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Geometry & Mensuration Quantitative Aptitude Questions | Prasnya
Quantitative Aptitude > Geometry & Mensuration
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Topic-Wise PYQs
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Type:
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Difficulty:
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42Q
01
The area of the closed region bounded by the equation
∣
x
∣
+
∣
y
∣
=
2
|x| + |y| = 2
∣
x
∣
+
∣
y
∣
=
2
in the two-dimensional plane is
Single correct
EASY
3 marks
26 November 2017
02
From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Single correct
MEDIUM
3 marks
26 November 2017
03
Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is
Single correct
HARD
3 marks
26 November 2017
04
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
Single correct
MEDIUM
3 marks
26 November 2017
05
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is
9
π
9\pi
9
π
cm
3
^3
3
. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is
Single correct
HARD
3 marks
26 November 2017
06
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
Single correct
MEDIUM
3 marks
26 November 2017
07
The shortest distance of the point
(
1
2
,
1
)
\left(\frac12,1\right)
(
2
1
,
1
)
from the curve
y
=
∣
x
−
1
∣
+
∣
x
+
1
∣
y = |x -1| + |x + 1|
y
=
∣
x
−
1∣
+
∣
x
+
1∣
is
Single correct
MEDIUM
3 marks
26 November 2017
08
Direction of the question: Solve the following question and mark the best possible option. Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
Single correct
MEDIUM
3 marks
26 November 2017
09
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
HARD
3 marks
26 November 2017
10
Direction of the question: Solve the following question and mark the best possible option. The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Single correct
MEDIUM
3 marks
26 November 2017
11
Direction of the question: Solve the following question and mark the best possible option. ABCD is a quadrilateral inscribed in a circle with centre O, such that O lies inside the quadrilateral. If
∠
C
O
D
=
120
∘
\angle COD = 120^\circ
∠
C
O
D
=
12
0
∘
and
∠
B
A
C
=
30
∘
\angle BAC = 30^\circ
∠
B
A
C
=
3
0
∘
, then the value of
∠
B
C
D
\angle BCD
∠
B
C
D
(in degrees) is
Numerical
MEDIUM
3 marks
26 November 2017
12
Direction of the question: Solve the following question and mark the best possible option. Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is
4
(
2
−
1
)
4(\sqrt{2} - 1)
4
(
2
−
1
)
cm, then the area, in sq cm, of the triangle ABC is
Numerical
HARD
3 marks
26 November 2017
13
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
14
Direction of the question: Solve the following question and mark the best possible option. In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
Single correct
HARD
3 marks
25 November 2018
15
Direction of the question: Solve the following question and mark the best possible option. Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
Single correct
EASY
3 marks
25 November 2018
16
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
17
Direction of the question: Solve the following question and key in your numerical answer. A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is
Numerical
MEDIUM
3 marks
25 November 2018
18
Direction of the question: Solve the following question and mark the best possible option. In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
Single correct
MEDIUM
3 marks
25 November 2018
19
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
20
Direction of the question: Solve the following question and mark the best possible option. A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is
Single correct
EASY
3 marks
25 November 2018
21
Direction of the question: Solve the following question and mark the best possible option. From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is
Single correct
MEDIUM
3 marks
25 November 2018
22
Direction of the question: Solve the following question and mark the best possible option. A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is
Single correct
MEDIUM
3 marks
25 November 2018
23
Direction of the question: Solve the following question and key in your numerical answer. On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
Numerical
HARD
3 marks
25 November 2018
24
Direction of the question: Solve the following question and mark the best possible option. 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?
Single correct
MEDIUM
3 marks
25 November 2018
25
In the XY-plane, the area, in sq. units, of the region defined by the inequalities
y
≥
x
+
4
y \ge x + 4
y
≥
x
+
4
and
−
4
≤
x
2
+
y
2
+
5
(
x
−
y
)
≤
0
-4 \le x^2 + y^2 + 5(x - y) \le 0
−
4
≤
x
2
+
y
2
+
5
(
x
−
y
)
≤
0
is
Single correct
VERY_HARD
3 marks
24 November 2024
26
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
Single correct
VERY_HARD
3 marks
24 November 2024
27
ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of
△
A
D
E
\triangle ADE
△
A
D
E
is
Numerical
HARD
3 marks
24 November 2024
28
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
Single correct
VERY_HARD
3 marks
24 November 2024
29
The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the in-circle of the triangle is
Numerical
MEDIUM
3 marks
24 November 2024
30
ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of
△
A
E
B
\triangle AEB
△
A
E
B
is
Single correct
MEDIUM
3 marks
24 November 2024
31
A circular plot of land is divided into two regions by a chord of length
10
3
10\sqrt{3}
10
3
meters such that the chord subtends an angle of
120
∘
120^\circ
12
0
∘
at the center. Then, the area, in square meters, of the smaller region is
Single correct
HARD
3 marks
24 November 2024
32
The midpoints of sides AB, BC, and AC in
△
A
B
C
\triangle ABC
△
A
B
C
are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of
△
A
B
C
\triangle ABC
△
A
B
C
is 1440 sq cm, then the area, in sq cm, of
△
X
Y
Z
\triangle XYZ
△
X
Y
Z
is
Numerical
VERY_HARD
3 marks
24 November 2024
33
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
Single correct
HARD
3 marks
24 November 2024
34
In a circle with center
C
C
C
and radius
6
2
6\sqrt{2}
6
2
cm,
P
Q
PQ
P
Q
and
S
R
SR
S
R
are two parallel chords separated by one of the diameters. If
∠
P
Q
C
=
45
∘
\angle PQC = 45^\circ
∠
P
QC
=
4
5
∘
, and the ratio of the perpendicular distance of
P
Q
PQ
P
Q
and
S
R
SR
S
R
from
C
C
C
is 3:2, then the area, in sq. cm, of the quadrilateral
P
Q
R
S
PQRS
P
QR
S
is
Single correct
HARD
3 marks
30 November 2025
35
The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a is
Single correct
MEDIUM
3 marks
30 November 2025
36
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is
Numerical
EASY
3 marks
30 November 2025
37
Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is
Single correct
MEDIUM
3 marks
30 November 2025
38
Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If
∠
A
O
B
=
50
°
\angle AOB = 50°
∠
A
O
B
=
50°
, then
∠
A
P
B
\angle APB
∠
A
P
B
, in degrees, equals.
Numerical
HARD
3 marks
30 November 2025
39
In a
△
A
B
C
\triangle ABC
△
A
B
C
, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that
A
D
:
A
T
=
4
:
3
AD:AT=4:3
A
D
:
A
T
=
4
:
3
, and
B
E
:
B
T
=
5
:
4
BE:BT=5:4
B
E
:
B
T
=
5
:
4
. Then, BD : CD is
Single correct
HARD
3 marks
30 November 2025
40
Direction of the question: A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is
Numerical
MEDIUM
3 marks
30 November 2025
41
Direction of the question: ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
Single correct
HARD
3 marks
30 November 2025
42
Direction of the question: In
△
\triangle
△
ABC, AB = AC = 12 cm and D is a point on side BC such that AD = 8 cm. If AD is extended to a point E such that
∠
A
C
B
=
∠
A
E
B
\angle ACB = \angle AEB
∠
A
C
B
=
∠
A
E
B
, then the length, in cm, of AE is
Single correct
HARD
3 marks
30 November 2025
Showing 42 questions.
Quantitative Aptitude > Geometry & Mensuration
All PYQs
Topic-Wise PYQs
Start Weekly Test
Type:
All
Difficulty:
All
Year:
All
42Q
01
The area of the closed region bounded by the equation
∣
x
∣
+
∣
y
∣
=
2
|x| + |y| = 2
∣
x
∣
+
∣
y
∣
=
2
in the two-dimensional plane is
Single correct
EASY
3 marks
26 November 2017
02
From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Single correct
MEDIUM
3 marks
26 November 2017
03
Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is
Single correct
HARD
3 marks
26 November 2017
04
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
Single correct
MEDIUM
3 marks
26 November 2017
05
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is
9
π
9\pi
9
π
cm
3
^3
3
. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is
Single correct
HARD
3 marks
26 November 2017
06
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
Single correct
MEDIUM
3 marks
26 November 2017
07
The shortest distance of the point
(
1
2
,
1
)
\left(\frac12,1\right)
(
2
1
,
1
)
from the curve
y
=
∣
x
−
1
∣
+
∣
x
+
1
∣
y = |x -1| + |x + 1|
y
=
∣
x
−
1∣
+
∣
x
+
1∣
is
Single correct
MEDIUM
3 marks
26 November 2017
08
Direction of the question: Solve the following question and mark the best possible option. Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
Single correct
MEDIUM
3 marks
26 November 2017
09
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
HARD
3 marks
26 November 2017
10
Direction of the question: Solve the following question and mark the best possible option. The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Single correct
MEDIUM
3 marks
26 November 2017
11
Direction of the question: Solve the following question and mark the best possible option. ABCD is a quadrilateral inscribed in a circle with centre O, such that O lies inside the quadrilateral. If
∠
C
O
D
=
120
∘
\angle COD = 120^\circ
∠
C
O
D
=
12
0
∘
and
∠
B
A
C
=
30
∘
\angle BAC = 30^\circ
∠
B
A
C
=
3
0
∘
, then the value of
∠
B
C
D
\angle BCD
∠
B
C
D
(in degrees) is
Numerical
MEDIUM
3 marks
26 November 2017
12
Direction of the question: Solve the following question and mark the best possible option. Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is
4
(
2
−
1
)
4(\sqrt{2} - 1)
4
(
2
−
1
)
cm, then the area, in sq cm, of the triangle ABC is
Numerical
HARD
3 marks
26 November 2017
13
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
14
Direction of the question: Solve the following question and mark the best possible option. In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
Single correct
HARD
3 marks
25 November 2018
15
Direction of the question: Solve the following question and mark the best possible option. Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
Single correct
EASY
3 marks
25 November 2018
16
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
17
Direction of the question: Solve the following question and key in your numerical answer. A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is
Numerical
MEDIUM
3 marks
25 November 2018
18
Direction of the question: Solve the following question and mark the best possible option. In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
Single correct
MEDIUM
3 marks
25 November 2018
19
Direction of the question: Solve the following question and mark the best possible option. 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
Single correct
MEDIUM
3 marks
25 November 2018
20
Direction of the question: Solve the following question and mark the best possible option. A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is
Single correct
EASY
3 marks
25 November 2018
21
Direction of the question: Solve the following question and mark the best possible option. From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is
Single correct
MEDIUM
3 marks
25 November 2018
22
Direction of the question: Solve the following question and mark the best possible option. A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is
Single correct
MEDIUM
3 marks
25 November 2018
23
Direction of the question: Solve the following question and key in your numerical answer. On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
Numerical
HARD
3 marks
25 November 2018
24
Direction of the question: Solve the following question and mark the best possible option. 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?
Single correct
MEDIUM
3 marks
25 November 2018
25
In the XY-plane, the area, in sq. units, of the region defined by the inequalities
y
≥
x
+
4
y \ge x + 4
y
≥
x
+
4
and
−
4
≤
x
2
+
y
2
+
5
(
x
−
y
)
≤
0
-4 \le x^2 + y^2 + 5(x - y) \le 0
−
4
≤
x
2
+
y
2
+
5
(
x
−
y
)
≤
0
is
Single correct
VERY_HARD
3 marks
24 November 2024
26
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
Single correct
VERY_HARD
3 marks
24 November 2024
27
ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of
△
A
D
E
\triangle ADE
△
A
D
E
is
Numerical
HARD
3 marks
24 November 2024
28
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
Single correct
VERY_HARD
3 marks
24 November 2024
29
The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the in-circle of the triangle is
Numerical
MEDIUM
3 marks
24 November 2024
30
ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of
△
A
E
B
\triangle AEB
△
A
E
B
is
Single correct
MEDIUM
3 marks
24 November 2024
31
A circular plot of land is divided into two regions by a chord of length
10
3
10\sqrt{3}
10
3
meters such that the chord subtends an angle of
120
∘
120^\circ
12
0
∘
at the center. Then, the area, in square meters, of the smaller region is
Single correct
HARD
3 marks
24 November 2024
32
The midpoints of sides AB, BC, and AC in
△
A
B
C
\triangle ABC
△
A
B
C
are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of
△
A
B
C
\triangle ABC
△
A
B
C
is 1440 sq cm, then the area, in sq cm, of
△
X
Y
Z
\triangle XYZ
△
X
Y
Z
is
Numerical
VERY_HARD
3 marks
24 November 2024
33
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
Single correct
HARD
3 marks
24 November 2024
34
In a circle with center
C
C
C
and radius
6
2
6\sqrt{2}
6
2
cm,
P
Q
PQ
P
Q
and
S
R
SR
S
R
are two parallel chords separated by one of the diameters. If
∠
P
Q
C
=
45
∘
\angle PQC = 45^\circ
∠
P
QC
=
4
5
∘
, and the ratio of the perpendicular distance of
P
Q
PQ
P
Q
and
S
R
SR
S
R
from
C
C
C
is 3:2, then the area, in sq. cm, of the quadrilateral
P
Q
R
S
PQRS
P
QR
S
is
Single correct
HARD
3 marks
30 November 2025
35
The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a is
Single correct
MEDIUM
3 marks
30 November 2025
36
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is
Numerical
EASY
3 marks
30 November 2025
37
Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is
Single correct
MEDIUM
3 marks
30 November 2025
38
Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If
∠
A
O
B
=
50
°
\angle AOB = 50°
∠
A
O
B
=
50°
, then
∠
A
P
B
\angle APB
∠
A
P
B
, in degrees, equals.
Numerical
HARD
3 marks
30 November 2025
39
In a
△
A
B
C
\triangle ABC
△
A
B
C
, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that
A
D
:
A
T
=
4
:
3
AD:AT=4:3
A
D
:
A
T
=
4
:
3
, and
B
E
:
B
T
=
5
:
4
BE:BT=5:4
B
E
:
B
T
=
5
:
4
. Then, BD : CD is
Single correct
HARD
3 marks
30 November 2025
40
Direction of the question: A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is
Numerical
MEDIUM
3 marks
30 November 2025
41
Direction of the question: ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
Single correct
HARD
3 marks
30 November 2025
42
Direction of the question: In
△
\triangle
△
ABC, AB = AC = 12 cm and D is a point on side BC such that AD = 8 cm. If AD is extended to a point E such that
∠
A
C
B
=
∠
A
E
B
\angle ACB = \angle AEB
∠
A
C
B
=
∠
A
E
B
, then the length, in cm, of AE is
Single correct
HARD
3 marks
30 November 2025
Showing 42 questions.
