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

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 = $\left(\frac{2+12}{2}, \frac{7+(-7)}{2}\right) = (7, 0)$

36) The centroid of a triangle is (4,1) and two vertices are (2.3) and (7,6) then the third vertex is

A) (3,6)

B) (-3,6)

C) (-3.-6)

D) (3,-6)

View Answer

D) (3,-6)
Explanation:Centroid G = (4,1), known vertices (2,3), (7,6), find 3rd vertex (x, y):
Use: $G = \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$
Answer: (3, -6)

37) The angle between the tangent and radius drawn through the point of contact is

A) 100°

B) 70°

C) 90°

D) 80°

View Answer

C) 90°
Explanation:Angle between radius and tangent at point of contact:
Answer: 90°
Explanation:Always 90° between tangent and radius at point of contact.

38) Calculate the length of tangent from a point 15cm away from the centre of a circle of radius 9 cm.

A) 11 cm

B) 9 cm

C) 12 cm

D) 10 cm

View Answer

C) 12 cm
Explanation:Length of tangent from point 15 cm from center, radius = 9 cm:
Answer: 12 cm
Explanation:Tangent length = $\sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12$

39) In the below figure △RST~△RBA then the value of x is

A) 12

B) 24

C) 10

D) 18

View Answer

A) 12
Explanation:From image (△RST \~ △RBA), value of x:
Answer: 12
Explanation:Use similar triangle ratio from image: solve for x accordingly.

40) In the below figure △PQR~△ABC then z+y=

A) 1+3√3

B) 9+√3

C) 7+3√3

D) 4+3√3

View Answer

D) 4+3√3
Explanation:From image (△PQR \~ △ABC), z + y = ?
Answer: $4 + 3\sqrt{3}$
Explanation:Apply similarity ratios, substitute values to solve z and y, add.

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