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Quadrilaterals

Q.No: 1
Test Name : CAT 2017 Actual Paper Slot 2

ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is

Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT 2017 Actual Paper Slot 2

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

A
1300
B
1340
C
1480
D
1520
Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT 2018 Actual Paper Slot 1

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

A
1 : 3
B
3 : 8
C
4 : 9
D
2 : 5
Answer key/Solution
Solution:
Q.No: 4
Test Name : CAT 2018 Actual Paper Slot 1

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

A
32√3
B
18√3
C
12√3
D
24√3
Answer key/Solution
Solution:
Q.No: 5
Test Name : CAT 2018 Actual Paper Slot 2

A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?

A
5 ≤ s ≤ 7
B
s ≠ 6
C
s ≥ 6
D
s ≤ 6
Answer key/Solution
Solution:
Q.No: 6
Test Name : CAT 2018 Actual Paper Slot 2

The area of a rectangle and the square of its perimeter are in the ratio 1 ∶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

A
2:9
B
1:3
C
3:8
D
1:4
Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT 2019 Actual Paper Slot 1


A
B
C
D
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT Actual Paper 2020 Slot-3

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq. cm is

Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT Actual Paper 2021 Slot-2

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side.P is the midpoint of CD and ABPD is a parallelogram. If the difference between theareas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sqcm, of the trapezium ABCD is

A
40
B
30
C
25
D
20
Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT Actual Paper 2021 Slot-2

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

A
B
C
D
Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT Actual Paper 2021 Slot-3


A
B
C
D
Answer key/Solution
Solution:
Q.No: 12
Test Name : CAT Actual Paper 2023 Slot 1

A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

A
8 : 5
B
5 : 8
C
1 : 2
D
2 : 1
Answer key/Solution
Solution:
Q.No: 13
Test Name : CAT Actual Paper 2023 Slot 2

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

A
1 : 2 : 1
B
2 : 4 : 1
C
1 : 1 : 2
D
1 : 2 : 4
Answer key/Solution
Solution:
Q.No: 14
Test Name : CAT Actual Paper 2023 Slot 3

A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

A
√2 : 1
B
√5 : 1
C
1 : 1
D
2 : 1
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