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

31)The mean of 20, 30, 38, 40, 50, 56, 60 is:

A) 42

B) 44

C) 46

D) 48

View Answer

A) 42
Explanation:Mean = \( \frac{294}{7} \) = 42
32)If the equations \( x + 2y = 5 \) and \( 3x + ky = 10 \) are inconsistent, then the value of k is:

A) 4

B) 6

C) 8

D) 10

View Answer

B) 6
Explanation:For inconsistency:
\( \frac{1}{3} = \frac{2}{k} \)
⇒ k = 6
33)If the pair of linear equations \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) represent coincident lines, then:

A) \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)

B) \( \frac{a_1}{a_2} = \frac{b_1}{b_2} \)

C) \( \frac{a_1}{a_2} = \frac{c_1}{c_2} \)

D) \( \frac{b_1}{b_2} = \frac{c_1}{c_2} \)

View Answer

A) \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)
Explanation:Coincident lines:
\( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)
34)From the top of a tower 60 meters high, the angle of depression of an object is 60°, then the distance of the object from the base of the tower is:

A) \( \frac{60}{\sqrt{3}} \, m \)

B) \( 60\sqrt{3} \, m \)

C) \( 60 \, m \)

D) \( 30\sqrt{3} \, m \)

View Answer

A) \( \frac{60}{\sqrt{3}} \, m \)
Explanation:tan60° = \( \frac{60}{d} \)
⇒ d = \( \frac{60}{\sqrt{3}} \)
35)The angle of elevation of the top of a building from a point 10 meters away from the base is 60°, then the height of the building is:

A) \( \frac{10}{\sqrt{3}} \, m \)

B) \( 10\sqrt{3} \, m \)

C) \( 10 \, m \)

D) \( \frac{10}{3} \, m \)

View Answer

B) \( 10\sqrt{3} \, m \)
Explanation:tan60° = \( \frac{h}{10} \)
⇒ h = 10√3
36)\( 5 + \sqrt{7} \) is:

A) an irrational number

B) a rational number

C) an integer

D) a whole number

View Answer

A) an irrational number
Explanation:5 + √7 is irrational
37)If \( x, y, z \) are distinct prime numbers, then the H.C.F. of \( x^2 y^3 z \) and \( x^3 y z^2 \) is:

A) \( x^2 y z \)

B) \( x y z^2 \)

C) \( x^3 y^3 z^3 \)

D) \( x^2 y^2 z^2 \)

View Answer

A) \( x^2 y z \)
Explanation:HCF = x²yz
38)The value of \( \log_3 81 \) is:

A) 2

B) 3

C) 4

D) 5

View Answer

C) 4
Explanation:log₃81 = 4
39)What is the median of 18, 14, 6, 7, 8?

A) 7

B) 8

C) 6

D) 14

View Answer

B) 8
Explanation:Arrange: 6, 7, 8, 14, 18
⇒ median = 8
40)If the mean of \( x, y, 3, 4 \) is 5, then \( x + y = ? \)

A) 8

B) 13

C) 15

D) 9

View Answer

B) 13
Explanation:Mean = \( \frac{x + y + 7}{4} = 5 \)
⇒ x + y = 13
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