PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in
Filtered questions
942 questions match
Filters
1
Download
· 942
Filtering by:
Exam: Maharashtra State Board Class 10
Clear all
Copy link
Q801
#801
Geometry → Geometric Constructions → Construction of a Similar Triangle
·
Moderate
Add
△
A
B
C
∼
△
L
M
N
\triangle ABC \sim \triangle LMN
△
A
B
C
∼
△
L
M
N
. In
△
A
B
C
\triangle ABC
△
A
B
C
,
A
B
=
5.5
AB = 5.5
A
B
=
5.5
cm,
B
C
=
6
BC = 6
B
C
=
6
cm,
C
A
=
4.5
CA = 4.5
C
A
=
4.5
cm. Construct
△
A
B
C
\triangle ABC
△
A
B
C
and
△
L
M
N
\triangle LMN
△
L
M
N
such that
B
C
M
N
=
5
4
\dfrac{BC}{MN} = \dfrac{5}{4}
M
N
B
C
=
4
5
.
Show model answer
[QQ3(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q802
#802
Geometry → Pythagoras Theorem → Applications of Pythagoras Theorem
·
Moderate
Add
Seg PM is a median of
△
P
Q
R
\triangle PQR
△
P
QR
,
P
M
=
9
PM = 9
P
M
=
9
and
P
Q
2
+
P
R
2
=
290
PQ^2 + PR^2 = 290
P
Q
2
+
P
R
2
=
290
. Then find QR.
Show model answer
[QQ3(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q803
#803
Geometry → Similarity → Basic Proportionality Theorem
·
Moderate
Add
Prove that: 'If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the remaining sides in the same proportion.'
Show model answer
[QQ3(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q804
#804
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Hard
Add
If
1
sin
2
θ
−
1
cos
2
θ
−
1
tan
2
θ
−
1
cot
2
θ
−
1
sec
2
θ
−
1
cosec
2
θ
=
−
3
\dfrac{1}{\sin^2\theta} - \dfrac{1}{\cos^2\theta} - \dfrac{1}{\tan^2\theta} - \dfrac{1}{\cot^2\theta} - \dfrac{1}{\sec^2\theta} - \dfrac{1}{\operatorname{cosec}^2\theta} = -3
sin
2
θ
1
−
cos
2
θ
1
−
tan
2
θ
1
−
cot
2
θ
1
−
sec
2
θ
1
−
cosec
2
θ
1
=
−
3
, then find the value of
θ
\theta
θ
.
Show model answer
[QQ4(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q805
#805
Geometry → Mensuration → Surface Area and Volume of Solids
·
Moderate
Add
A cylinder of radius 12 cm contains water up to a height of 20 cm. A spherical iron ball is dropped into the cylinder and the water level rises by 6.75 cm. What is the radius of the iron ball?
Show model answer
[QQ4(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q806
#806
Geometry → Geometric Constructions → Construction of a Tangent to a Circle
·
Moderate
Add
Draw a circle with centre O and radius 3 cm. Draw tangent segments PA and PB through a point P outside the circle such that
∠
A
P
B
=
70
∘
\angle APB = 70^\circ
∠
A
P
B
=
7
0
∘
.
Show model answer
[QQ4(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q807
#807
Geometry → Similarity → Tests of Similarity of Triangles
·
Moderate
Add
□
A
B
C
D
\square ABCD
□
A
B
C
D
is a trapezium with
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
. The diagonals of the trapezium intersect at point P. (a) Draw the figure using the given information. (b) Write any one pair of alternate angles and one pair of opposite (vertically opposite) angles. (c) Write the names of the similar triangles with the test of similarity.
Show model answer
[QQ5(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q808
#808
Geometry → Circle → Tangent and Secant to a Circle
·
Moderate
Add
AB is a chord of a circle with centre O. AOC is a diameter of the circle and AT is a tangent at A. (a) Draw the figure using the given information. (b) Find the measures of
∠
C
A
T
\angle CAT
∠
C
A
T
and
∠
A
B
C
\angle ABC
∠
A
B
C
with reasons. (c) Are
∠
C
A
T
\angle CAT
∠
C
A
T
and
∠
A
B
C
\angle ABC
∠
A
B
C
congruent? Justify your answer.
Show model answer
[QQ5(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2024 board paper · 2024]
Report
Q809
#809
Geometry → Pythagoras Theorem → Pythagoras Theorem and its Converse
·
Easy
Add
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are sides of a triangle and
a
2
+
b
2
=
c
2
a^2 + b^2 = c^2
a
2
+
b
2
=
c
2
, name the type of triangle:
A
Obtuse angled triangle
B
Acute angled triangle
C
Right angled triangle
D
Equilateral triangle
Tap an option to check your answer.
Show solution
[QQ1(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q810
#810
Geometry → Circle → Theorems on Chords and Tangents
·
Easy
Add
Chords AB and CD of a circle intersect inside the circle at point E. If
A
E
=
4
AE = 4
A
E
=
4
,
E
B
=
10
EB = 10
E
B
=
10
,
C
E
=
8
CE = 8
C
E
=
8
, then find ED:
A
7
B
5
C
8
D
9
Tap an option to check your answer.
Show solution
[QQ1(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q811
#811
Geometry → Co-ordinate Geometry → Coordinates and the Cartesian Plane
·
Easy
Add
Co-ordinates of the origin are ________.
A
(
0
,
0
)
(0, 0)
(
0
,
0
)
B
(
0
,
1
)
(0, 1)
(
0
,
1
)
C
(
1
,
0
)
(1, 0)
(
1
,
0
)
D
(
1
,
1
)
(1, 1)
(
1
,
1
)
Tap an option to check your answer.
Show solution
[QQ1(A)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q812
#812
Geometry → Mensuration → Surface Area and Volume of Solids
·
Easy
Add
If the radius of the base of a cone is 7 cm and its height is 24 cm, then find its slant height:
A
23 cm
B
26 cm
C
31 cm
D
25 cm
Tap an option to check your answer.
Show solution
[QQ1(A)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q813
#813
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
(
△
A
B
C
)
A
(
△
P
Q
R
)
=
16
25
\dfrac{A(\triangle ABC)}{A(\triangle PQR)} = \dfrac{16}{25}
A
(
△
P
QR
)
A
(
△
A
B
C
)
=
25
16
, then find
A
B
:
P
Q
AB : PQ
A
B
:
P
Q
.
Show model answer
[QQ1(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q814
#814
Geometry → Pythagoras Theorem → 30-60-90 Triangle Theorem
·
Easy
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.
Show model answer
[QQ1(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q815
#815
Geometry → Circle → Theorems on Chords and Tangents
·
Easy
Add
If the radius of a circle is 5 cm, then find the length of the longest chord of the circle.
Show model answer
[QQ1(B)(3) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q816
#816
Geometry → Co-ordinate Geometry → Distance Formula
·
Easy
Add
Find the distance between the points
O
(
0
,
0
)
O(0, 0)
O
(
0
,
0
)
and
P
(
3
,
4
)
P(3, 4)
P
(
3
,
4
)
.
Show model answer
[QQ1(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q817
#817
Geometry → Circle → Inscribed Angle and Intercepted Arc
·
Easy
·
Has image
Add
In the given figure, points L, M, N lie on a circle and
∠
L
=
35
∘
\angle L = 35^\circ
∠
L
=
3
5
∘
. Complete the activity to find (i)
m
(
arc
M
N
)
m(\text{arc } MN)
m
(
arc
M
N
)
and (ii)
m
(
arc
M
L
N
)
m(\text{arc } MLN)
m
(
arc
M
L
N
)
.
Show model answer
[QQ2(A)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q818
#818
Geometry → Trigonometry → Trigonometric Ratios and Identities
·
Easy
Add
Show that
cot
θ
+
tan
θ
=
csc
θ
×
sec
θ
\cot\theta + \tan\theta = \csc\theta \times \sec\theta
cot
θ
+
tan
θ
=
csc
θ
×
sec
θ
.
Show model answer
[QQ2(A)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q819
#819
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]
Report
Q820
#820
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.
Show model answer
[QQ2(B)(1) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q821
#821
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.
Show model answer
[QQ2(B)(2) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q822
#822
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]
Report
Q823
#823
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.
Show model answer
[QQ2(B)(4) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q824
#824
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.
Show model answer
[QQ2(B)(5) · Maharashtra State Board Class 10 (SSC) — Geometry (Mathematics Part II), March 2023 board paper · 2023]
Report
Q825
#825
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]
Report
Prev
Page 33 of 38
Next
1
…
32
33
34
…
38
PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in