TS Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

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Polycet Mock Test

31) If the point P(x,y) divides the line segment joining the points A(x1,y1)and B(x2,y2) internally in the ratio m1:m2 then P(x,y)

A) \left(\frac{m_1x_2-m_2x_1}{m_1-m_2},\frac{m_1y_2-m_2y_1}{m_1-m_2}\right)
B) \left(\frac{m_1x_2+m_2x_1}{m_1-m_2},\frac{m_1y_2+m_2y_1}{m_1-m_2}\right)
C) \left(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}\right)
D) \left(\frac{m_1x_2-m_2x_1}{m_1+m_2},\frac{m_1y_2-m_2y_1}{m_1+m_2}\right)

View Answer
C) \left(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}\right)

Explanation:Internal division formula:
Answer: \left(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2}\right)

32) The radius of the sphere is increased by 100% then the volume of the resultant sphere is increased by

A) 200%
B) 700%
C) 500%
D) 900%

View Answer
B) 700%

Explanation:Radius increased by 100% ⇒ becomes 2r:
Answer: 700%
Explanation:New volume = \frac{4}{3}\pi(2r)^3 = 8 × \text{original} ⇒ increase = 700%

33) If the radius of a sphere is ‘2r’ then the volume will be

A) \frac43\mathrm{πr}^3
B) 4\mathrm{πr}^3
C) \frac83\mathrm{πr}^3
D) \frac{32}3\mathrm{πr}^3

View Answer
D) \frac{32}3\mathrm{πr}^3

Explanation:Volume of sphere of radius 2r:
Answer: \frac{32}{3}\pi r^3
Explanation:\frac{4}{3} \pi (2r)^3 = \frac{32}{3} \pi r^3

34) △ABC~△PQR; ∠P=60°,∠Q=60° then ∠A =

A) 90°
B) 75°
C) 40°
D) 60°

View Answer
D) 60°

Explanation:∆ABC \~ ∆PQR and ∠P = ∠A = 60°
Answer: 60°

35) The mid-point of the line segment joining the points (2,7) and (12,-7) is

A) (-7,0)
B) (7,0)
C) (0,-7)
D) (0,7)

View Answer
B) (7,0)

Explanation:Mid-point of (2,7) and (12,-7):
Answer: (7,0)
Explanation:Midpoint = \left(\frac{2+12}{2}, \frac{7+(-7)}{2}\right) = (7, 0)

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