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

Q). 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°

Q). 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

Q). 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.

Q). 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

Q). 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°

Q). 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

Q). 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

Q). 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)

Q). 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

Q). 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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