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Exam: Maharashtra State Board Class 10
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Q726
#726
Geometry → Mensuration → Surface Area and Volume of Solids
·
Easy
Add
If the side of the cube is
5
5
5
cm, then the volume of that cube is ________.
A
10
10
10
cm
3
^3
3
B
100
100
100
cm
3
^3
3
C
125
125
125
cm
3
^3
3
D
25
25
25
cm
3
^3
3
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[QQ1(A)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q727
#727
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Easy
Add
The ratio of corresponding sides of similar triangles is
3
:
5
3 : 5
3
:
5
, then find the ratio of their areas.
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[QQ1(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q728
#728
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Easy
Add
Find the side of a square if its diagonal is
10
2
10\sqrt{2}
10
2
cm.
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[QQ1(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q729
#729
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Easy
Add
If the measure of minor arc is
70
∘
70^\circ
7
0
∘
, then find the measure of the corresponding major arc.
Show model answer
[QQ1(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q730
#730
Geometry → Co-ordinate Geometry → Slope of a Line
·
Easy
Add
Angle made by the line with the positive direction of X-axis is
45
∘
45^\circ
4
5
∘
, find the slope of the line.
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[QQ1(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q731
#731
Geometry → Circle → Tangent and Secant to a Circle
·
Moderate
·
Has image
Add
In the following figure, seg PS is a tangent segment and line PR is a secant. If
P
Q
=
3.6
PQ = 3.6
P
Q
=
3.6
,
Q
R
=
6.4
QR = 6.4
QR
=
6.4
, complete the activity to find PS.
Show model answer
[QQ2(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q732
#732
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
Add
If
sec
θ
=
25
7
\sec\theta = \dfrac{25}{7}
sec
θ
=
7
25
, complete the activity to find the value of
tan
θ
\tan\theta
tan
θ
.
Show model answer
[QQ2(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q733
#733
Geometry → Mensuration → Area of Combined Figures
·
Moderate
·
Has image
Add
In the following figure, side of square ABCD is
7
7
7
cm. With centre D and radius DA, sector D-AXC is drawn. Complete the activity to find the area of the shaded region. (Area of sector
D
-
A
X
C
=
38.5
D\text{-}AXC = 38.5
D
-
A
X
C
=
38.5
cm
2
^2
2
.)
Show model answer
[QQ2(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q734
#734
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
·
Has image
Add
Find QP using the given information in the figure. (In
△
M
N
P
\triangle MNP
△
M
N
P
, Q lies on side MP, seg NQ bisects
∠
M
N
P
\angle MNP
∠
M
N
P
,
M
N
=
25
MN = 25
M
N
=
25
,
M
Q
=
14
MQ = 14
M
Q
=
14
,
N
P
=
40
NP = 40
N
P
=
40
.)
Show model answer
[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q735
#735
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Moderate
Add
In
△
R
S
T
\triangle RST
△
R
S
T
,
∠
S
=
90
∘
\angle S = 90^\circ
∠
S
=
9
0
∘
,
∠
T
=
30
∘
\angle T = 30^\circ
∠
T
=
3
0
∘
,
R
T
=
12
RT = 12
R
T
=
12
cm, then find RS and ST.
Show model answer
[QQ2(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q736
#736
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 DN.
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[QQ2(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q737
#737
Geometry → Co-ordinate Geometry → Section Formula
·
Easy
Add
Find the co-ordinates of the midpoint of the line segment joining the points
P
(
0
,
6
)
P(0, 6)
P
(
0
,
6
)
and
Q
(
12
,
20
)
Q(12, 20)
Q
(
12
,
20
)
.
Show model answer
[QQ2(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q738
#738
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Moderate
Add
Prove that:
sin
2
θ
+
cos
2
θ
=
1
\sin^2\theta + \cos^2\theta = 1
sin
2
θ
+
cos
2
θ
=
1
.
Show model answer
[QQ2(B)(5) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q739
#739
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
·
Has image
Add
In the following figure, seg XY
∥
\parallel
∥
side 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 2026 board paper · 2026]
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Q740
#740
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Moderate
·
Has image
Add
For finding AB and BC with the help of the information given in the following figure, complete the following activity. (In
△
A
B
C
\triangle ABC
△
A
B
C
,
∠
B
=
90
∘
\angle B = 90^\circ
∠
B
=
9
0
∘
,
A
B
=
B
C
AB = BC
A
B
=
B
C
and hypotenuse
A
C
=
8
AC = \sqrt{8}
A
C
=
8
.)
Show model answer
[QQ3(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q741
#741
Geometry → Circle → Tangent Segment Theorem
·
Moderate
Add
Prove that: The tangent segments drawn from an external point to the circle are congruent.
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[QQ3(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q742
#742
Geometry → Geometric Constructions → Construction of a Tangent to a Circle
·
Moderate
Add
Draw a circle with centre O and radius
3.5
3.5
3.5
cm, take a point P at a distance
5.7
5.7
5.7
cm from the centre. Draw tangents to the circle from point P.
Show model answer
[QQ3(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q743
#743
Geometry → Co-ordinate Geometry → Section Formula
·
Moderate
Add
Find the co-ordinates of point P, if P divides the line segment joining the points
A
(
−
1
,
7
)
A(-1, 7)
A
(
−
1
,
7
)
and
B
(
4
,
−
3
)
B(4, -3)
B
(
4
,
−
3
)
in the ratio
2
:
3
2 : 3
2
:
3
.
Show model answer
[QQ3(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q744
#744
Geometry → Mensuration → Combination of Solids and Frustum
·
Hard
Add
A bucket is frustum shaped. Its height is
28
28
28
cm. Radii of circular faces are
12
12
12
cm and
15
15
15
cm. Find the capacity of the bucket in litres.
(
π
=
22
7
)
\left(\pi = \dfrac{22}{7}\right)
(
π
=
7
22
)
Show model answer
[QQ3(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q745
#745
Geometry → Geometric Constructions → Construction of a Similar Triangle
·
Hard
Add
△
A
B
C
∼
△
A
D
E
\triangle ABC \sim \triangle ADE
△
A
B
C
∼
△
A
D
E
. In
△
A
B
C
\triangle ABC
△
A
B
C
,
A
B
=
6.3
AB = 6.3
A
B
=
6.3
cm,
∠
C
A
B
=
50
∘
\angle CAB = 50^\circ
∠
C
A
B
=
5
0
∘
,
A
C
=
5.6
AC = 5.6
A
C
=
5.6
cm and
A
B
A
D
=
7
5
\dfrac{AB}{AD} = \dfrac{7}{5}
A
D
A
B
=
5
7
. Construct
△
A
D
E
\triangle ADE
△
A
D
E
.
Show model answer
[QQ4(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q746
#746
Geometry → Mensuration → Surface Area and Volume of Solids
·
Hard
Add
Surface area of a sphere and total surface area of a cube are same. Show that the ratio of the volume of the sphere to that of the cube is
6
:
π
\sqrt{6} : \sqrt{\pi}
6
:
π
.
Show model answer
[QQ4(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q747
#747
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Hard
Add
In
△
A
B
C
\triangle ABC
△
A
B
C
, A-X-B and A-Y-C is such that segment XY
∥
\parallel
∥
side BC. Segment XY divides
△
A
B
C
\triangle ABC
△
A
B
C
in two equal areas, then find
B
X
A
B
\dfrac{BX}{AB}
A
B
B
X
.
Show model answer
[QQ4(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q748
#748
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Hard
Add
Seg PQ is a chord of a circle. Arc PXQ is a major arc and arc PYQ is a minor arc.
∠
P
O
Q
\angle POQ
∠
P
O
Q
is the central angle of the circle. (a) Draw the figure from the given information. (b) Find the measure of
∠
P
X
Q
\angle PXQ
∠
P
X
Q
,
∠
P
Y
Q
\angle PYQ
∠
P
Y
Q
and add
m
∠
P
X
Q
,
m
∠
P
Y
Q
m\angle PXQ,\ m\angle PYQ
m
∠
P
X
Q
,
m
∠
P
Y
Q
. (c) Find the measure of
∠
P
O
Q
\angle POQ
∠
P
O
Q
. Write the relation between
∠
P
X
Q
\angle PXQ
∠
P
X
Q
and
∠
P
O
Q
\angle POQ
∠
P
O
Q
.
Show model answer
[QQ5(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q749
#749
Geometry → Trigonometry → Heights and Distances
·
Hard
Add
Two eagles are flying in the sky at a height of
10
3
10\sqrt{3}
10
3
m above the ground. A boy standing at a point on the ground looks towards the eagles making angles of elevation of
60
∘
60^\circ
6
0
∘
and
30
∘
30^\circ
3
0
∘
respectively. Find the distance between these two eagles.
Show model answer
[QQ5(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2026 board paper · 2026]
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Q750
#750
Geometry → Pythagoras Theorem → Pythagoras Theorem and its Converse
·
Easy
Add
Out of the following which is a Pythagorean triplet?
A
(
1
,
5
,
10
)
(1, 5, 10)
(
1
,
5
,
10
)
B
(
3
,
4
,
5
)
(3, 4, 5)
(
3
,
4
,
5
)
C
(
2
,
2
,
2
)
(2, 2, 2)
(
2
,
2
,
2
)
D
(
5
,
5
,
2
)
(5, 5, 2)
(
5
,
5
,
2
)
Tap an option to check your answer.
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[QQ1(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2025 board paper · 2025]
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