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Exam: Maharashtra State Board Class 10
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Q751
#751
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Easy
Add
∠
A
C
B
\angle ACB
∠
A
C
B
is an inscribed angle in a circle with centre O. If
∠
A
C
B
=
65
∘
\angle ACB = 65^\circ
∠
A
C
B
=
6
5
∘
, then what is the measure of its intercepted arc AXB?
A
65
∘
65^\circ
6
5
∘
B
230
∘
230^\circ
23
0
∘
C
295
∘
295^\circ
29
5
∘
D
130
∘
130^\circ
13
0
∘
Tap an option to check your answer.
Show solution
[QQ1(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q752
#752
Geometry → Co-ordinate Geometry → Distance Formula
·
Easy
Add
Distance of the point
(
3
,
4
)
(3, 4)
(
3
,
4
)
from the origin is ________.
A
7
7
7
B
1
1
1
C
5
5
5
D
−
5
-5
−
5
Tap an option to check your answer.
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[QQ1(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q753
#753
Geometry → Mensuration → Surface Area and Volume of Solids
·
Easy
Add
If the radius of a cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ________.
A
17 cm
B
4 cm
C
13 cm
D
60 cm
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[QQ1(A)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q754
#754
Geometry → Similarity → Ratio of Areas of Two Triangles
·
Easy
·
Has image
Add
In the following figure
△
A
B
C
\triangle ABC
△
A
B
C
,
B
–
D
–
C
B\text{–}D\text{–}C
B
–
D
–
C
and
B
D
=
7
BD = 7
B
D
=
7
,
B
C
=
20
BC = 20
B
C
=
20
, then find
A
(
△
A
B
D
)
A
(
△
A
B
C
)
\dfrac{A(\triangle ABD)}{A(\triangle ABC)}
A
(
△
A
B
C
)
A
(
△
A
B
D
)
.
Show model answer
[QQ1(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q755
#755
Geometry → Pythagoras Theorem → Similarity in Right Angled Triangles
·
Moderate
·
Has image
Add
In the following figure
∠
M
N
P
=
90
∘
\angle MNP = 90^\circ
∠
M
N
P
=
9
0
∘
, seg
N
Q
⊥
NQ \perp
N
Q
⊥
seg
M
P
MP
M
P
,
M
Q
=
9
MQ = 9
M
Q
=
9
,
Q
P
=
4
QP = 4
QP
=
4
, find
N
Q
NQ
N
Q
.
Show model answer
[QQ1(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q756
#756
Geometry → Co-ordinate Geometry → Slope of a Line
·
Easy
Add
The angle made by a line with the positive direction of the X-axis is
30
∘
30^\circ
3
0
∘
. Find the slope of that line.
Show model answer
[QQ1(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q757
#757
Geometry → Circle → Cyclic Quadrilateral
·
Easy
Add
In cyclic quadrilateral ABCD,
m
∠
A
=
100
∘
m\angle A = 100^\circ
m
∠
A
=
10
0
∘
, then find
m
∠
C
m\angle C
m
∠
C
.
Show model answer
[QQ1(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q758
#758
Geometry → Mensuration → Area of Sector and Segment of a Circle
·
Moderate
·
Has image
Add
The radius of a circle with centre P is 10 cm. If chord AB of the circle subtends a right angle at P, find the area of the minor sector P-AXB by completing the activity. (
π
=
3.14
\pi = 3.14
π
=
3.14
)
Show model answer
[QQ2(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q759
#759
Geometry → Circle → Theorems on Chords and Tangents
·
Moderate
·
Has image
Add
In the following figure, chord MN and chord RS intersect at point D. If
R
D
=
15
RD = 15
R
D
=
15
,
D
S
=
4
DS = 4
D
S
=
4
,
M
D
=
8
MD = 8
M
D
=
8
, find
D
N
DN
D
N
by completing the activity.
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[QQ2(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q760
#760
Geometry → Trigonometry → Heights and Distances
·
Moderate
·
Has image
Add
An observer at a distance of 10 m from a tree looks at the top of the tree; the angle of elevation is
60
∘
60^\circ
6
0
∘
. Find the height of the tree by completing the activity. (
3
=
1.73
\sqrt{3} = 1.73
3
=
1.73
)
Show model answer
[QQ2(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q761
#761
Geometry → Similarity → Basic Proportionality Theorem
·
Easy
·
Has image
Add
In
△
A
B
C
\triangle ABC
△
A
B
C
,
D
E
∥
B
C
DE \parallel BC
D
E
∥
B
C
. If
D
B
=
5.4
DB = 5.4
D
B
=
5.4
cm,
A
D
=
1.8
AD = 1.8
A
D
=
1.8
cm,
E
C
=
7.2
EC = 7.2
E
C
=
7.2
cm, then find
A
E
AE
A
E
.
Show model answer
[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q762
#762
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
·
Has image
Add
In the figure given below, find
R
S
RS
R
S
and
P
S
PS
P
S
using the information given in
△
P
S
R
\triangle PSR
△
P
S
R
.
Show model answer
[QQ2(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q763
#763
Geometry → Circle → Tangent and Secant to a Circle
·
Moderate
·
Has image
Add
In the following figure, a circle with centre D touches the sides of
∠
A
C
B
\angle ACB
∠
A
C
B
at A and B. If
∠
A
C
B
=
52
∘
\angle ACB = 52^\circ
∠
A
C
B
=
5
2
∘
, find the measure of
∠
A
D
B
\angle ADB
∠
A
D
B
.
Show model answer
[QQ2(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q764
#764
Geometry → Co-ordinate Geometry → Distance Formula
·
Moderate
Add
Verify whether the points
A
(
1
,
−
3
)
A(1, -3)
A
(
1
,
−
3
)
,
B
(
2
,
−
5
)
B(2, -5)
B
(
2
,
−
5
)
and
C
(
−
4
,
7
)
C(-4, 7)
C
(
−
4
,
7
)
are collinear or not.
Show model answer
[QQ2(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q765
#765
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Easy
Add
If
sin
θ
=
11
61
\sin\theta = \dfrac{11}{61}
sin
θ
=
61
11
, find the value of
cos
θ
\cos\theta
cos
θ
using a trigonometric identity.
Show model answer
[QQ2(B)(5) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q766
#766
Geometry → Similarity → Tests of Similarity of Triangles
·
Moderate
·
Has image
Add
In the following figure,
X
Y
∥
XY \parallel
X
Y
∥
seg AC. If
2
A
X
=
3
B
X
2AX = 3BX
2
A
X
=
3
B
X
and
X
Y
=
9
XY = 9
X
Y
=
9
, complete the activity to find the value of AC.
Show model answer
[QQ3(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q767
#767
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Moderate
·
Has image
Add
Complete the activity to prove that the sum of the squares of the diagonals of a rhombus is equal to the sum of the squares of its sides. (
□
P
Q
R
S
\square PQRS
□
P
QR
S
is a rhombus; diagonals PR and SQ intersect each other at point T.)
Show model answer
[QQ3(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q768
#768
Geometry → Co-ordinate Geometry → Distance Formula
·
Moderate
Add
Show that the points
P
(
1
,
−
2
)
P(1, -2)
P
(
1
,
−
2
)
,
Q
(
5
,
2
)
Q(5, 2)
Q
(
5
,
2
)
,
R
(
3
,
−
1
)
R(3, -1)
R
(
3
,
−
1
)
,
S
(
−
1
,
−
5
)
S(-1, -5)
S
(
−
1
,
−
5
)
are the vertices of a parallelogram.
Show model answer
[QQ3(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q769
#769
Geometry → Circle → Tangent Segment Theorem
·
Moderate
Add
Prove that the tangent segments drawn from an external point to a circle are congruent.
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[QQ3(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q770
#770
Geometry → Geometric Constructions → Construction of a Tangent to a Circle
·
Moderate
Add
Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance of 7.3 cm from the centre.
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[QQ3(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q771
#771
Geometry → Mensuration → Surface Area and Volume of Solids
·
Moderate
Add
How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?
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[QQ3(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Set · 2 questions
In the following figure
D
E
∥
B
C
DE \parallel BC
D
E
∥
B
C
, then:
Q772
#772
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Moderate
·
Has image
Add
If
D
E
=
4
DE = 4
D
E
=
4
cm,
B
C
=
8
BC = 8
B
C
=
8
cm,
A
(
△
A
D
E
)
=
25
A(\triangle ADE) = 25
A
(
△
A
D
E
)
=
25
cm
2
^2
2
, find
A
(
△
A
B
C
)
A(\triangle ABC)
A
(
△
A
B
C
)
.
Show model answer
[QQ4(1)(i) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q773
#773
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Moderate
·
Has image
Add
If
D
E
:
B
C
=
3
:
5
DE : BC = 3 : 5
D
E
:
B
C
=
3
:
5
, then find
A
(
△
A
D
E
)
:
A
(
□
D
B
C
E
)
A(\triangle ADE) : A(\square DBCE)
A
(
△
A
D
E
)
:
A
(
□
D
B
C
E
)
.
Show model answer
[QQ4(1)(ii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q774
#774
Geometry → Geometric Constructions → Construction of a Similar Triangle
·
Moderate
Add
△
A
B
C
∼
△
P
Q
R
\triangle ABC \sim \triangle PQR
△
A
B
C
∼
△
P
QR
. In
△
A
B
C
\triangle ABC
△
A
B
C
,
A
B
=
3.6
AB = 3.6
A
B
=
3.6
cm,
B
C
=
4
BC = 4
B
C
=
4
cm and
A
C
=
4.2
AC = 4.2
A
C
=
4.2
cm. The corresponding sides of
△
A
B
C
\triangle ABC
△
A
B
C
and
△
P
Q
R
\triangle PQR
△
P
QR
are in the ratio
2
:
3
2 : 3
2
:
3
. Construct
△
A
B
C
\triangle ABC
△
A
B
C
and
△
P
Q
R
\triangle PQR
△
P
QR
.
Show model answer
[QQ4(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
Report
Set · 1 question
The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. The height of the frustum is 8 cm. (
π
=
3.14
\pi = 3.14
π
=
3.14
)
Q775
#775
Geometry → Mensuration → Combination of Solids and Frustum
·
Moderate
Add
Find the curved surface area of the frustum.
Show model answer
[QQ4(3)(i) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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