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Exam: Maharashtra State Board Class 10
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Q351
#351
Geometry → Mensuration → Surface Area and Volume of Solids
·
Easy
Add
Complete the activity to 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(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q352
#352
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
·
Has image
Add
In trapezium ABCD, side AB
∥
\parallel
∥
side PQ
∥
\parallel
∥
side DC, with P on side AD and Q on side BC.
A
P
=
15
AP = 15
A
P
=
15
,
P
D
=
12
PD = 12
P
D
=
12
,
Q
C
=
14
QC = 14
QC
=
14
. Find BQ.
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[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q353
#353
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Easy
Add
Find the length of the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
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[QQ2(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q354
#354
Geometry → Circle → Measure of an Arc and Central Angle
·
Moderate
·
Has image
Add
In the given figure, points G, D, E, F lie on a circle with centre C.
∠
E
C
F
=
70
∘
\angle ECF = 70^\circ
∠
E
C
F
=
7
0
∘
and
m
(
arc
D
G
F
)
=
200
∘
m(\text{arc } DGF) = 200^\circ
m
(
arc
D
GF
)
=
20
0
∘
. Find (i)
m
(
arc
D
E
)
m(\text{arc } DE)
m
(
arc
D
E
)
and (ii)
m
(
arc
D
E
F
)
m(\text{arc } DEF)
m
(
arc
D
E
F
)
.
Show model answer
[QQ2(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q355
#355
Geometry → Co-ordinate Geometry → Distance Formula
·
Moderate
Add
Show that the points
A
(
−
1
,
−
1
)
A(-1, -1)
A
(
−
1
,
−
1
)
,
B
(
0
,
1
)
B(0, 1)
B
(
0
,
1
)
,
C
(
1
,
3
)
C(1, 3)
C
(
1
,
3
)
are collinear.
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[QQ2(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q356
#356
Geometry → Trigonometry → Heights and Distances
·
Easy
Add
A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is
45
∘
45^\circ
4
5
∘
. Find the height of the temple.
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[QQ2(B)(5) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q357
#357
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
·
Has image
Add
In
△
P
Q
R
\triangle PQR
△
P
QR
, seg PM is a median. The angle bisectors of
∠
P
M
Q
\angle PMQ
∠
P
M
Q
and
∠
P
M
R
\angle PMR
∠
P
M
R
intersect side PQ and side PR in points X and Y respectively. Complete the activity to prove that XY
∥
\parallel
∥
QR.
Show model answer
[QQ3(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q358
#358
Geometry → Co-ordinate Geometry → Section Formula
·
Easy
Add
Find the co-ordinates of point P, where P is the midpoint of the line segment AB with
A
(
−
4
,
2
)
A(-4, 2)
A
(
−
4
,
2
)
and
B
(
6
,
2
)
B(6, 2)
B
(
6
,
2
)
.
Show model answer
[QQ3(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q359
#359
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Moderate
Add
In
△
A
B
C
\triangle ABC
△
A
B
C
, seg AP is a median. If
B
C
=
18
BC = 18
B
C
=
18
and
A
B
2
+
A
C
2
=
260
AB^2 + AC^2 = 260
A
B
2
+
A
C
2
=
260
, find AP.
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[QQ3(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q360
#360
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Moderate
Add
Prove that, "Angles inscribed in the same arc are congruent."
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[QQ3(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q361
#361
Geometry → Geometric Constructions → Construction of a Tangent to a Circle
·
Moderate
Add
Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q.
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[QQ3(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q362
#362
Geometry → Mensuration → Combination of Solids and Frustum
·
Moderate
Add
The radii of the circular ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area.
(
π
=
3.14
)
(\pi = 3.14)
(
π
=
3.14
)
Show model answer
[QQ3(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q363
#363
Geometry → Similarity → Theorem of Areas of Similar Triangles
·
Hard
Add
In
△
A
B
C
\triangle ABC
△
A
B
C
, seg DE
∥
\parallel
∥
side BC. If
2
A
(
△
A
D
E
)
=
A
(
□
D
B
C
E
)
2A(\triangle ADE) = A(\square DBCE)
2
A
(
△
A
D
E
)
=
A
(
□
D
B
C
E
)
, find
A
B
:
A
D
AB : AD
A
B
:
A
D
and show that
B
C
=
3
D
E
BC = \sqrt{3}\, DE
B
C
=
3
D
E
.
Show model answer
[QQ4(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q364
#364
Geometry → Geometric Constructions → Construction of a Similar Triangle
·
Moderate
Add
△
S
H
R
∼
△
S
V
U
\triangle SHR \sim \triangle SVU
△
S
H
R
∼
△
S
V
U
. In
△
S
H
R
\triangle SHR
△
S
H
R
,
S
H
=
4.5
SH = 4.5
S
H
=
4.5
cm,
H
R
=
5.2
HR = 5.2
H
R
=
5.2
cm,
S
R
=
5.8
SR = 5.8
S
R
=
5.8
cm and
S
H
S
V
=
3
5
\dfrac{SH}{SV} = \dfrac{3}{5}
S
V
S
H
=
5
3
. Construct
△
S
V
U
\triangle SVU
△
S
V
U
.
Show model answer
[QQ4(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q365
#365
Geometry → Mensuration → Surface Area and Volume of Solids
·
Moderate
Add
An ice-cream pot has a right circular cylindrical shape. The radius of the base is 12 cm and the height is 7 cm. This pot is completely filled with ice-cream. The entire ice-cream is given to students in the form of right circular ice-cream cones having diameter 4 cm and height 3.5 cm. If each student is given one cone, how many students can be served?
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[QQ4(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q366
#366
Geometry → Circle → Tangent Segment Theorem
·
Hard
·
Has image
Add
In the given figure, a circle touches side BC of
△
A
B
C
\triangle ABC
△
A
B
C
at point P from outside the triangle. Lines AC and AB, when extended, are tangents to the circle at points N and M respectively. Prove that
A
M
=
1
2
(
Perimeter of
△
A
B
C
)
AM = \dfrac{1}{2}(\text{Perimeter of } \triangle ABC)
A
M
=
2
1
(
Perimeter of
△
A
B
C
)
.
Show model answer
[QQ5(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q367
#367
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Easy
Add
Eliminate
θ
\theta
θ
if
x
=
r
cos
θ
x = r\cos\theta
x
=
r
cos
θ
and
y
=
r
sin
θ
y = r\sin\theta
y
=
r
sin
θ
.
Show model answer
[QQ5(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
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Q368
#368
Algebra → Financial Planning → Goods and Services Tax (GST)
·
Easy
Add
Rate of GST on essential commodities is ____.
A
5%
B
12%
C
0%
D
18%
Tap an option to check your answer.
Show solution
[QQ1(A)(i) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q369
#369
Algebra → Quadratic Equations → Roots of a Quadratic Equation
·
Easy
Add
Out of the following equations which one is not a quadratic equation?
A
x
2
+
4
x
=
11
+
x
2
x^2 + 4x = 11 + x^2
x
2
+
4
x
=
11
+
x
2
B
x
2
=
4
x
x^2 = 4x
x
2
=
4
x
C
5
x
2
=
90
5x^2 = 90
5
x
2
=
90
D
2
x
−
x
2
=
x
2
+
5
2x - x^2 = x^2 + 5
2
x
−
x
2
=
x
2
+
5
Tap an option to check your answer.
Show solution
[QQ1(A)(ii) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q370
#370
Algebra → Linear Equations in Two Variables → Graph of Linear Equations
·
Easy
Add
To draw graph of
4
x
+
5
y
=
19
4x + 5y = 19
4
x
+
5
y
=
19
, find the value of
y
y
y
when
x
=
1
x = 1
x
=
1
.
A
4
B
3
C
2
D
−
3
-3
−
3
Tap an option to check your answer.
Show solution
[QQ1(A)(iii) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q371
#371
Algebra → Arithmetic Progression → Sum of n Terms of an A.P.
·
Easy
Add
Sum of first five multiples of 3 is ____.
A
45
B
55
C
15
D
75
Tap an option to check your answer.
Show solution
[QQ1(A)(iv) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q372
#372
Algebra → Financial Planning → Goods and Services Tax (GST)
·
Easy
Add
On certain article if rate of CGST is
9
%
9\%
9%
, then what is the rate of GST?
Show model answer
[QQ1(B)(i) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q373
#373
Algebra → Linear Equations in Two Variables → Determinant Method (Cramer's Rule)
·
Easy
Add
For simultaneous equations in variables
x
x
x
and
y
y
y
, if
D
x
=
−
42
D_x = -42
D
x
=
−
42
and
D
=
−
3
D = -3
D
=
−
3
, then find the value of
x
x
x
.
Show model answer
[QQ1(B)(ii) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q374
#374
Algebra → Probability → Sample Space and Events
·
Easy
Add
When two coins are tossed simultaneously, write the sample space
S
S
S
.
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[QQ1(B)(iii) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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Q375
#375
Algebra → Quadratic Equations → Roots of a Quadratic Equation
·
Easy
Add
Write the following quadratic equation in the form
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
:
2
y
=
10
−
y
2
2y = 10 - y^2
2
y
=
10
−
y
2
.
Show model answer
[QQ1(B)(iv) · Maharashtra State Board Class 10 (SSC) — Algebra (Mathematics Part I), March 2026 board paper · 2026]
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