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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