TS POLYCET 2025 Question Paper with Solutions Free (Set-wise Answer Key)

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°
Your Score: 0 / 0
Spread the love

Leave a Comment

About Us | Contact Us | Privacy Polocy
error: Content is protected !!