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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

36) The perimeter of a rhombus is 52 cm, if its one diagonal is 24 cm then the length of its other diagonal is

A) 5 cm

B) 7 cm

C) 9 cm

D) 10 cm

View Answer

D) 10 cm
Explanation:Perimeter of rhombus = 52 → side = 52/4 = 13 cm
One diagonal = 24 cm → use Pythagoras to find the other:
$\text{Half diagonals: } ⇒ \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = 13^2 ⇒ (12)^2 + \left(\frac{d_2}{2}\right)^2 = 169 ⇒ 144 + x^2 = 169 ⇒ x^2 = 25 ⇒ x = 5 ⇒ d_2 = 10$
Correct Answer: 10 cm

37) The radius of a cone is 7 m and its height is 10 m. then its slant height is …….

A) 12.2 m

B) 13.5 m

C) 14.5 m

D) 16.2 m

View Answer

A) 12.2 m
Explanation:Cone radius r = 7 m, height h = 10 m → slant height = √(r² + h²)
$l = \sqrt{7^2 + 10^2} = \sqrt{49 + 100} = \sqrt{149} ≈ 12.2$
Correct Answer: 12.2 m

38) If tanθ=cotθ then the value of secθ= ……
A) $\frac1{\sqrt2}$
B) $\frac{\sqrt3}2$
C)√2
D)1

A) A

B) B

C) C

D) D

View Answer

C) C
Explanation:If $\tan\theta = \cot\theta$ , then $\tan\theta = 1 ⇒ \theta = 45°$
Then, $\sec\theta = \frac{1}{\cos\theta} = \frac{1}{\cos 45°} = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}$
Correct Answer: √2

39) The angle at tangent to a circle and the radius drawn at the point of contact is

A) 60°

B) 90°

C) 40°

D) 30°

View Answer

B) 90°
Explanation:Angle between tangent and radius at point of contact is always
Correct Answer: 90°

40) The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3

A) 4:5

B) 9:5

C) 3:5

D) 2:5

View Answer

B) 9:5
Explanation:Volume of cone = $\frac{1}{3}\pi r^2 h$
Given: $\text{Volume ratio} = 4:5, \quad \text{radius ratio} = 2:3 ⇒ r_1^2 = 4, r_2^2 = 9$
Let height be $h_1, h_2$ .
$\frac{V_1}{V_2} = \frac{r_1^2 h_1}{r_2^2 h_2} = \frac{4 h_1}{9 h_2} = \frac{4}{5} ⇒ \frac{h_1}{h_2} = \frac{9}{5}$
Correct Answer: 9:5
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