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AP Polycet (Polytechnic) 2025 Previous Question Paper with Answers And Model Papers With Complete Analysis

41)Each one of 100 boxes is filled with 50 one-rupee coins on the first day and 25 more coins are added every next day. The Arithmetic Progression (AP) representing this situation is

A) 100, 50, 25, 10, …

B) 50, 25, 25, 25, …

C) 50, 75, 100, 125, …

D) 50, 25, 75, 100, …

View Answer

C) 50, 75, 100, 125, …
Explanation:Starts with 50 and increases by 25 → AP: 50, 75, 100, 125…
→ 50, 75, 100, 125, …

42)Common difference of the AP 3, 1, -1, -3, … is

A) 1

B) -2

C) -1

D) 2

View Answer

B) -2
Explanation:1 – 3 = -2
→ common difference = B. -2

43)Tenth term of the AP 1, -1, -3, -5, … is

A) -15

B) -17

C) -13

D) -10

View Answer

B) -17
Explanation:a = 1, d = -2 → 10th term = a + (10 – 1)d = 1 + 9(–2) = –17
→ -17

44)The sum of the first 22 terms of the AP 8, 3, -2, … is

A) -979

B) 979

C) 1028

D) -1028

View Answer

A) -979
Explanation:a = 8, d = -5 →
Sum = $\frac{n}{2} [2a + (n - 1)d] = \frac{22}{2} [16 + 21(-5)] = 11(16 - 105) = 11(-89) = -979$

→ -979

45)D and E are the midpoints of sides AB and AC of a triangle ABC respectively and BC = 10 cm. If DE ∥ BC, then the length of DE is

A) 3 cm

B) 5 cm

C) 4 cm

D) 6 cm

View Answer

B) 5 cm
Explanation:DE ∥ BC and D, E midpoints → DE = ½ BC = ½ × 10 = B. 5 cm

46)Which of the following are not similar figures?

A) Circles

B) Squares

C) Isosceles triangles

D) Equilateral triangles

View Answer

C) Isosceles triangles
Explanation:Isosceles triangles are not always similar
→ Isosceles triangles

47)If △ODC ∼△OBA and ∠BOC =125◦,then ∠DOC = ?

A) 60°

B) 55°

C) 50°

D) 65°

View Answer

B) 55°
Explanation:△ODC ∼ △OBA, so ∠DOC = ∠BOC = 125° (but in triangle ODC, angle should be < 90°, so it must be the matching corresponding angle). Since ∠BOC = 125°, ∠DOC is corresponding to ∠BOA = 180° – 125° = 55°
→ 55°

48)If $M\left(\frac{p}{3}, 4\right)$ is the midpoint of the line segment joining A(-6, 5) and B(-4, 3), then p = ?

A) -10

B) -8

C) -9

D) -15

View Answer

D) -15
Explanation:Midpoint of A(-6, 5) and B(-4, 3):
Midpoint = $\left( \frac{-6 + (-4)}{2}, \frac{5 + 3}{2} \right) = (-5, 4) \Rightarrow \frac{p}{3} = -5 \Rightarrow p = -15$

→ -15

49)The distance between the points (2, 3) and (4, 1) is

A) 2√2

B) 2

C) √2

D) 2√3

View Answer

A) 2√2
Explanation:Distance = $\sqrt{(4-2)^2 + (1-3)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$

→ 2√2

50)The coordinates of the point P(x, y) which divides the line segment joining the points $A(x_1, y_1)$ and $B(x_2, y_2)$ internally in the ratio $m_1 : m_2$ are

A) $\left( \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}, \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2} \right)$

B) $\left( \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right)$

C) $\left( \frac{m_1 x_2 - m_2 x_1}{m_1 + m_2}, \frac{m_1 y_2 - m_2 y_1}{m_1 + m_2} \right)$

D) $\left( \frac{m_1 x_2 - m_2 x_1}{m_1 - m_2}, \frac{m_1 y_2 - m_2 y_1}{m_1 - m_2} \right)$

View Answer

A) $\left( \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}, \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2} \right)$

Explanation:Internal division formula:
→ $\left( \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right)$

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