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Exam: Maharashtra State Board Class 10
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Set · 2 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
)
Q776
#776
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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Q777
#777
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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Q778
#778
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:
Q779
#779
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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Q780
#780
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
Show model answer
[QQ5(2)(ii) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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Q781
#781
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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Q782
#782
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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Q783
#783
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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Q784
#784
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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Q785
#785
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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Q786
#786
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
)
.
Show model answer
[QQ1(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q787
#787
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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Q788
#788
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.
Show model answer
[QQ1(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q789
#789
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.
Show model answer
[QQ1(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q790
#790
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
.
Show model answer
[QQ2(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q791
#791
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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Q792
#792
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.
Show model answer
[QQ2(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q793
#793
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.
Show model answer
[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q794
#794
Geometry → Pythagoras Theorem → Pythagoras Theorem and its Converse
·
Easy
Add
Find the length of the hypotenuse of a right-angled triangle if its remaining sides are 9 cm and 12 cm.
Show model answer
[QQ2(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q795
#795
Geometry → Circle → Tangent and Secant to a Circle
·
Moderate
·
Has image
Add
In the figure,
m
(
arc
N
S
)
=
125
∘
m(\text{arc } NS) = 125^\circ
m
(
arc
N
S
)
=
12
5
∘
and
m
(
arc
E
F
)
=
37
∘
m(\text{arc } EF) = 37^\circ
m
(
arc
E
F
)
=
3
7
∘
. Find the measure of
∠
N
M
S
\angle NMS
∠
N
M
S
.
Show model answer
[QQ2(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q796
#796
Geometry → Co-ordinate Geometry → Slope of a Line
·
Easy
Add
Find the slope of the line passing through the points
A
(
2
,
3
)
A(2, 3)
A
(
2
,
3
)
and
B
(
4
,
7
)
B(4, 7)
B
(
4
,
7
)
.
Show model answer
[QQ2(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q797
#797
Geometry → Mensuration → Surface Area and Volume of Solids
·
Easy
Add
Find the surface area of a sphere of radius 7 cm.
(
π
=
22
7
)
\left(\pi = \dfrac{22}{7}\right)
(
π
=
7
22
)
Show model answer
[QQ2(B)(5) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q798
#798
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
·
Has image
Add
In
△
A
B
C
\triangle ABC
△
A
B
C
, ray BD bisects
∠
A
B
C
\angle ABC
∠
A
B
C
with
A
−
D
−
C
A - D - C
A
−
D
−
C
, and seg
D
E
∥
DE \parallel
D
E
∥
side BC with
A
−
E
−
B
A - E - B
A
−
E
−
B
. Complete the following activity to show that
A
B
B
C
=
A
E
E
B
\dfrac{AB}{BC} = \dfrac{AE}{EB}
B
C
A
B
=
E
B
A
E
.
Show model answer
[QQ3(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q799
#799
Geometry → Circle → Theorems on Chords and Tangents
·
Moderate
·
Has image
Add
Chords AB and CD of a circle with centre P intersect at point E. Draw seg AC and seg BD, then complete the following activity to prove that
A
E
×
E
B
=
C
E
×
E
D
AE \times EB = CE \times ED
A
E
×
E
B
=
C
E
×
E
D
.
Show model answer
[QQ3(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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Q800
#800
Geometry → Co-ordinate Geometry → Slope of a Line
·
Moderate
Add
Determine whether the points
A
(
1
,
−
3
)
A(1, -3)
A
(
1
,
−
3
)
,
B
(
2
,
−
5
)
B(2, -5)
B
(
2
,
−
5
)
,
C
(
−
4
,
7
)
C(-4, 7)
C
(
−
4
,
7
)
are collinear.
Show model answer
[QQ3(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
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