TS Polycet (Polytechnic) 2021 Previous Question Paper with Answers And Model Papers With Complete Analysis

31) In the figure OB=13cm, OP⊥AB, OP=12cm then AB=

A) 100 cm
B) 50 cm
C) 75 cm
D) 10 cm

View Answer

D) 10 cm

Explanation:Given OB = 13 cm, OP ⊥ AB, OP = 12 cm. Find AB.
In right triangle OPB:
OB² = OP² + PB² ⇒ 13² = 12² + PB² ⇒ 169 = 144 + PB² ⇒ PB = 5
Since OP ⊥ AB and lies at midpoint, AB = 2 × PB = 2 × 5 = 10 cm

32) In the △ABC; D, E and F are the mid points of the sides BC, CA and Ab. The are of △DEF: area of △ABC = ……

A) 1:4
B) 4:1
C) 1:3
D) 3:4

View Answer

A) 1:4

Explanation:D, E, F are midpoints of triangle ABC. Then triangle DEF is the midpoint triangle.
Area of triangle formed by joining midpoints is one-fourthof original triangle:
Correct Answer: 1:4

33) In the given figure ∠BAC=90°, AD⊥BC, BD=9cm and CD=16cm then AC=

A) 10 cm
B) 15 cm
C) 20 cm
D) 25 cm

View Answer

C) 20 cm

Explanation:∠BAC = 90°, AD ⊥ BC, BD = 9 cm, CD = 16 cm → AC = ?
This is a right triangle with altitude from right angle to hypotenuse:
$AC = \sqrt{AD^2 + DC^2} = \sqrt{? + 16^2}$
Use Pythagorean relation:
In right triangle with perpendicular from right angle, AB² = BD × BC
$AC^2 = CD × CB = 16 × (9 + 16) = 16 × 25 = 400 ⇒ AC = \sqrt{400} = 20$
Correct Answer: 20 cm

34) The base of two similar triangles are 24 cm and 18 cm. If one side of the first triangle is 8 cm then corresponding side of other triangle is

A) 8 cm
B) 6 cm
C) 4 cm
D) 2 cm

View Answer

B) 6 cm

Explanation:Similar triangles: base ratio = 24:18 = 4:3
So corresponding sides are in same ratio:
$\text{If one side = 8 cm in 1st triangle} ⇒ \text{corresponding side} = 8 × (3/4) = 6$
Correct Answer: 6 cm

35) If a parallelogram is cyclic, then it is a ……..

A) rectangle
B) square
C) quadrilateral
D) rhombus

View Answer

A) rectangle

Explanation:A cyclic parallelogram has all angles = 90°, because opposite angles in a cyclic quadrilateral are supplementary.
Only parallelogram with all 90° angles is a rectangle.
Correct Answer: A. Rectangle

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