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Exam: Maharashtra State Board Class 10
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Q301
#301
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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Q302
#302
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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Q303
#303
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:
Q304
#304
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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Q305
#305
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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Q306
#306
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
.
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[QQ4(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Set · 3 questions
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
)
Q307
#307
Geometry → Mensuration → Combination of Solids and Frustum
·
Moderate
Add
Find the curved surface area of the frustum.
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[QQ4(3)(i) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q308
#308
Geometry → Mensuration → Combination of Solids and Frustum
·
Moderate
Add
Find the total surface area of the frustum.
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[QQ4(3)(ii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q309
#309
Geometry → Mensuration → Combination of Solids and Frustum
·
Moderate
Add
Find the volume of the frustum.
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[QQ4(3)(iii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q310
#310
Geometry → Pythagoras Theorem → Similarity in Right Angled Triangles
·
Hard
Add
□
A
B
C
D
\square ABCD
□
A
B
C
D
is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If
A
B
=
12
AB = 12
A
B
=
12
cm,
A
D
=
9
AD = 9
A
D
=
9
cm, then find the values of BD and BX.
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[QQ5(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Set · 3 questions
Taking
θ
=
30
∘
\theta = 30^\circ
θ
=
3
0
∘
, verify the following trigonometric identities:
Q311
#311
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
Add
sin
2
θ
+
cos
2
θ
=
1
\sin^2\theta + \cos^2\theta = 1
sin
2
θ
+
cos
2
θ
=
1
Show model answer
[QQ5(2)(i) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q312
#312
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
Add
1
+
tan
2
θ
=
sec
2
θ
1 + \tan^2\theta = \sec^2\theta
1
+
tan
2
θ
=
sec
2
θ
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[QQ5(2)(ii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q313
#313
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
Add
1
+
cot
2
θ
=
cosec
2
θ
1 + \cot^2\theta = \operatorname{cosec}^2\theta
1
+
cot
2
θ
=
cosec
2
θ
Show model answer
[QQ5(2)(iii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q314
#314
Geometry → Pythagoras Theorem → Pythagoras Theorem and its Converse
·
Easy
Add
Out of the dates given below, which date constitutes a Pythagorean triplet?
A
15/8/17
B
16/8/16
C
3/5/17
D
4/9/15
Tap an option to check your answer.
Show solution
[QQ1(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q315
#315
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Easy
Add
sin
θ
×
cosec
θ
=
\sin\theta \times \operatorname{cosec}\theta =
sin
θ
×
cosec
θ
=
?
A
1
1
1
B
0
0
0
C
1
2
\dfrac{1}{2}
2
1
D
2
\sqrt{2}
2
Tap an option to check your answer.
Show solution
[QQ1(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q316
#316
Geometry → Co-ordinate Geometry → Slope of a Line
·
Easy
Add
Slope of the X-axis is ____.
A
1
1
1
B
−
1
-1
−
1
C
0
0
0
D
Cannot be determined
Tap an option to check your answer.
Show solution
[QQ1(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q317
#317
Geometry → Circle → Theorems on Chords and Tangents
·
Easy
Add
A circle has radius 3 cm. Then the length of its largest chord is ____.
A
1.5 cm
B
3 cm
C
6 cm
D
9 cm
Tap an option to check your answer.
Show solution
[QQ1(A)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q318
#318
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Easy
Add
If
△
A
B
C
∼
△
P
Q
R
\triangle ABC \sim \triangle PQR
△
A
B
C
∼
△
P
QR
and
A
B
:
P
Q
=
2
:
3
AB : PQ = 2 : 3
A
B
:
P
Q
=
2
:
3
, then find the value of
A
(
△
A
B
C
)
A
(
△
P
Q
R
)
\dfrac{A(\triangle ABC)}{A(\triangle PQR)}
A
(
△
P
QR
)
A
(
△
A
B
C
)
.
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[QQ1(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q319
#319
Geometry → Circle → Touching Circles
·
Easy
Add
Two circles of radii 5 cm and 3 cm touch each other externally. Find the distance between their centres.
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[QQ1(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q320
#320
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Easy
Add
Find the side of a square whose diagonal is
10
2
10\sqrt{2}
10
2
cm.
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[QQ1(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q321
#321
Geometry → Co-ordinate Geometry → Slope of a Line
·
Easy
Add
Angle made by a line with the positive direction of the X-axis is
45
∘
45^\circ
4
5
∘
. Find the slope of that line.
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[QQ1(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q322
#322
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Moderate
·
Has image
Add
In the figure,
∠
A
B
C
\angle ABC
∠
A
B
C
is inscribed in arc ABC. If
∠
A
B
C
=
60
∘
\angle ABC = 60^\circ
∠
A
B
C
=
6
0
∘
, complete the following activity to find
m
∠
A
O
C
m\angle AOC
m
∠
A
O
C
.
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[QQ2(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q323
#323
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
·
Has image
Add
In right-angled
△
A
B
C
\triangle ABC
△
A
B
C
,
∠
A
B
C
=
90
∘
\angle ABC = 90^\circ
∠
A
B
C
=
9
0
∘
and
∠
C
=
θ
\angle C = \theta
∠
C
=
θ
. Complete the following activity to find the value of
sin
2
θ
+
cos
2
θ
\sin^2\theta + \cos^2\theta
sin
2
θ
+
cos
2
θ
.
Show model answer
[QQ2(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q324
#324
Geometry → Mensuration → Areas of Combined Figures
·
Moderate
·
Has image
Add
In the figure,
□
A
B
C
D
\square ABCD
□
A
B
C
D
is a square and a circle is inscribed in it so that all sides of the square touch the circle. If
A
B
=
14
AB = 14
A
B
=
14
cm, complete the following activity to find the area of the shaded region.
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[QQ2(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q325
#325
Geometry → Mensuration → Area of Sector and Segment of a Circle
·
Easy
Add
Radius of a sector of a circle is 3.5 cm and the length of its arc is 2.2 cm. Find the area of the sector.
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[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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