 (2) a (3) √2 : √3 (4) 1 : √2
7
41 2 1 8. The area of the largest circle, that can be
(3) a (4) a 2
7 7 drawn inside a rectangle with sides 18 cm.
by 14 cm, is
3. The area of circle whose radius is 6 cm is (1) 49 cm2 (2) 154 cm2
trisected by two concentric circles. The (3) 378 cm 2 (4) 1078 cm2
radius of the smallest circle is
(1) 2√3 cm (2) 2 √6 cm 9. A circle is inscribed in an equilateral triangle
(3) 2 cm (4) 3 cm of side 8 cm. The area of the portion between
the triangle and the circle is
4. The radius of circle A is twice that of circle B (1) 11 cm2 (2) 10.95 cm
and the radius of circle B is twice that of (3) 10 cm2 (4) 10.50 cm2
circle C. Their area will be in the ratio
(1) 16 : 4 : 1 (2) 4 : 2 : 1 10. If the difference between areas of the
(3) 1 : 2 : 4 (4) 1 : 4 : 16 circum-circle and the in-circle of an
equilateral triangle is 44 cm2, then the area
5. The four equal circles of radius 4 cm drawn of the triangle is
on the four corners of a square touch each (1) 28 cm2 (2) 7√3 cm2
other externally. Then the area of the portion (3) 14√3 cm 2 (4) 21 cm2
between the square and the four sectors is
(1) 9 (π – 4) sq. cm. 11. Three circles of diameter 10 cm each, are
(2) 16 (π – 4) sq. cm. bound together by a rubber band, as shown
(3) 9 (4 – π) sq. cm. in the figure.
(4) 16 (4 – π) sq.cm.

6. The area of a circle is proportional to the

square of its radius. A small circle of radius
3 cm is drawn within a larger circle of radius
5 cm. Find the ratio of the area of the
annular zone to the area of the larger circle.
(Area of the annular zone is the difference

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 The length of the rubber band, (in cm) if it is
stretched as shown, is
(2) (a + b + c) ab  bc  ca )
(1) 30 (2) 30 + 10π (3) ab + bc + ca
(3) 10π (4) 60 + 20π (4) None of the above

12. A circular road runs around a circular 20. The area of a circle is proportional to the
ground. If the difference between the square of its radius. A small circle of radius
circumference of the outer circle and the 3 cm is drawn within a larger circle of radius
inner circle is 66 metres, the width of the 5 cm. Find the ratio of the area of the
road is: annular zone to the area of the larger circle.
(1) 10.5 metres (2) 7 metres (Area of the annular zone is the difference
(3) 5.25 metres (4) 21 metres between the area of the larger circle and that
of the smaller circle).
13. A person observed that he required 30 (1) 9 : 16 (2) 9 : 25
seconds less time to cross a circular ground (3) 16 : 25 (4) 16 : 27
along its diameter than to cover it once
along the boundary. If his speed was 30 21. The diameter of two circles are the side of a
m/minute, then the radius of the circular square and the diagonal of the square. The
ground. ratio of the area of the smaller circle and the
(1) 5.5 m (2) 7.5 m larger circle is
(3) 10.5 m (4) 3.5 m (1) 1 : 2 (2) 1 : 4
(3) 2 : 3 (4) 1 : 2
14. If the four equal circles of radius 3 cm touch
each other externally, then the area of the 22. Three circles of equal radius ‘a’ cm touch
region bounded by the four circles is each other. The area of the shaded region is:
(1) 4(9 – π) sq.cm (2) 9(4 –π) sq.cm
(3) 5(6 – π) sq.cm (4) 6(5 – π) sq.cm

15. The area of a circle is increased by 22 cm2

when its radius is increased by 1 cm. The
original radius of the circle is
(1) 3 cm (2) 5 cm
(3) 7 cm (4) 9 cm
 3   2  6 3 
 2
16. The radii of two circles are 5cm and 12cm. (a)   a (b)   a
 
The area of a third circle is equal to the sum  2   2 
of the area of the two circles. The radius of
the third circle is : (c)  
3   a2
 2 3   2
(d) 
 2
 a
(1) 13 cm (2) 21 cm  
(3) 30 cm (4) 17 cm
23. The radii of two circles are 10 cm and 24
17. The perimeter of a semicircular path is 36 cm. The radius of a circle whose area is the
m. Find the area of this semicircular path. sum of the area of these two circles is
(1) 42sq.m (2) 54 sq. m (1) 36 cm (2) 17 cm
(3) 63 sq.m (4) 77 sq. m (3) 34 cm (4) 26 cm

18. The ratio between the area of two circles is 24. The perimeter of a rhombus is 60 cm and
4 : 7. What will be the ratio of their radii? one of its diagonal is 24 cm. The area of the
(1) 2 : √7 (2) 4 : 7 rhombus is
(3) 16 : 49 (4) 4 : √7 (1) 108 sq. cm. (2) 216 sq. cm.
(3) 432 sq. cm. (4) 206 sq. cm.
19. Three circles of radius a, b, c touch each
other externally. The area of the triangle
formed by joining their centre is
(1) (a  b  c)abc

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25. The ratio of circumference and diameter of a 29. If the perimeter of circle A is equal to
4 perimeter of semi circle B, what is the ratio
circle is 22 : 7. If the circumference be 1 of their areas?
7 (1) (π + 2)2 : 2π2 (2) 2π2 : (π + 2)2
m, then the radius of the circle is :
(3) (π + 2) : 4π
2 2 (4) 4 π2 : (π + 2)2
1 1
(1) m (2) m
3 2 30. PS is a diameter of a circle of radius 6 cm. In
1 the diameter PS, Q and R are two points
(3) m (4) 1 m such that PQ, QR and RS are all equal.
4 Semicircles are drawn on PQ and QS as
diameter (as shown in the figure). The
26. Four circles of equal radii are described perimeter of shaded portion is :
about the four corners of a square so that
each touches two of the other circles. If each
side of the square is 140 cm then area of the
space enclosed between the circumference of
the circle is Take
(1) 4200 cm2 (2) 2100 cm2
(3) 7000 cm 2 (4) 2800 cm2

27. The perimeter of a triangle is 67 cm. The

first side is twice the length of the second
side. The third side is 11 cm more than the
second side. Find the length of the shortest 6 3
(1) 15 cm (2) 75
side of the triangle. 7 7
(1) 12 cm. (2) 14 cm. 5 6
(3) 17 cm. (4) 25 cm. (3) 37 cm (4) 18 cm
7 7
28. The radius of a wheel is 25 cm. How many
rounds it will take to complete 11 km.
(1) 5000 (2) 6000
(3) 7000 (4) 4000

ANSWER KEY
1. (2) 2. (2) 3. (1) 4. (1) 5. (4) 6. (3) 7. (1) 8. (2) 9. (2) 10. (3)
11. (2) 12. (1) 13. (4) 14. (2) 15. (1) 16. (1) 17. (4) 18. (1) 19. (1) 20. (3)
21. (1) 22. (4) 23. (4) 24. (2) 25. (3) 26. (1) 27. (2) 28. (3) 29. (3) 30. (4)

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 CDS PYQ
1. In the figure given below, the area of [CDS 2013(I)]
rectangle ABCD is 100 sq. cm. O is any (a) 4:9 (b) 2:9
point on AB and CD = 20cm. Then, the area (c) 2:3 (d) 1:27
of COD is:
A O B 7. The arc AB of the circle with centre at O and
radius 10cm has length 16cm. What is the
area of the sector bounded by the radii OA,
OB and he arc AB?
[CDS 2013(I)]
(a) 40 sq cm (b) 40 sq cm
D C (c) 80 sq cm (d) 20 sq cm
[CDS 2013(I)]
(a) 40 sq cm (b) 45 sq cm 8. The minute hand of a watch is 2.5 cm long.
(c) 50 sq cm (d) 80 sq cm The distance its extreme end transverses in
40 min is:
2. If an isosceles right angled triangle has area [CDS 2013(I)]
1 sq unit, then what is its perimeter? (a) 10/3cm (b) 3/10cm
[CDS 2013(I)] (c) 10/3cm (d) 10cm
(a) 3 units (b) 2 2  1 units
(c)  
2  1 units (d) 2  
2  1 units 9. If the area of a regular hexagon is 96 3 sq
cm, then its perimeter is:
[CDS 2013(I)]
3. A circular water fountain 6.6 m in diameter
(a) 36cm (b) 48cm
is surrounded outside by a path of width
(c) 54cm (d) 64cm
1.5m. The area of this path (in sq m) is:
[CDS 2013(I)]
10. What is the area of a circle whose area is
(a) 13.62 (b) 13.15
equal to that of a triangle with sides 7cm,
(c) 12.15 (d) None of these
24cm and 25cm?
[CDS 2013(II)]
4. The area of a rectangular field is 4500 sq m.
(a) 80cm2 (b) 84cm2
If its length and breadth are in the ratio 9:5,
(c) 88cm2 (d) 90cm2
then its perimeter is:
[CDS 2013(I)]
11. If the area of an equilateral triangle is x and
(a) 90m (b) 150m
its perimeter is y, then which one of the
(c) 280m (d) 360m
following is correct?
[CDS 2013(II)]
5. The area of a square inscribed in a circle of
(a) y4 = 432x2 (b) y4 = 21 x2
radius 8cm is:
(c) y2 = 432 x2 (d) None of these
[CDS 2013(I)]
(a) 32 sq cm (b) 64 sq cm
12. The area of an isosceles ABC with AB = AC
(c) 128 sq cm (d) 256 sq cm
and altitude AD = 3 cm is 12 sq cm. What is
its perimeter?
6. The short and long hands of a clock are 4
[CDS 2013(II)]
cm and 6 cm long, respectively. Then, the
(a) 18cm (b) 16cm
ratio of distances travelled by tips of short
(c) 14cm (d) 12cm
hand in 2 days and long hand in 3 days is:

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13. How many 200mm lengths can be cut from (a) 8 cm and 10cm
10m of ribbon? (b) 9 cm and 11cm
[CDS 2013(II)] (c) 10 cm and 12 cm
(d) 11 cm and 13 cm
(a) 50 (b) 40
(c) 30 (d) 20
20. How many circular plates of diameter d be
taken out of a square plate of side 2d with
14. What is the area between a square of side 10
minimum loss of material?
cm and two inverted semi-circular, cross
[CDS 2014(I)]
sections each of radius 5cm inscribed in the
(a) 8 (b) 6
square?
(c) 4 (d) 2
[CDS 2013(II)]
(a) 17.5cm2 (b) 18.5cm2
21. What is the total area of three equilateral
(c) 20.5cm 2 (d) 21.5cm2
triangles inscribed in a semi-circle of radius
2cm?
15. The perimeter of a rectangle having area
[CDS 2014(I)]
equal to 144cm2 and sides in the ratio 4 : 9
is: 3 3
(a)12cm2 (b) cm2
[CDS 2013(II)] 4
(a) 52cm (b) 56cm 9 3
(c) cm2 (d) 3 3 cm
(c) 60cm (d) 64cm 4

16. One side of a parallelogram is 8.06 cm and 22. The area of sector of a circle of radius 36cm
its perpendicular distance from opposite side is 72 cm2. The length of the corresponding
is 2.08 cm. What is the approximate area of arc of the sector is:
the parallelogram? [CDS 2014(I)]
[CDS 2013(II)] (a) cm (b) 2cm
(a) 12.56cm2 (b) 14.56cm2 (c) 3cm (d) 4cm
(c) 16.76cm 2 (d) 22.56cm2
23. A square is inscribed in a circle of diameter
17. If the diagonals of a rhombus are 4.8 cm 2a anDd another square is circumscribing
and 1.4 cm, then what is the perimeter of circle. The difference between the area of
the rhombus? outer and inner squares is:
[CDS 2013(II)] [CDS 2014(I)]
(a) 5cm (b) 10cm (a) a2 (b) 2a2
(c) 12cm (d) 20cm (c) 3a2 (d) 4a2

18. A regular hexagon is inscribed in a circle of 24. ABC is a triangle right angled at A. AB = 6
radius 5cm. If x is the area inside the circle cm and AC = 8 cm. Semi-circles drawn
but outside the regular hexagon, then which (outside the triangle) on AB, AC and BC as
one of the following is correct? diameters which enclose areas x, z square
[CDS 2013(II)] units, respectively. What is x + y – z equal
(a) 13cm2 < x < 15 cm2 to?
(b) 15cm2 < x < 17 cm2
[CDS 2014(I)]
(c) 17cm2 < x < 19 cm2
(d) 19 cm < x < 21 cm
2 2 (a) 48cm 2 (b) 32cm 2

(c) 0 (d) None of these

19. The area of a rectangle lies between 40 cm2
and 45 cm2. If one of the sides is 5 cm, then 25. Consider an equilateral triangle of a side of
its diagonal lies between: unit length. A new equilateral triangle is
[CDS 2014(I)] formed by joining the mid points of one,

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 then a third equilateral triangle is formed by (c) 275 m (d) 264 m
joining the mid points of seconds. The 31. The sides of a triangular field are 41m, 40m
process is continued. The perimeter of all and 9m. The number of rose bend that can
triangles, thus formed is: be prepared in the field if each rose bed, on
[CDS 2014(I)] an average, needs 900 square cam space, is:
(a) 2 units (b) 3 units [CDS 2015(I)]
(c) 6 units (d) Infinity (a) 2000 (b) 1800
(c) 900 (d) 800
26. What is the area of the larger segment of a
circle formed by a chord of length 5cm 32. The ratio of the outer and inner perimeters
subtending an angle of 90° at the centre? of a circular path is 23:22. If the path is 5m
[CDS 2014(I)] wide, the diameter of the inner circle is:
25    25    [CDS 2015(I)]
(a)  cm2 (b) 
4  2  4  2 
1 1 (a) 55m (b) 110m
 
(c) 220m (d) 230m
25  3 
(c)  1 (d) None of these
4  2  33. For equal-sized maximum circular plate are
cut off from a square paper sheet of area
27. A rectangle of maximum area of drawn 784 square cm. The circumference of each
inside a circle of diameter 5cm. What is the plate is:
maximum area of such a rectangle? [CDS 2015(I)]
[CDS 2014(I)] (a) 11cm (b) 22cm
(a) 25cm2 (b) 12.5cm2 (c) 33cm (d) 44cm
(c) 12cm2 (d) None of these
34. A boy is cycling such that the wheels of the
28. If AB and CD are two diameters of a circle of cycle are making 140 revolutions per
radius r and they are mutually minute. If the radius of the wheel is 30 cm,
perpendicular, then what is the ratio of the the speed of the cycle is:
[CDS 2015(II)]
area of the circle to the area of the ACD?
(a) 15.5km/hour (b) 15.84km/hour
[CDS 2014(I)] (c) 16km/hour (d) 16.36km/hour

(a) (b) 
2 35. There are 437 fruit plants in an orchard
 planted in rows. The distance between any
(c) (d) 2 two adjacent rows in 2m and the distance
4
between any two adjacent plants in 2m.
Each rows has the same number of plants.
29. If every side of an equilateral triangle is There is 1m clearance on all sides of the
doubled, then the area of new triangle orchard. What is the cost of fencing the area
becomes k times the area of the old one. at the rate of Rs100 per meter.
What is k equal to? [CDS 2015(II)]
(a) Rs 15,600
[CDS 2014(II)]
(b) Rs 16,800
(a) 3 (b) 2 (c) Rs 18,200
(c) 4 (d) 8 (d) More information is required

36. The circumference of a circle is 100cm. The

30. A railroad curve is to be laid on a circle.
side of the square inscribed in the circle is:
What radius (approx) should be used. If the [CDS 2015(II)]
track is to change direction by 25° in a 100
distance of 120m? (a) 50 2 cm (b) cm

[CDS 2014(II)]
(a) 300 m (b) 280 m

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 50 2 100 2
(c) cm (d) cm 43. The number of rounds that a wheel of
 
diameter 7/11 meter will make in traversing
4 km will be:
37. The diameter of a wheel that makes 452
[CDS 2016(I)]
revolutions to move 2km and 26 decameter
(a) 500 (b) 1000
is equal to:
(c) 1700 (d) 2000
[CDS 2015(II)]
9 13 44. The base of an isosceles triangle is 300 unit
(a) 1 m (b) 1 m
22 22 and each for its equal sides is 170 units.
5 7 Then the area of the triangle is:
(c) 2 m (d) 2 m
11 11 [CDS 2016(I)]
(a) 9600 square units
38. A square is inscribed in a right triangle with (b) 1000 square units
legs x and y and has common right angle (c) 12000 square units
with the triangle. The perimeter of the (d) None of the above
square is given by:
[CDS 2015(II)] 45. Four equal disc are placed such that each
2xy 4xy one touches two others. If the area of empty
(a) (b) space enclosed by them is 150/847 square
x y x y
centimeter, then the radius of each disc is
2xy 4xy equal to:
(c) (d)
x y
2 2
x y
2 2 [CDS 2016(I)]
(a) 7/6 cm (b) 5/6cm
(c) 1/2cm (d) 5/11cm
39. The area of a trapezium is 336 cm2. If is
parallel sides are in the ratio 5:7 and the 46. A square is inscribed in a right-angled
perpendicular distance between them is triangle with legs p and q, and has a
14cm, then the smaller of the parallel sides common right angle with the triangle. The
is: diagonals of the square is given by:
[CDS 2015(II)] [CDS 2016(I)]
(a) 20cm (b) 22cm
pq pq
(c) 24cm (d) 26cm (a) (b)
p  2a 2p  q
40. ABCD is a square. If the sides AB and CD 2 pq 2 pq
are increased by 30%, sides BC and AD are (c) (d)
pq pq
increased by 20%, then the area of the
resulting rectangle exceeds the area of the
square by: 47. A circle of 3m radius is divided into three
[CDS 2015(II)] areas by semicircles of radii 1m and 2m as
(a) 50% (b) 52% shown in the figure above. The ratio of the
(c) 54% (d) 56% three areas A, B and C will be:

41. From a rectangular sheet of sides 18 cm and [CDS 2016(I)]

14cm, a semicircular portion with smaller
side as diameter is taken out. Then the area
of the remaining sheet will be:
[CDS 2015(II)]
(a) 98cm2 (b) 100cm2 (a) 2:3:2 (b) 1:1:1
(c) 108cm2 (d) 175cm2 (c) 4:3:4 (d) 1:2:1

42. A square and an equilateral triangle have 48. AD is the diameter of a circle with area 707
equal perimeter. If the diagonal of the square m 2 and AB = BC = CD as shown in the figure

above. All curves inside the circle are

is 12√2 cm, then the area of the triangle is:
semicircles with their diameters on AD.
[CDS 2015(II)]
What is the cost of leveling the shaded
(a) 24√2 (b) 24√3 region at the rate of 63 per square meter?
(c) 48√3 (d) 64√3 [CDS 2016(I)]

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 54. What is the number of round that a wheel of
5
diameter m will make in traversing 7km?
11
[CDS 2016(II)]
(a) 3300 (b) 3500
(c) 4400 (d) 4900

55. If a quadrilateral has an inscribed circle,

then the sum of a pair of opposite sides
(a) 29,700
equal.
(b) 22,400
[CDS 2016(II)]
(c) 14,847
(a) Half the sum of the diagonals
(d) None of the above
(b) Sum of the other pair of opposite sides
(c) Sum of two adjacent sides
49. If a square of side x and an equilateral
(d) None of the above
triangle of side y are inscribed in a circle,
then what is the ratio of x to y?
56. The wheel of a car are of diameter 80cm
[CDS 2016(II)]
each. The car is travelling at a speed of
(a)
2
(b)
3 66km/hr. What is the number of complete
3 2 revolutions each wheel makes in 10
minutes?
3 2
(c) (d) [CDS 2016(II)]
2 3 (a) 4275 (b) 4350
(c) 4375 (d) 4450
50. A circle and a square have the same
perimeter. Which one of the following is 57. If the perimeter of a circle is equal to that of
correct? a square, then what is the ratio of area of
[CDS 2016(II)] circle to that of square?
(a)The areas are equal [CDS 2016(II)]
(b)The area of the circle is larger (a) 22:7 (b) 14:11
 (c) 7:22 (d) 11:14
(c)The area of the square is times area of
2
circle 58. If the perimeter of a rectangle is 10 cm and
(d)The area of the square is  times are of the area is 4cm2, then its length is:
circle [CDS 2017(I)]
(a) 6cm (b) 5cm
51. What is the area of a triangle with sides of (c) 4.5cm (d) 4cm
length 12cm, 13cm and 5cm?
[CDS 2016(II)] 59. The areas of two circular field are in the
(a) 30cm 2 (b) 35cm2 ratio 16:49. If the radius of the bigger field is
(c) 40cm 2 (d) 42cm 2 14m, then what is the radius of the smaller
field?
52. What is area of largest triangle inscribed in a [CDS 2017(I)]
semi circle of radius r units? (a) 4m (b) 8m
[CDS 2016(II)] (c) 9m (d) 10m
(a) r2 square units (b) 2r2 square units
(c) 3r2 square unit (d) 4r2 square unit 60. The area of a regular hexagon of side ‘a’ is
equal to:
53. The diameter of the front wheel of an engine [CDS 2017(I)]
is 2x cm and that of rear wheel is 2y cm. To 2 2
cover the same distance, what is the number (a) a square units
3
of times the rear wheel revolves when front
wheel revolves n times? 3 3 2
(b) a square units
[CDS 2016(II)] 2
(a) n/xy (b) ny/x 1
(c) a2 square units
(c) nx/y (d) xy/n 3

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 3 2 smaller circle, then what must be the angle
(d) a square units A?
2
[CDS 2017(II)]
(a) 45° (b) 60°
61. If each of the dimensions of a rectangle is
(c) 75° (d) 90°
increased by 200%, the area is increased by:
[CDS 2017(I)]
68. The diameters of two given circles are in the
(a) 300% (b) 400%
ratio 12:5 and the sum of their areas is
(c) 600% (d) 800%
equal to the area of a circle of diameter
65cm. What are their radii?
62. Three circles each of radius 3.5 cm touch
[CDS 2017(II)]
one another. The area subtended between
(a) 12cm and 5cm
them is:
(b) 24cm and 10cm
[CDS 2017(I)]
(c) 60 cm and 25cm
(a) 6( 3  2) (b) 6(2  3 ) (d) 30cm and 12.5cm
49 49
(c) (2 3   ) (d) ( 3  ) 69. Segment QR of length r is a tangent at Q to a
8 8 circle of radius r with center at P. What is
the area of the part of the triangle PQR,
63. A copper wire when bent in the form of a which is outside the circular region?
square encloses an area of 121 cm. If the [CDS 2017(II)]
same wire is bent in the form of a circle, it r 2
r 2
r 2
encloses an area equal to (a) (b) 
[CDS 2017(I)] 16 2 8
(a) 121 cm2 (b) 144 cm2 r 2
r 2
r 2
r 2
(c)  (d) 
(c) 154 cm2 (d) 168 cm2 2 16 4 8

64. The radius of a circle is increased so that it's 70. If the length of a side of a square is
circumference increases by 15%. The area of increased by 8cm, its area increases by 120
the circle will increase by square cm. What is the length of a side of
[CDS 2017(I)] the square?
(a) 31.25% (b) 32.25% [CDS 2018(I)]
(c) 33.25% (d) 34.25% (a) 2.5cm (b) 3.5cm
(c) 4.5cm (d) 5.5cm
65. An isosceles triangle is drawn outside on one
of the sides of a square as base in such a 71. A rectangular pathway having width 4.5m
way that the perimeter of the complete figure and length 10m will have to be titled using
7 square tiles of side 50cm. Each packet of
is times the perimeter of the original
6 such tiles contains 20 pieces and costs
square. What is the ratio of area of the Rs100. What will be the total cost of tiles for
triangle to the area of the original square? the pathway?
[CDS 2017(II)] [CDS 2018(I)]
(a) 1:1 (b) 2:2 (a) Rs 1,200 (b) Rs 1,100
(c) 1:2 (d) 1:3 (c) Rs 1,000 (d) Rs 900

66. What is the area of the triangle whose sides 72. The product of the length of the diagonals of
are 51 cm, 37cm and 20cm? a square is 50 square units. What is the
[CDS 2017(II)] length of a side of the square?
(a) 300 square cm (b) 305 square cm [CDS 2018(I)]
(c) 306 square cm (d) 307 square cm (a) 5 2 units (b) 5 units
(c) 10 units (d) 2 5 units
67. Two straight lines AB and AC include an
angle. A circle is drawn in this angle which
touches both these lines. One more circle is 73. Two equal circular regions of greatest
drawn which touches both these lines as possible area are cut off from a given
well as the previous circle. If the area of the circular sheet of area A. What is the
bigger circle is 9 times the area of the remaining area of the sheet?

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 [CDS 2018(I)]
79. If base and hypotenuse of a right triangle are
(a) A/2 (b) A/3 (u2 – v2) and (u2 + v2) respectively and the
(c) 3A/5 (d) 2A/5
area of the triangle is 2016 square units,
74. A square and an equilateral triangle have then the perimeter of the triangle may be:
the same perimeter. If the diagonal of the [CDS 2018(II)]
(a) 224 units (b) 288 units
square is 6√2 cm, the what is the area of the
(c) 448 units (d) 576 units
triangle?
[CDS 2018(I)]
80. Let S be the parallelogram obtained by
(a) 12√2 cm2 (b) 12√3 cm2
joining the mid points of the parallelogram
(c) 16√2 cm2 (d) 16√3 cm2
T. Consider the following statements:
75. What is the area of the region bound 1.The ratio of area of T to that of S is 2 : 1
externally by a square if side of length ‘a’ 2.The perimeter of S is half of the sum of
and internally by a square of side of length diagonals T
‘a’ and internally by a circle passing Which of the above statements is/are
through the four corners of the square? correct?
[CDS 2018(I)] [CDS 2018(II)]
(a) (𝜋 − 1)𝑎2 square units (a) 1 only (b) 2 only
(𝜋−1)𝑎2 (c) Both 1 and 2 (d) Neither 1 nor 2
(b) square units
2
(c) (𝜋 − 2)𝑎2 square units
(𝜋−2)𝑎2 81. The sides of a triangle are 5 cm, 6 cm and 7
(d) square units
2 cm. The area of the triangle is
approximately:
76. A region of area A bounded by a circle C is [CDS 2018(II)]
divided into n regions, each of area A/n by
(a) 14.9cm 2 (b) 14.7cm2
drawing circle of radii r1, r2, r3,... rn–1 such
that r1 < r2 < r3 < ... rn–1 concentric with the (c) 14.5 cm2 (d) 14.3 cm2
r
circle C. If pm = m 1 where m =1, 2, 3 ,... (n– 82. There is a path of width 5 m around a
rm
2),then which one of the following is correct? circular plot of land whose area is 144 m2.
[CDS-2018-1] The total area of the circular plot including
(a)p increases as m increases the path surrounding it is:
(b)p decreases as m increases [CDS 2018(II)]
(c)p remains constant as m increases (a) 349m2 (b) 289m2
(d)p increases for some values of m as m
(c) 209m2 (d) 149m2
increases and then decreases thereafter
83. An equilateral triangle, a square and a circle
77. A wire is in the form of a circle of radius
have equal perimeter. If T, S and C denote
98cm. A square is formed out of the wire.
What is the length of a side of the square? the area of the triangle, area of the square
(Use  =22/7) and area of the circle respectively, then
[CDS-2018-1] which one of the following is correct?
(a) 146cm (b) 152cm [CDS 2018(II)]
(c) 154cm (d) 156cm (a) T < S < C (b) S < T < C
(c) C < S < T (d) T < C < S
78. What is the area of the largest circular disc
2
cut from a square of side units? 84. The area of the region bounded externally by
 a square of side 2a cm and internally by the
[CDS-2018-1] circle touching the four sides of the square
(a)  square units (b) 1 square unit
is:
(c) 2 square units (d) 2 square units

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 [CDS 2018(II)] (c) 405cm2 (d) 769.5cm2
(a)(4–)a2 (b) (–2)a2 88. In the figure given below, ABCD is a square
(c) (8–)a2/2 (d) (–2)a2/2 of side 4 cm. Quadrants of a circle of
diameter 2 cm are removed from the four
85. In the figure given below, ABC is a right- corners and a circle of diameter 2 cm is
angled triangle where A = 90°, AB = p cm also removed. What is the area of the
and AC = q cm. On the three sides as shaded region?
D C
diameters semicircles are drawn as shown in
the figure. The area of the shaded portion, in
square cm, is:
A

B C
A B
[CDS 2018(II)] [CDS 2018(II)]
(a) pq (b) (p + q2)/2
2
7 7
(c) (p2 + q2) (d) pq/2 (a) 5 cm2 (b) 7 cm2
9 9
5 5
86. In the figure given below, ABCD is the (c) 9 cm 2 (d) 9 cm2
diameter of a circle of radius 9 cm. The 9 6
lengths AB, BC and CD are equal.
Semicircles are drawn on AB and BD as 89. In a rectangle, length is three times its
diameters as shown in the figure. What is breadth. If the length and the breadth of
the area of the shaded region? the rectangle are increased by 30% and
10% respectively, then its perimeter
increases by :
[CDS 2019(I)]

A B
.
C
D (a)
40
3
% (b) 20%

(c) 25% (d) 27%

90. What is the percentage decrease in the area

[CDS 2018(II)] of a triangle if its each side is halved?
(a) 9 (b) 27 [CDS 2019(I)]
(c) 36 (d) 81 (a) 75% (b) 50%
(c) 25% (d) No change
87. In the figure given below, the diameter of
bigger semicircle is 108cm. What is the 91. Considering two opposite vertices of square
area of the shaded region? of side ‘a’ as centres, two circular area are
drawn within the square joining the other
two vertices, thus forming two sectors.
What is the common area in these two
sectors?
[CDS 2019(I)]
 1  1
(a) a2     (b) a2    
54cm 54cm  2  2
[CDS 2018(II)]
(a) 201cm2 (b) 186.3 cm2

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    
(c) a2   1 (d) a2   1
 2   2  98. The perimeter of a triangle is 22cm.
Through each vertex of the triangle, a
straight line parallel to the opposite side is
92. A rectangular red carpet of size 6ft  12 ft
drawn. What is the perimeter of triangle
has a dark red border 6 inches wide. What
formed by these lines?
is the area of the dark red border?
[CDS 2019(II)]
[CDS 2019(I)]
(a) 33cm (b) 44cm
(a) 9 square feet (b) 15 square feet
(c) 66cm (d) 88cm
(c) 17 square feet (d) 18 square feet

99. The sides AD, BC of a trapezium ABCD are

93. A 12 m long wire is cut into two pieces, one
parallel and the diagonals AC and BD meet
of which is bent into a circle and the other
O. If the area of triangle AOB is 3 cm 2 and
into a square enclosing the circle. What is
the area of triangle BDC is 8cm2, then what
the radius of the circle?
is the area of triangle AOD?
[CDS 2019(I)]
[CDS 2019(II)]
12 6
(a) (b) (a) 8cm2 (b) 5cm2
 4  4 (c) 3.6cm2 (d) 1.8cm2
3 6
(c) (d)
 4  2 2 100. An equilateral triangle and a square are
constructed using metallic wires of equal
94. The hypotenuse of a right-angled triangle is length. What is the ratio of area of triangle
10 cm and its area is 24 cm . If the shorter
2 to that of square?
side is halved and the longer side is [CDS 2019(II)]
doubled, the new hypotenuse becomes: (a) 3:4 (b)2:3
[CDS 2019(I)] (c) 4 3 : 9 (d) 2 3 : 9
(a) 245cm (b) 255cm
(c) 265cm (d) 275cm 101. All the four sides of a parallelogram are of
equal length. The diagonals are in the ratio
1:2. If the sum of the lengths of the
Direction (for next three): ABCD is a
diagonals is 12cm, then what is the area of
quadrilateral with AB = 9cm, BC = 40cm,
the parallelogram?
CD = 28cm, DA = 15 cm and angle ABC is a
[CDS 2019(II)]
right angle.
(a) 9cm2 (b) 12cm2
95. What is the area of triangle ADC?
(c) 16cm2 (d) 25cm2
[CDS 2019(I)]
(a) 126cm2 (b) 124cm2
102. The length and breadth of a rectangle are
(c) 122cm2 (d) 120cm2
increased by 20% and 10% respectively.
What is the percentage increase in the area
96. What is the area of quadrilateral ABCD?
of the rectangle?
[CDS 2019(I)]
[CDS 2019(II)]
(a) 300cm2 (b) 306cm2
(a) 32% (b) 30%
(c) 312cm2 (d) 316cm2
(c) 25% (d) 15%
97. What is the difference between perimeter of
103. A square is drawn such that its vertices are
triangle ABC and perimeter of triangle
lying on a circle of radius 201 mm. What is
ADC?
the ratio of area of circle to that of square?
[CDS 2019(I)]
[CDS 2019(II)]
(a) 4cm (b) 5cm
(a) 11:7 (b) 7:11
(c) 6cm (d) 7cm

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 (c) 20:19 (d) 19:20  
(c) (d)
2 4
104. What is the ratio of the area of a square 110. A square and a rectangle have equal areas.
inscribed in a semicircle of radius r to the If one side of the rectangle is of length
area of square inscribed in a circle of radius numerically equal to the square of the
r? length of the side of the square then the
[CDS 2019(II)] other side of the rectangle is:
(a) 1:2 (b) 2:5 [CDS 2020(I)]
(c) 2:3 (d) 3:5 (a) Square root of the side of the square
(b) Half the side of the square
105. The area of a sector of a circle of radius (c) Of unit length
4cm is 25.6cm2. What is the radian (d) Double the side of the square
measure of the arc of the sector?
[CDS 2019(II)] 111. The length and breadth of a rectangle are in
(a) 2.3 (b) 3.2 the ratio 4:3. Then what is the ratio of the
(c) 3.3 (d) 3.4 area of the triangle formed by the parts of
the diagonals with a long side to the area of
106. What is the area of the triangle having side the triangle formed by the parts of
y z z x x y
lengths  ,  ,  ? diagonals with a short side?
z x x y y z [CDS 2020(I)]
[CDS 2020(I)] (a) 3:4 (b) 4:3
(c) 16:9 (d) 1:1
 x  y  z 2
xyz
(a) (b)
xyz x yz 112. Suppose a region is formed by removing a
x y z xy  yz  zx sector of 20° from a circular region of
(c)   (d) radius 30 feet. What is the area of this new
y z x xyz
region?
[CDS 2020(I)]
107. If the angles of a triangle are 30° and 45°
(a) 150 square feet (b) 550 square feet
and the included side is 
3  1 cm , then 
(c) 650 square feet (d) 850 square feet
what is the area of the triangle?
[CDS 2020(I)] 113. If the diagonals of a rhombus are x and y,
(a) 3  1 cm2 (b) 
3  3 cm2  then what is its area?
[CDS 2020(I)]

(c)
1
2

3  1 cm 2 (d) 2 3  1 cm2 
(a)
xy
2
(b)
xy
4
(c) xy (d) x2–y2
108. Two circles touch internally. The sum of
their areas is 136 cm2 and distance 114. What is the area of the largest square plate
between their centres is 4cm. What are the cut from a circular disk of radius one unit?
radii of the circles? [CDS 2020(I)]
[CDS 2020(I)] (a) 4 square units (b) 2 2 square units
(a) 11cm, 7cm (b) 10cm, 6cm (c)  square units (d) 2 square units
(c) 9cm, 5cm (d) 8cm, 4cm
115. ABCD is a quadrilateral such that AD = DC
109. If area of a circle and a square are same, = CA = 20 units, BC = 12 units and ABC =
then what is the ratio of their perimeters? 90°. What is the approximate area of the
[CDS 2020(I)] quadrilateral ABCD?
(a) 2  (b)  [CDS 2020(I)]

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 (a) 269 sq. units (b) 300 sq. units In the given figure, what is the area of the
(c) 325 sq. units (d) 349 sq. units shaded region?
116. [CDS 2020(I)]
 
(a) 9   3 squareunits

(b) 3  4  3 3  square units

P Q
. R
S
(c) 3  3  4 3  squareunits

(d) 9  3    squareunits

Let PQRS be the diameter of a circle of 119. ABCD is a trapezium, where AB is parallel
radius 9 cm. The length PQ, QR and RS are to DC. If AB = 4cm, BC = 3cm, CD = 7cm
equal. Semi-Circle is drawn with QS as and DA = 2cm, then what is the area of the
diameter (as shown in the given figure). trapezium?
What is the ratio of the shaded region to [CDS 2020(I)]
that of the unshaded region? 2 3
[CDS 2020(I)] (a) 22 cm2 (b) 22 cm2
3 2
(a) 25:121 (b) 5:13
(c) 5 : 18 (d) 1:2 22 2
(c) 22 3 cm2 (d) cm2
3
117.
120.

A B

8 cm

6 cm 6 cm
C

8 cm

What is the area of the shaded region in the

given figure, if the radius of each of the
circles is 2cm? What is the approximate area of the shaded
[CDS 2020(I)] region in the figure given?
[CDS 2020(I)]
(a) 4 3  2cm
2
(b) 3   cm2
(a) 15.3cm2 (b) 25.5cm2

(c) 3 cm 2 (d) 2  2 3 cm2 (c) 28.4cm2 (d) 30.5cm2
2
121. A circle of diameter 8cm is placed in such a
118. manner that it touches two perpendicular
lines. Then another smaller circle is placed
in the gap such that it touches the lines
6 3units and the circle. What is the diameter of the
smaller circle?
6 units 6 units [CDS 2020(I)]
6 3units  
(a) 4 3 2 cm  
(b) 4 3 2 2 cm

(c) 8 3 2 cm (d) 8 3 2 2  cm

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122. 127. Areas of two squares are in the ratio m2:n4,
what is the ratio of their perimeter?
[CDS 2020(II)]
(a) m : n (b) n : m
(c) m : n2 (d) m2 : n

128. Four circular coins of equal radius are

placed with their centres coinciding four
vertices of a square. Each coin touches two
other coins. If the uncovered area of the
In the given figure, there are three semi
square is 42 cm2 , then what is the radius
circle ABC, AEF and CDF. The distance
of each coin
between A and C is 28 units and F is the
[CDS 2020(II)]
midpoint of AC. What is the total area of the
(a) 5 cm (b) 7 cm
three semi circles?
(c) 10 cm (d) 14 cm
[CDS 2020(I)]
(a) 924 square units (b) 824 square units
129. A sector is cut from a circle of radius 21
(c) 624 square units (d) 462 square units
cm. If the length of the arc of the sector is
55cm, then what is the area of the sector?
123. The two sides of a triangle are 40cm and
[CDS 2021(I)]
41cm. If the perimeter of the triangle is
(a) 577.5cm2 (b) 612.5 cm2
90cm, what is its area?
(c) 705.5 cm2 (d) 725.5 cm2
[CDS 2020(II)]
(a) 90 cm2 (b) 135 cm2
130. A wire is in the form of a circle of radius 70
(c) 150 cm 2 (d) 180 cm2
cm. If it is bent in the form of a rhombus,
124. The diagonals of a rhombus differ by 2  22 
then what is its side length?  Take   .
units and its perimeter exceeds the sum of  7 
the diagonals by 6 units. What is the area [CDS 2021(I)]
of the rhombus? (a) 55cm (b) 75cm
[CDS 2020(II)] (c) 95cm (d) 110cm
(a) 48 square units (b) 36 square units
(c) 24 square units (d) 12 square units 131. If the perimeter of a semicircular park is
 22 
360m, then what is its area?  Take  
125. The length of a rectangle is increased by  7 
10% and breadth is decreased by 10%. [CDS 2021(I)]
Then the area of new rectangle is (a) 3850 m2 (b) 7700m2
[CDS 2020(II)] (c) 11550 m2 (d) 15400 m2
(a) neither increased nor decreased
(b) increased by 1% 132. The radius of circum-circle of a right angled
(c) decreased by 1% triangle is 10cm and the altitude drawn to
(d) decreased by 10% the hypotenuse is 8cm. What is the area of
the triangle?
126. If the perimeter of a circle and square are [CDS 2021(II)]
equal , then what is the ratio of the area of (a) 60cm2 (b) 80cm2
the circle to that of the square ? (c) 100cm2 (d) 120cm2
[CDS 2020(II)]
(a) 1 : π (b) 2 : π 133. Two circles touch externally. The sum of
(c) 3 : π (d) 4 : π their areas is 41 square cm. If the distance

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 between their centres is 9cm, then what is [CDS 2021(II)]
difference between their diameters? (a) 80m (b) 84m
[CDS 2021(II)] (c) 90m (d) 100m
(a)1cm (b) 1.5cm
(c) 2cm (d) 4cm 140. A bicycle wheel of radius 35cm makes n
revolutions in moving 11km. What is the
134. Let p be the area of a square X and q be the 22
value of n? (take  = )
7
area of the square formed on the diagonal
𝑝
[CDS 2022(I)]
of the square X. What is the value of ? (a) 500 (b) 1000
𝑞
[CDS 2021(II)] (c) 2500 (d) 5000

1 1 141. A farmland is in the shape of a rhombus.

(a) (b)
8 4 The perimeter of the land is 100 m and the
1 1 length of one of the diagonals is 40m. The
(c) (d)
3 2 land is divided into four equal parts. What
is the area of each part?
135. The area of a rhombus is 336 square cm. If
[CDS 2022(I)]
the length of one of its diagonals is 48cm, (a) 150 square meter
then what is the perimeter of the rhombus? (b) 225 square meter
[CDS 2021(II)] (c) 300 square meter
(a) 200cm (b) 120cm (d) 450 square meter
(c) 100cm (d) 90cm
142. If the perimeter of an isosceles right triangle
136. The minute hand of a clock is 21cm long. is 4(2 +√2)cm, then what is its area in
What is the area on the face of the clock square cm?
described by the minute hand between [CDS 2022(I)]
22
10.10 a.m and 10.30 a.m.? (take = ). (a) 8 (b) 12
7
[CDS 2021(II)] (c) 16 (d) 24
(a) 231 cm2 (b) 331 cm2
(c) 462 cm2 (d) 492 cm2 143. A rectangle of length 10 units and breadth
8 unit is split into two squares each of area
Consider the following for the next two x square units and two rectangles each of
(02) items that follow: area y square units. Consider the following
A chord of a circle of radius 2.1 cm statements:
subtends an angle of 120° at the centre. 1.y is always greater than x
22
(take  = 𝑎𝑛𝑑 √3 = 1.732) 2.y can be 15 square units.
7
137. What is the approximate area of minor Which of the above statement is/are
segment of the circle? correct?
[CDS 2022(I)]
[CDS 2021(II)]
(a) 1 only (b) 2 only
(a) 2.71 cm 2 (b) 2.42 cm 2
(c) Both 1 and 2 (d) Neither 1 nor 2
(c) 1.91 cm2 (d) 1.71 cm2
144. A square sheet is formed by joining n
138. What is the approximate area of major
identical square sheets of same size. If the
segment of the circle?
length of the diagonal of the bigger square
[CDS 2021(II)]
(a) 10.05 cm2 (b) 10.15 cm2 sheet so formed is m, then what is the side
(c) 11.05 cm2 (d) 11.15 cm2 length of a smaller square sheet?
[CDS 2022(I)]
139. A person wishes to fence 375 m2 m m
(a) (b)
rectangular garden. He has 65m of barbed n 2 n
wire and is able to fence only three sides of
m 2m
the garden. What is the perimeter of the (c) (d)
2n n
garden?

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 each is of length 8.5 cm. What is the area of
145. What is the area of the region enclosed by the trapezium?
three identical circles (each of radius 4cm) [CDS 2022 (II)]
touching each other? (a) 187.5 square cm
(b) 227.5 square cm
[CDS 2022(I)]
(c) 375 square cm
8 (d) 455 square cm
(a) square cm
3
 8  151. A square copper plate of side 16cm weighs
(b) 16 3   square cm
 3  128 gm. A circular disc of diameter 14 cm
is cut off from the plate. What is the weight
 
(c) 16 3  8 square cm of the remaining part? ( =
22
7
)
16 [CDS 2022 (II)]
(d) square cm (a) 48gm (b) 49gm
3 (c) 50gm (d) 51gm

146. X, Y and Z are three equilateral triangles. 152. The area of a rhombus is 96 square cm and
The sum of the areas of X and Y is equal to one of its diagonals is of length 12cm. What
the area of Z. If the side lengths of X and Y is the perimeter of the rhombus?
are 6cm and 8cm respectively, then what is [CDS 2022 (II)]
the side length of Z? (a) 36cm (b) 40cm
[CDS 2022 (II)] (c) 44cm (d) 48cm
(a) 9cm (b) 9.5cm
(c) 10cm (d) 10.5cm 153. Two circles touch externally. The sum of
their areas is 89 square cm and the
147. What is the time taken by a person to cover distance between their centres is 13cm.
one round of a circular park of diameter What is the difference in their radii?
210 m if he walks at a speed of 6km/hr? [CDS 2022 (II)]
22
(= ) (a) 2cm (b) 2.5cm
7
[CDS 2022 (II)] (c) 3cm (d) 3.5cm
(a) 6.6 minutes (b) 5.5 minutes
(c) 4.4 minutes (d) 3.3 minutes 154. A square and a rectangle have same
perimeter. They differ in areas by 1 square
148. In an equilateral triangle of side 2√3 cm, a cm. The length of the rectangle exceeds its
circle is inscribed touching the sides. What breadth by:
is the area of the remaining portion of the [CDS 2022 (II)]
triangle? (a) 1cm (b) 2cm
(c) 3cm (d) 4cm
[CDS 2022 (II)]
(a) (2√3 − ) square cm 155. Two rectangles are of same area equal to
(b) (3√3 − ) square cm 480 square cm. They differ in lengths by
(c) (4√3 − 2) square cm 6cm and breadths by 4cm. What is the
(d) (4√3 − ) square cm
difference in their perimeters?
149. A triangle has side lengths x cm, x + 13cm [CDS 2022 (II)]
(a) 2cm (b) 4cm
and x + 26cm. If its area is 126 square cm,
(c) 6cm (d) 10cm
then what is the value of x?
[CDS 2022 (II)] Consider the following for the next two
(a) 18 (b) 17 (02) items that follow:
(c) 16 (d) 15 A chord of length l of a circle makes an
angle 90° at the centre of the circle.
150. Two parallel sides of a trapezium are 29cm
and 21cm. Non-parallel sides are equal and 156. What is the area of the minor segment?

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 [CDS 2022 (II)] In the following figure, a rectangle ABCD is
l 2
 1 l 2
1 inscribed in a circle of radius r. given DAE
(a)    (b)    = 30° and ACD = 30°.
2  2 4  2
l2   l2  1
(c)   1 (d)   
4 2  2  2 2

157. What is the area of the major segment?

[CDS 2022 (II)]
2 2
l  3  l  3 
(a)   1 (b)   1
4  2  4  2 
l 2  3  l 2  3  161. What is the ratio of the area of the circle to
(c)   1 (d)   1
2  2  2  2  the area of the rectangle?
[CDS – 2023 (1)]
Consider the following for the next three  
(a) (b)
(03) items that follow: 2 3
In the figure given below, a circle is 2 3
inscribed in a square PQRS. A rectangle at (c) (d)
the corner P that measures 4cm  2cm and 3 2
a square at the corner R are drawn.
162. What is the area of AEC?
[CDS – 2023 (1)]
r2 r2
(a) (b)
3 2 3
2
r 3r 2
(c) (d)
3 3 3

163. The plinth of a house has an area of 200

square metres. It is rectangular in shape
158. What is the area of the circle? and its length and breadth are in the ratio
[CDS – 2023 (1)] 2:1. The owner of the house extends the
(a)100 square cm (b) 96 square cm
terrace by 1 m on each side. What is the
(c) 50 square cm (d) 48 square cm
percentage of area that has increased in the
159. What is the area of the smaller square? terrace relative to the plinth?
[CDS – 2023 (1)] [CDS – 2023 (1)]
(a) 50 (3–2) square cm (a) 40% (b) 32%
(b) 25 (3–22) square cm (c) 20% (d) 15.5%
(c) 25 (3+22) square cm
164. A square sheet of side length 44 cm is
(d) 50 (3 – 22) square cm
rolled along one of its sides to form a
160. What is the area of the shaded region? cylinder by making opposite edges just to
[CDS – 2023 (1)] touch each other. What is the volume of the
22
(a) (96–25) square cm cylinder? (Take  = ).
7
(b) (92–25) square cm [CDS – 2023 (1)]
(c) (96–16) square cm (a) 6776 cubic cm (b) 6248 cubic cm
(d) (92–16) square cm (c) 5896 cubic cm (d) 5680 cubic cm
Consider the following for the next two 165. The perimeter and the area of a right-
(02) items that follow:
angled triangle are 36 cm and 54 square

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 cm respectively. What is the length of the 172. What is the maximum area that can be
hypotenuse? covered by three non-intersecting circles
[CDS – 2023 (1)] drawn inside a rectangle of sides 8 cm and
(a) 12cm (b) 14cm 12cm?
(c) 15cm (d) 16cm [CDS – 2023 (1)]
(a) 16 square cm (b) 18 square cm
166. The perimeter of a sector of a circle of (c) 20 square cm (d) 24 square cm
radius 5.2cm is 16.4 cm. What is the area
of the sector? 173. A triangle ABC has been divided into four
[CDS – 2023 (1)] smaller triangles P, Q, R, S whose
(a) 15.6 square cm (b) 15 square perimeters are 16cm, 12cm, 4cm and 12cm
(c) 14.4 square cm (d) 14.1 square cm respectively. P, R and S contain the vertices
A, B and C respectively. What is the
167. What is the area of the circle
perimeter of the triangle ABC?
(approximately) inscribed in a triangle with
[CDS – 2023 (1)]
side lengths 12cm, 16cm and 20cm?
(a) 18cm (b) 20cm
[CDS – 2023 (1)] (c) 22cm (d) 24cm
(a) 48 square cm (b) 50 square cm
(c) 52 square cm (d) 54 square cm 174. OABC is a rhombus whose three vertices lie
on a circle with centre at O. If the area of
168. A floor of a big hall has dimensions 30m
60cm and 23m 40cm. Its is to be paved the rhombus is 323 square cm, then what
with square tiles of same size. What is the is the radius of the circle?
minimum number of tiles required? [CDS – 2023 (1)]
(a) 4cm (b) 6cm
[CDS – 2023 (1)]
(c) 8cm (d) 16cm
(a) 30 (b) 36
(c) 169 (d) 221
175. Question: What is the area of the circle C?
169. How long will a man take to walk around Statement I: an arc of length 7 cm subtends
an angle 30° at the centre of C.
the boundary of a square field of area 25
Statement II: A chord of length 10cm
hectares at the rate of 5km/hr? subtends an angle 90° at the centre of C.
[CDS – 2023 (1)] [CDS – 2023 (1)]
(a) 36 minutes (b) 30 minutes (a)choose this option if the question can be
(c) 24 minutes (d) 18 minutes answered by one of the statements alone
but not by the other.
170. Let x be the area of a square inscribed in a (b)choose this option if the question can be
circle of radius r and y be the area of an answered by either statement alone.
equilateral triangle inscribed in the same (c)Choose this option if the question can be
circle. Which one of the following is correct? answered by using both the statements
together, but cannot be answered by using
[CDS – 2023 (1)]
either statement alone
(a) 9x2 = 16y2 (b) 27x2 = 64y2
(d)Choose this option if the question cannot
(c) 36x2 = 49y2 (d) 16x2 = 21y2
be answered even by using both statements
together.
171. If the length of a rectangle is increased by
2
66 %, then by what percent should the 176. A chord PQ of the circle C divides it into two
3 segments such that 3 times the area of the
width of the rectangle be decreased in order major segment is 4 times the area of the
to maintain the same area? minor segment.
[CDS – 2023 (1)] Question: What is the radius of C?
(a) 50% (b) 45% Statement I: Area of the minor segment is
(c) 40% (d) 35% 66 square cm.
Statement II: Area of the major segment is
88 square cm.

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 [CDS – 2023 (1)] 182. The circumference of a circle exceeds the
(a)choose this option if the question can be diameter by 16.8 cm. What is the diameter
answered by one of the statements alone 22
the circle? (Take  = )
7
but not by the other.
[CDS-2023 (2)]
(b)choose this option if the question can be
(a) 6.24cm (b) 6.42cm
answered by either statement alone.
(c) 7.64cm (d) 7.84cm
(c)Choose this option if the question can be
answered by using both the statements
183. What is the area of the region between the
together, but cannot be answered by using
concentric circles if the chord of the out
either statement alone
circle of length 14cm is a tangent of the inn
(d)Choose this option if the question cannot 22
be answered even by using both statements circle? (Take = )
7
together. [CDS-2023 (2)]
(a) 125 square cm (b) 132 square cm
177. An isosceles triangle has its base length 2a (c) 144 square cm (d) 154 square cm
and its height is h. On each side of the
triangle a square is drawn external to the Consider the following for the next two
triangle. What is the area of the figure thus (02) items that follow:
formed? A line segment AB is bisected at C and semi
[CDS-2023 (2)] circles S1, S2 and S3 are drawn respectively
(a) 6a2 + 2h2 + 2ah (b) 6a2 + 2h2 + ah on AB, AC and CB as diameters such that
(c) 4a2 + 2h2 + ah (d) 6a2 + h2 + ah they all lie on same side of AB. A circle S is
drawn touching internally S1 and externally
178. A pendulum swings through an angle of 9° S2 and S3.
and its end describes an are of length
14.3cm. What is the length of the 184. If r is the radius of S and R is the radius of
pendulum? (Take = )
22 S2, then which one of the following is
7 correct?
[CDS-2023 (2)]
[CDS-2023 (2)]
(a) 88cm (b) 91cm
(a) R=3r (b) R=2r
(c) 95cm (d) 98cm
(c) 3R=4R (d) 2R=3r
179. The corners of an equilateral triangular
185. If m is the area of the circle S and n is the
plate were cut in such a manner that it
area of semi-circle S1, then which one of the
forms a regular hexagonal plate. What is
following is correct?
the ratio of the area of the triangular plate
[CDS-2023 (2)]
to the area of the hexagonal plate?
(a) 9m=2n (b) 9m=4n
[CDS-2023 (2)]
(c) 3m=2n (d) 7m=3n
(a) 2:1 (b) 3:2
(c) 4:3 (d) 5:3
Consider the following for the next three
(03) items that follow:
180. Two equal arcs of different circles C1 and C2
Consider two identical semicircles and one
subtend angles of 60° and 75° respectively,
circle inscribed in a rectangle of length 10
at the centres. What is the ratio of the
cm as shown in the figure given below.
radius of C1 to the radius of C2? D O C
[CDS-2023 (2)]
(a) 4:5 (b) 5:4
(c) 1:1 (d) 3:2 P

181. ABC is a triangle with sides AB = 41cm, BC E F

= 28cm and CA = 15cm. If D, E and F are
Q
the mid points of AB, BC and CA
respectively, then what is the area of the
triangle DEF? A B
[CDS-2023 (2)]
(a) 63 square cm (b) 45 square cm
(Take  = 3.14 and 2  1.4 )
(c) 31.5 square cm (d) 22.5 square cm [CDS-2024 (1)]

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186. What is the area of triangle EOF?
(a) 12.5 3 squarecm (b) 6.25 3 squarecm
(c) 12.5 square cm (d) 6.25 square cm

187. What is the area of trapezium AEFB?

(a) 30 square cm (b) 25 square cm
(c) 20 square cm (d) 18.75 square cm

188. What is the area of the shaded region?

(a) 14.75 square cm (b) 14.25 square cm
(c) 7.225 square cm (d) 7.625 square cm [CDS-2024 (1)]
191. What is the sum of the areas of the two
Consider the following for the next two circles?
(02) items that follow: (a) 17 square unit
Consider a circle of area 9 square unit and (b) 16.75 square unit
an equilateral triangle ABC as shown in the (c) 16.5 square unit
figure given below. (d) 16.25 square unit
A
192. Which one of the following is correct in
respect of angle ?
(a) 0 <  < 30° (b) 30° <  < 45°
(c) 45° <  < 60° (d) 60° <  < 90°

193. What is the area of the shaded region?

240  10  
B C (a) square unit
[CDS-2024 (1)] 24
189. What is the length of the side of the triangle 240  6  
ABC? (b) square unit
24
(a) 2 3 unit (b) 4 3 unit 120  12  
(c) square unit
(c) 6 3 unit (d) 8 3 unit 24
240  12  
(d) square unit
190. What is the area of the shaded region? 24
(a) 6(  3) square unit
Consider the following for the next two
(b) 3(  2 3) square unit (02) items that follow:
(c) 1.5(3  8 3) square unit Let ABCD be the diameter of a circle of
radius 6 cm. The lengths AB, BC and CD
(d) 6(  2 3) square unit are equal. Semi-circles are drawn with AB
and BD as diameters as shown in the figure
Consider the following for the next three given below.
(03) items that follow:
Two circles with centres at O1 and O2
touching each other are placed inside a
rectangle of sides 9 cm and 8 cm as shown
in the figure given below:

[CDS-2024 (1)]
194. What is the ratio of the area of the shaded
region to that of the non-shaded region?
(a) 2:7 (b) 2:5
(c) 3:5 (d) 5:8

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 ABCD is a circle with centre O and taking
195. What is the perimeter of the shaded region? OC as a diameter, a circle is drawn as
(a) 24 cm (b) 18 cm shown in the figure given below. Let OB = 7
(c) 15 cm (d) 12 cm 22
cm. (use  = )
7
Consider the following for the next two
(02) items that follow:
Consider the two identical rectangles ABCD
and BEDF as shown in the figure given
below. Let AB = 1 cm and BC = 2 cm.

[CDS-2024 (1)] 200. What is the area of the shaded region?

196. What is the area of the overlapping region? (a) 38.5 square cm (b) 48 square cm
8 5 (c) 52.5 square cm (d) 66.5 square cm
(a) square cm (b) square cm
5 4 201. What is the ratio of the area of the shaded
(c)
4
square cm (d)
3
square cm region to the area of the non-shaded
5 4 region?
19 18
(a) (b)
197. What is the area of the non-overlapping 25 25
region?
17 16
3 11 (c) (d)
(a) square cm (b) square cm 25 25
4 4
3 5 202. The chord AB of a circle with centre at O is
(c) square cm (d) square cm
2 4 2 3 times the height of the minor segment.
Consider the following for the next two
If P is the area of the sector OAB and Q is
(02) items that follow:
the area of the minor segment of the circle,
In a pie-diagram (with radius 7 cm), the
central angles of the sectors are in the ratio P
then what is the approximate value of ?
2 : 3 : 7 : 5 : 1. Q
22 (Take 3 = 1.7 and  = 3.14)
(Take  = )
7 [CDS-2024 (1)]
[CDS-2024 (1)] (a) 1.4 (b) 1.7
198. If P is the area of the smallest sector and Q (c) 2.2 (d) 2.6
is the area of the largest sector, then what
is P + Q equal to? 203. In a right-angled triangle ABC, AB = 15 cm,
(a) 88/3 square cm (b) 77/3 square cm BC = 20 cm and AC = 25 cm. Further, BP is
(c) 149/6 square cm (d)616/9square cm the perpendicular on AC. What is the
difference in the area of triangles PAB and
199. If p is the perimeter of the smallest sector, PCB?
then what is the value of 9p? [CDS-2024 (1)]
(a) 142 cm (b) 148 cm (a) 40 square cm (b) 42 square cm
(c) 156 cm (d) 221 cm (c) 45 square cm (d) 48 square cm

Consider the following for the next two 204. What is the area of the region between two
(02) items that follow: concentric circles, if the length of a chord of
the outer circle touching the inner circle at

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 a particular point of its circumference is 14 around a ground with radius 50 m
22 (described by right wheel). if the size of each
cm? (Take  = ) wheel is of 1 foot radius and the right wheel
7
turns 1000 times, how many times will the
[CDS-2024 (1)]
other will turn ?
(a) 154 square cm
[CDS-2024 (2)]
(b) 144 square cm
(a) 1010 (b) 1015
(c) 132 square cm
(c) 1020 (d) 1025
(d) Cannot be determined due to
insufficient data
210. A square is drawn inside a square of side
14 cm in such a way that the corners of the
205. ABC is a right-angled triangle, right-angled
inner square coincide with the mid points of
at B such that AB = 6 cm and BC = 8 cm.
the sides of the outer square, what is the
What is the perimeter of the square
area lying between the two squares
inscribed in the triangle ABC with
[CDS-2024 (2)]
maximum area?
(a) 98 sq cm (b) 56 sq cm
[CDS-2024 (1)]
(c) 49 sq cm (d) 24.5 sq cm
(a) 24/7 cm (b) 96/7 cm
(c) 24 cm (d) 32 cm
211. The base of a right angle triangle is 4/3
times the height of triangle. if the area of
206. Area of a rectangle with length x and
the triangle is 54 square cm, then what is
breadth y is P and area of a parallelogram
the perimeter of the triangle ?
(which is strictly not a rectangle) with
[CDS-2024 (2)]
adjacent sides of length x and y is Q.
(a) 30 cm (b) 32cm
Question: Is P > Q?
(c) 36 cm (d) 40 cm
Statement-I: x : y = 2 : 1
Statement-II: The angle between the two
212. What is the area of a triangle having sides
adjacent sides of the parallelogram is 60 ̊
4, 4 and 6 units ?
[CDS-2024 (1)]
[CDS-2024 (2)]
(a) If the Question can be answered by one
of the Statements alone, but not by the (a) 37 sq cm (b) 8 sq cm
other. (c) 7 sq cm (d) 73 sq cm
(b) If the Question can be answered by
either Statement alone 213. What is the maximum area of a rectangle ,
(c) If the Question can be answered by in square cm, whose perimeter is 400 cm ?
using both the Statements together, but [CDS-2024 (2)]
cannot be answered by using either (a) 100 (b) 200
Statement alone. (c) 1000 (d) 10,000
(d) If the Question cannot be answered even
by using both Statements together 214. There are n concentric square. The area of
the innermost square is 1 unit and the
distance between corresponding corners of
207. In a triangle ABC, ABC = 60 ̊ and AD is
any two consecutive squares is 1 unit.
the altitude. If AB = 6cm and BC = 8cm,
consider the following statements
then what is the area of the triangle ?
[CDS-2024 (2)] I. the diagonal of the nth square is
(a) 12 sq cm (b) 123 sq cm 2n  2  2
(c) 24 sq cm (d) 243 sq cm II. the area included between nth sphere
and (n – 1)th square is independent of n
208. Let ABC be a triangle with area 36 square Which of the statements given above is/are
cm. If AB = 9cm, BC = 12cm, and ABC = correct?
, then what is cos is equal to [CDS-2024 (2)]
[CDS-2024 (2)] (a) Only I (b) Only II
(c) Both I and II (d) Neither I nor II
(a) 5/3 (b) 5/4
(c) 1/3 (d) 2/3
215. In a rectangle ABCD, AC is one of the
diagonals. if AC + AB is = 3AD and AC – AD
209. A trolley with two wheels 1 m apart is
= 4 units, then what is the area of the
moved clockwise on the circular track
rectangle ?

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 [CDS-2024 (2)] 
 2 3 
2

(a) 24 sq cm (b) 36 sq cm 3square cm what is the radius of

(c) 48 sq cm (d) 72 sq cm
one of the smaller circles
[CDS-2024 (2)]
216. The area of the circle circumscribing 3
(a) 0.5 cm (b) 1 cm
identical circles touching is each other is
(c) 1.5 cm (d) 3 cm

ANSWER KEY
1. c 2. d 3. c 4. c 5. c 6. d 7. c 8. a 9. b 10. b
11. a 12. a 13. a 14. a 15. a 16. c 17. b 18. a 19. b 20. c
21. d 22. d 23. b 24. c 25. c 26. c 27. c 28. b 29. c 30. c
31. a 32. c 33. d 34. b 35. b 36. c 37. b 38. b 39. a 40. d
41. d 42. d 43. d 44. c 45. b 46. c 47. d 48. c 49. a 50. b
51. a 52. a 53. b 54. d 55. b 56. c 57. b 58. d 59. b 60. b
61. d 62. c 63. c 64. b 65. d 66. c 67. b 68. d 69. b 70. b
71. b 72. a 73. a 74. d 75. d 76. b 77. c 78. b 79. b 80. a
81. b 82. b 83. a 84. a 85. d 86. c 87. c 88. c 89. c 90. a
91. c 92. c 93. b 94. c 95. a 96. b 97. c 98. b 99. d 100. c
101. c 102. a 103. a 104. b 105. b 106. c 107. c 108. b 109. c 110. c
111. d 112. d 113. a 114. d 115. a 116. b 117. a 118. b 119. d 120. d
121. b 122. d 123. d 124. c 125. c 126. d 127. c 128. b 129. a 130. d
131. b 132. b 133. c 134. d 135. c 136. c 137. a 138. d 139. a 140. d
141. a 142. a 143. b 144. c 145. c 146. c 147. a 148. b 149. d 150. a
151. d 152. b 153. c 154. b 155. b 156. c 157. a 158. a 159. d 160. b
161. b 162. a 163. b 164. a 165. c 166. a 167. b 168. d 169. c 170. b
171. c 172. d 173. b 174. c 175. b 176. b 177. b 178. b 179. b 180. b
181. c 182. d 183. d 184. d 185. a 186. c 187. a 188. b 189. b 190. *
191. a 192. c 193. d 194. a 195. d 196. b 197. c 198. d 199. b 200. d
201. a 202. b 203. b 204. a 205. b 206. b 207. d 208. a 209. c 210. a
211. c 212. a 213. d 214. a 215. c 216. b

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 CAPF PYQ
1. If a circle and a square have the same (a) 25 3 (b) 25 3
perimeter , then 6 4
[CAPF 2019] 25 3
(c) (d) 25 3
(a) their areas are equal 2
(b) The area of circle is greater than the area
of square 3. On a large ground, there is a straight tall
(c) the area of square is greater than the area vertical wall of length 28 m. A goat is tied to a
of circle point on the ground which is at the middle of
(d) the area of circle is two times the area of the wall, using a rope. If the length of the
the square rope is 21 m, what is the area of the region
(in square metre) around the wall that the
2. Three circles of radius 5 cm each, touch each goat can access ?
other. If the points of contact are P,Q and R, [CAPF 2023]
then what is the area of the triangle PQR in (a) 847 (b) 851
sq. cm (c) 693 (d) 654
[CAPF 2023]
ANSWER KEY
1. b 2. b 3. a

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