51) In \( \triangle PQR \), \( ST \parallel QR \), \( PQ = 12 \) cm, \( PR = 24 \) cm, and \( SP = 4 \) cm, then \( PT = \):
A) 8 cm
B) 6 cm
C) 12 cm
D) 10 cm
View Answer
A) 8 cm
Explanation:By similarity (Basic Proportionality Theorem):
\( \frac{SP}{PQ} = \frac{PT}{PR} \)
⇒ \( \frac{4}{12} = \frac{PT}{24} \)
⇒ PT = 8 cm
52) The maximum number of parallel tangents that can be drawn to a circle is:
A) 2
B) 3
C) 4
D) 1
View Answer
A) 2
Explanation:At most two parallel tangents can be drawn to a circle
53) The parallelogram circumscribing a circle is a:
A) Square
B) Rectangle
C) Rhombus
D) Trapezium
View Answer
C) Rhombus
Explanation:A parallelogram that circumscribes a circle must have all sides equal ⇒ rhombus
54) \( \log 2 \) is:
A) A rational number
B) An irrational number
C) A whole number
D) An integer
View Answer
B) An irrational number
Explanation:log 2 is irrational
55) The distance between two parallel tangents of a circle of radius 4 cm is:
A) 8 cm
B) 4 cm
C) 16 cm
D) 2 cm
View Answer
A) 8 cm
Explanation:Distance between parallel tangents = diameter = 2r = 8 cm
56) In \( \triangle ABC \), \( DE \) is a line such that \( \frac{AD}{DB} = \frac{AE}{EC} \) and \( \angle EDA = \angle ACB \), then \( \triangle ABC \) is a/an:
A) Scalene triangle
B) Isosceles triangle
C) Equilateral triangle
D) Right-angled triangle
View Answer
B) Isosceles triangle
Explanation:Given proportional sides and equal angles ⇒ triangle is isosceles
57) All the circles are:
A) Different
B) Similar
C) Equal
D) Congruent
View Answer
B) Similar
Explanation:All circles have same shape ⇒ similar
58) If the angle between two radii of a circle is \( 120^\circ \), then the angle between the tangent and the ends of the radii is:
A) \( 30^\circ \)
B) \( 60^\circ \)
C) \( 90^\circ \)
D) \( 120^\circ \)
View Answer
B) \( 60^\circ \)
Explanation:Angle between tangent and radius = 90°
Remaining angle = 180° – 120°
= 60°
59) A line which intersects a circle at two points is called:
A) Secant
B) Tangent
C) Chord
D) Arc
View Answer
A) Secant
Explanation:A line cutting a circle at two points is called a secant
60) In the given figure, if \( \angle AOB = 125^\circ \), then \( \angle COD = \):
A) \( 125^\circ \)
B) \( 55^\circ \)
C) \( 90^\circ \)
D) \( 45^\circ \)
View Answer
B) \( 55^\circ \)
Explanation:Angles in circle geometry:
∠COD = 180° – 125°
= 55°
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