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All questions of October Week 3 for Class 10 Exam
In the given figure, AR=5cm, BR=4cm and AC =11cm. What is the length of BC?
- a)6 cm
- b)10 cm
- c)4 cm
- d)8 cm
Correct answer is option 'B'. Can you explain this answer?
In the given figure, AR=5cm, BR=4cm and AC =11cm. What is the length of BC?
a)
6 cm
b)
10 cm
c)
4 cm
d)
8 cm
|
Vivek Rana answered |
Since the sides of the triangles are tangent to the circle. BR = BP,AR = AQ and CP = CQ
So, BP = 4cm and AQ = 5
CQ = 11-5 = 6 = CP
BC = BP + CP = 4 + 6 = 10 cm
So, BP = 4cm and AQ = 5
CQ = 11-5 = 6 = CP
BC = BP + CP = 4 + 6 = 10 cm
PT is a tangent from an external point P and PAB is a secant. If PT = 6cm and PA = 3cm, then the length of PB is __- a)6
- b)36
- c)12
- d)2
Correct answer is option 'C'. Can you explain this answer?
PT is a tangent from an external point P and PAB is a secant. If PT = 6cm and PA = 3cm, then the length of PB is __
a)
6
b)
36
c)
12
d)
2
|
Rahul Kapoor answered |
We know that:
PT^2 = PA X PB
therfore PB = PT^2/PA = 36/3 = 12
ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is
- a)3 cm
- b)8 cm
- c)2 cm
- d)5 cm
Correct answer is option 'C'. Can you explain this answer?
ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is
a)
3 cm
b)
8 cm
c)
2 cm
d)
5 cm
|
Coachify answered |
By pythagoras theorem ,
H2 = P2 + B2
=36 + 64=100
H=10
We have a square BPOQ so all sides are equal.
Since tangents from a point are equal in length
Let AP = AR = x
BP=BQ=y
RC = QC = z
x + y = 8
x = 8 - y
x + z = 10 ⇒ 8 - y + z = 10 ⇒ z = 2 + y
y + z = 6 ⇒ y + 2 + y = 6 ⇒ y = 2
x = 6, z= 4
Since BP = OQ = y = 2
H2 = P2 + B2
=36 + 64=100
H=10
We have a square BPOQ so all sides are equal.
Since tangents from a point are equal in length
Let AP = AR = x
BP=BQ=y
RC = QC = z
x + y = 8
x = 8 - y
x + z = 10 ⇒ 8 - y + z = 10 ⇒ z = 2 + y
y + z = 6 ⇒ y + 2 + y = 6 ⇒ y = 2
x = 6, z= 4
Since BP = OQ = y = 2
A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be
- a)AD = 4cm, BE = 6cm, CF = 8cm
- b)AD = 5cm, BE = 9cm, CF = 4cm
- c)AD = 3cm, BE = 7cm, CF = 5cm
- d)AD = 2cm, BE = 6cm, CF = 7cm
Correct answer is option 'C'. Can you explain this answer?
A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be
a)
AD = 4cm, BE = 6cm, CF = 8cm
b)
AD = 5cm, BE = 9cm, CF = 4cm
c)
AD = 3cm, BE = 7cm, CF = 5cm
d)
AD = 2cm, BE = 6cm, CF = 7cm
|
Tanishka Gupta answered |
Segment joining the points of contact of two parallel tangents- a)may or may not pass through the centre.
- b)will pass through the centre.
- c)will not pass through the centre.
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Segment joining the points of contact of two parallel tangents
a)
may or may not pass through the centre.
b)
will pass through the centre.
c)
will not pass through the centre.
d)
none of these
|
Omprakash Meena answered |
Because that is diameter which definitely pass through the centre
How does the relationship between the central government and state governments differ in federations compared to unitary systems?
- a)The central government in federations has no authority over state governments
- b)State governments in federations are subordinate to the central government
- c)The central government in unitary systems can not order state governments
- d)State governments in unitary systems have more autonomy than in federations
Correct answer is option 'B'. Can you explain this answer??
How does the relationship between the central government and state governments differ in federations compared to unitary systems?
a)
The central government in federations has no authority over state governments
b)
State governments in federations are subordinate to the central government
c)
The central government in unitary systems can not order state governments
d)
State governments in unitary systems have more autonomy than in federations
|
Kalyan singh answered |
The Nature of Federalism vs. Unitary Systems
In understanding the dynamics between central and state governments, it’s essential to differentiate between federations and unitary systems.
Federations: Distribution of Power
- In a federal system, power is divided between the central (national) government and state (regional) governments.
- Each level of government has its own sphere of authority, often enshrined in a constitution.
State Governments' Authority in Federations
- Option B correctly states that state governments in federations are subordinate to the central government. This means:
- The central government has the ultimate authority in areas defined by the constitution, including defense, foreign affairs, and immigration.
- State governments have their own powers but can be overridden or regulated by the central government.
- This relationship ensures a balance of power, where the central government can maintain national consistency while allowing states some autonomy.
Unitary Systems: Centralized Control
- In contrast, unitary systems concentrate power in a single central government.
- State or regional authorities exist but primarily serve to implement the directives of the central government.
Key Differences
- In unitary systems, the central government can easily direct state governments, often leading to less autonomy for regions.
- Federations encourage a degree of independence for states, yet they remain under the overarching authority of the central government.
In summary, while state governments in federations have a degree of independence, they remain subordinate to the central government, which is not the case in unitary systems where the central authority holds greater control.
In understanding the dynamics between central and state governments, it’s essential to differentiate between federations and unitary systems.
Federations: Distribution of Power
- In a federal system, power is divided between the central (national) government and state (regional) governments.
- Each level of government has its own sphere of authority, often enshrined in a constitution.
State Governments' Authority in Federations
- Option B correctly states that state governments in federations are subordinate to the central government. This means:
- The central government has the ultimate authority in areas defined by the constitution, including defense, foreign affairs, and immigration.
- State governments have their own powers but can be overridden or regulated by the central government.
- This relationship ensures a balance of power, where the central government can maintain national consistency while allowing states some autonomy.
Unitary Systems: Centralized Control
- In contrast, unitary systems concentrate power in a single central government.
- State or regional authorities exist but primarily serve to implement the directives of the central government.
Key Differences
- In unitary systems, the central government can easily direct state governments, often leading to less autonomy for regions.
- Federations encourage a degree of independence for states, yet they remain under the overarching authority of the central government.
In summary, while state governments in federations have a degree of independence, they remain subordinate to the central government, which is not the case in unitary systems where the central authority holds greater control.
In the given figure, length of BC is:
- a)15 cm
- b)10 cm
- c)13 cm
- d)21 cm
Correct answer is option 'B'. Can you explain this answer?
In the given figure, length of BC is:
a)
15 cm
b)
10 cm
c)
13 cm
d)
21 cm
|
|
Mehak Jaju answered |
Theorem use krna if 2 tangents are arising from same point are of equal length
In the figure, PQ is a tangent at a point R of the circle with centre O. If ∠TRQ = 30°.The measure of ∠PRS is
- a)45°
- b)120°
- c)90°
- d)60°
Correct answer is option 'D'. Can you explain this answer?
In the figure, PQ is a tangent at a point R of the circle with centre O. If ∠TRQ = 30°.The measure of ∠PRS is
a)
45°
b)
120°
c)
90°
d)
60°
|
|
Arwin answered |
TRQ=30,
TSR=TRQ=30( alternate segment theorem)-1
TRS=90( angle in semicircle)--2,
from 1&2 and by angle sum property of a triangle,
RTS=60,
since RTS=PRS ( by alternate segment theory)
PRS=60
TSR=TRQ=30( alternate segment theorem)-1
TRS=90( angle in semicircle)--2,
from 1&2 and by angle sum property of a triangle,
RTS=60,
since RTS=PRS ( by alternate segment theory)
PRS=60
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Weekly Tests for Class 10 Preparation
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