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

41)The mean and mode of 5, 3, 9, 1, 9, 8, 9, 4 are m and n respectively, the value of m+n is?

A) 12

B) 15

C) 14

D) 10

View Answer

B) 15
Explanation:Mean = \( \frac{5+3+9+1+9+8+9+4}{8} \) = \( \frac{48}{8} \) = 6
Mode = 9 (occurs most)
⇒ m + n = 6 + 9 = 15
42)LCM of 9, 12 and 15 is?

A) 90

B) 180

C) 60

D) 45

View Answer

B) 180
Explanation:LCM of 9, 12, 15:
9 = 3², 12 = 2² × 3, 15 = 3 × 5
⇒ LCM = 2² × 3² × 5
= 180
43)Median of \( x, 20x, \frac{x}{20}, 200x, \frac{x}{200} \) (where \( x > 0 \)) is 20, then the value of \( x \) is:

A) 20

B) 40

C) 10

D) 30

View Answer

A) 20
Explanation:Arrange terms:
\( \frac{x}{200}, \frac{x}{20}, x, 20x, 200x \)
Median = x
⇒ x = 20
44)If \( 3^x = 9^{x-1} \), then the value of \( x \) is:

A) 2

B) 1

C) '0'

D) 3

View Answer

A) 2
Explanation:\( 3^x = (3²)^(x-1) = 3^(2x-2) \)
⇒ x = 2x – 2
⇒ x = 2
45)Mode of the data \( 19, 2, 6, 12, 12, 3, 5, 6, 18, 14, 6, 17, 2 \) is:

A) 6

B) 12

C) 2

D) 3

View Answer

A) 6
Explanation:6 appears most frequently
⇒ mode = 6
46)In \( \triangle ABC \), \( DE \parallel BC \), if \( AD = x + 1 \), \( DB = 3x – 1 \), \( AE = x \), and \( EC = 4x – 3 \), then the value of \( x \) is:

A) 1

B) 2

C) 3

D) 4

View Answer

A) 1
Explanation:Using Basic Proportionality Theorem:
\( \frac{AD}{DB} = \frac{AE}{EC} \)
⇒ \( \frac{x+1}{3x-1} = \frac{x}{4x-3} \)
⇒ solving gives x = 1
47)In \( \triangle ABC \), if \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm and \( BC = 6 \) cm, then the angle \( B \) is:

A) \( 90^\circ \)

B) \( 60^\circ \)

C) \( 45^\circ \)

D) \( 30^\circ \)

View Answer

A) \( 90^\circ \)
Explanation:Using cosine rule:
AB² = AC² + BC²
⇒ (6√3)² = 12² + 6²
⇒ 108 = 144 + 36
⇒ angle B = 90°
48)A regular brick is in the shape of:

A) Cube

B) Cuboid

C) Cone

D) Cylinder

View Answer

B) Cuboid
Explanation:A brick is a cuboid
49)A cylinder and a cone have bases of equal radii and heights, then the ratio of volumes is:

A) 3:1

B) 2:1

C) 1:1

D) 4:1

View Answer

A) 3:1
Explanation:Volume of cylinder : cone
= πr²h : \( \frac{1}{3} \)πr²h
= 3 : 1
50)The ratio of the areas of two similar triangles is equal to the ratio of the ______ their corresponding sides.

A) Cube of

B) Square of

C) Square root of

D) Twice of

View Answer

B) Square of
Explanation:Ratio of areas = square of ratio of sides
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