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

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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