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

11)The terms 4, 7, 10, \dots form an A.P. The sum of the first 15 terms is?

A) 340

B) 360

C) 375

D) 390

View Answer

C) 375
Explanation:a = 4, d = 3, n = 15
Sum = \( \frac{n}{2} \)[2a + (n-1)d] = \( \frac{15}{2} \)[8 + 42] = \( \frac{15}{2} \) × 50 = 375

12)If a line is passing through the points (2, 5) and (x, 3) and its slope is 2, then the value of x is?

A) 6

B) 7

C) 8

D) 9

View Answer

A) 6
Explanation:Slope = \( \frac{3 – 5}{x – 2} \) = 2
⇒ \( \frac{-2}{x – 2} \) = 2
⇒ -2 = 2(x – 2)
⇒ x = 6

13)The distance of point (2, 4) from the x-axis is?

A) 2

B) 4

C) 6

D) 8

View Answer

B) 4
Explanation:Distance from x-axis = |y| = 4

14)The area of the triangle with vertices (1, 1), (-4, 6), (-3, -5) is?

A) 20

B) 24

C) 30

D) 35

View Answer

B) 24
Explanation:Area = \( \frac{1}{2} \) |x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)|
= \( \frac{1}{2} \) |1(6+5) + (-4)(-6) + (-3)(-5)|
= \( \frac{1}{2} \) × 48
= 24

15)If \( A = 45^\circ \), then the value of \( \sin A + \cos A + \cos 2A \) is?

A) \( \sqrt{2} \)

B) 1

C) 2

D) '0'

View Answer

A) \( \sqrt{2} \)
Explanation:sin45° = cos45° = \( \frac{1}{\sqrt{2}} \), cos90° = 0
⇒ total = \( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \)
= √2

16)\( \cot(90^\circ – \theta) = ? \)

A) \( \sin \theta \)

B) \( \cos \theta \)

C) \( \tan \theta \)

D) \( \sec \theta \)

View Answer

B) \( \cos \theta \)
Explanation:cot(90° – θ) = tan θ

17)If A is the set of odd numbers less than 6 and B is the set of prime factors of 30, then:

A) \( A \cup B = \{1, 3, 5, 2, 3, 5\} \)

B) \( A \cap B = \{3, 5\} \)

C) \( A \neq B \)

D) \( A \cup B = \{1, 3, 5, 2, 3\} \)

View Answer

C) \( A \neq B \)
Explanation:A = {1, 3, 5}, B = {2, 3, 5}
⇒ A ≠ B

18)If the pair of equations \( 3x + 4y = k \) and \( 9x + 12y = 6 \) has infinite number of solutions, then the value of k is:

A) 1

B) 2

C) 3

D) 4

View Answer

B) 2
Explanation:For infinite solutions:
\( \frac{3}{9} = \frac{4}{12} = \frac{k}{6} \)
⇒ \( \frac{1}{3} = \frac{k}{6} \)
⇒ k = 2

19)The product of the zeroes of a polynomial \( x^3 – 3x^2 + x + 1 \) is:

A) 1

B) -1

C) 3

D) -3

View Answer

B) -1
Explanation:Product of zeroes
= \( \frac{-1}{1} \)
= -1

20)The sum of the first n natural numbers is:

A) \( \frac{n(n+1)}{2} \)

B) \( \frac{n(n-1)}{2} \)

C) \( n^2 \)

D) \( n(n+1) \)

View Answer

A) \( \frac{n(n+1)}{2} \)
Explanation:Sum of n natural numbers = \( \frac{n(n+1)}{2} \)

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