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TS Polycet (Polytechnic) 2019 Previous Question Paper with Answers And Model Papers With Complete Analysis

31) In an isosceles triangle ABC with AC = BC if AB² = 2AC², then ∠C =

A) 30°

B) 90°

C) 45°

D) 60°

View Answer

B) 90°
Explanation:AB² = 2AC² => ∠C= 90°

32) In a right-angled triangle ABC right-angled at B. If P and Q are points on the sides AB and BC respectively, then which of the following is true?

A) AQ² + CP² = 2(AC² + PQ²)

B) 2(AQ² + CP²) = AC² + PQ²

C) AQ² + CP² = AC² + PQ²

D) None

View Answer

C) AQ² + CP² = AC² + PQ²
Explanation:AQ² + CP² = AC² – PQ²

33) In △ABC the sides are 6, 10 and 8, then △ABC is

A) Right-angled triangle

B) Acute angled triangle

C) Obtuse angled triangle

D) None

View Answer

A) Right-angled triangle
Explanation:(6)² – (8)² =36 + 64
= 100 = (10)²;
Right-angled triangle.

34) From the given figure, value of OP is

A) 5

B) 4

C) √8

D) 3

View Answer

A) 5
Explanation:OP² = OA² + AP² = 32 + 42 = 9 + 16 = 25 OP =5

35) The angle between a tangent to a circle and the radius at the point of contact is

A) 60°

B) 30°

C) 45°

D) 90°

View Answer

D) 90°
Explanation:90°

36) If two circles touch each other internally, then how many common tangents can be drawn?

A) 5

B) 4

C) 0

D) 1

View Answer

D) 1
Explanation:1

37) Number of parallel tangents to a circle with a given tangent is

A) 1

B) 2

C) 4

D) 3

View Answer

A) 1
Explanation:1

38) In the figure, area of the segment PAQ is ……………. sq. units.

A) $\frac{a2}4\left[\pi+2\right]$

B) $\frac{a2}4\left[\pi-2\right]$

C) $\frac{a2}4\left[\pi-1\right]$

D) $\frac{a2}4\left[\pi+1\right]$

View Answer

B) $\frac{a2}4\left[\pi-2\right]$
Explanation:Area of the segment PAQ
= Area of sector—Area of triangle
= $\frac{x^\circ}{360^\circ}\;X\;\pi r2\;-\;\frac12ab$
= $\frac{90^\circ}{360^\circ}\;X\;\pi a2\;-\;\frac12a2$
= $\frac{\pi a2}4\;-\;\frac{a2}4(\pi\;-\;2)$

39) In the below figure, if PT = 6 cm, PA = 3 cm, then AB equals to

A) 2 cm

B) 9 cm

C) 5 cm

D) 6 cm

View Answer

B) 9 cm
Explanation:PT² = PA. PB
(6)² = 3-PB
36 = 3PB=> PB = 12
PA + AB = 12
3 + AB = 12
AB = 9 cm

40) The volume of a vessel in the form of cylinder is 448π cm³ and its height is 7 cm, then the radius of the base is

A) 2 cm

B) 8 cm

C) 6 cm

D) 4 cm

View Answer

B) 8 cm
Explanation:V = 448π, h = 7
π r²-h = 448π
π r²-7 = 448 k
r² = 448/7 = 64 => r = 8 cm

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