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

41)Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube then the length of the edge of the new cube is

A) 9 cm

B) 8 cm

C) 7 cm

D) 6 cm

View Answer

A) 9 cm
Explanation:Three cubes with sides 6 cm, 8 cm, and 1 cm are melted to form a new cube.
Volume of cube = a³

Total volume:
= 6³ + 8³ + 1³
= 216 + 512 + 1
= 729 cm³
New cube's edge:
$= \sqrt[3]{729} = 9 \, \text{cm}$
Correct Answer: 9 cm

42)If A+B=90° and cot B= $\frac34$ then the value of tan A= …..

A) $\frac34$

B) $\frac45$

C) $\frac13$

D) $\frac14$

View Answer

A) $\frac34$

Explanation:If A + B = 90° and $\cot B = \frac{3}{4}$

, find $\tan A$

Since A = 90° – B,
Then $\tan A = \cot B = \frac{3}{4}$

Correct Answer: $\frac{3}{4}$

43)In the figure, AP=12cm,PB=16cm. Let π=3, then the perimeter of the shaded portion is

A) 52 cm

B) 58 cm

C) 56 cm

D) 62 cm

View Answer

B) 58 cm

44)If the diameter of a sphere is 'd' then its volume is

A) $\frac16\mathrm{πd}^3$

B) $\frac43\mathrm{πd}^3$

C) $\frac1{24}\mathrm{πd}^3$

D) $\frac13\mathrm{πd}^3$

View Answer

A) $\frac16\mathrm{πd}^3$

Explanation:Diameter = d → radius = d/2
Volume of sphere:
$V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \left( \frac{d}{2} \right)^3 = \frac{4}{3} \pi \cdot \frac{d^3}{8} = \frac{\pi d^3}{6}$

Correct Answer: $\frac{1}{6} \pi d^3$

45)A reservoir is in the shape of frustum of right circular cone. It is 8 m across at the top and 4 m cross at the bottom. It is 6 m deep then its capacity is

A) 704 m³

B) 174 m³

C) 127 m³

D) 170 m³

View Answer

A) 704 m³
Explanation:Volume of a frustum:
$V = \frac{1}{3} \pi h (R^2 + r^2 + Rr)$

Given:
Top radius R = 4, bottom radius r = 2, height h = 6, π = 3.14
$V = \frac{1}{3} \cdot 3.14 \cdot 6 \cdot (16 + 4 + 8) = \frac{1}{3} \cdot 3.14 \cdot 6 \cdot 28 = 3.14 \cdot 56 = 175.84$

Closest option:
Correct Answer: 170 m³

46)A dice is thrown twice. Then the probability of that '5' will come up at least once

A) $\frac{11}{36}$

B) $\frac{25}{36}$

C) $\frac{23}{36}$

D) $\frac{12}{36}$

View Answer

A) $\frac{11}{36}$

Explanation:Dice is thrown twice. Probability of getting at least one '5'
Total outcomes = 36
Probability of not getting 5in a single throw = 5/6
So, probability of not getting 5 at allin two throws:
$\left( \frac{5}{6} \right)^2 = \frac{25}{36} ⇒ \text{At least one 5} = 1 - \frac{25}{36} = \frac{11}{36}$

Correct Answer: $\frac{11}{36}$

47)If the mean of 6, 7, x, 8, y, 14 is 9 then x+y= …..

A) 17

B) 18

C) 19

D) 20

View Answer

C) 19
Explanation:Mean of 6, 7, x, 8, y, 14 = 9
Total sum = 6 + 7 + x + 8 + y + 14 = 35 + x + y
$\text{Mean} = \frac{35 + x + y}{6} = 9 ⇒ 35 + x + y = 54 ⇒ x + y = 19$

Correct Answer: 19

48)From the figure, θ=,

A) 45°

B) 60°

C) 30°

D) 75°

View Answer

B) 60°
Explanation:From the figure, if opposite side is √3 and adjacent side is 1, then
$\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{3}}{1} ⇒ \theta = 60°$

Correct Answer: 60°

49)The top of two poles are of height 20 m and 14 m are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is

A) 11 m

B) 12 m

C) 13 m

D) 10 m

View Answer

B) 12 m
Explanation:Two poles 20 m and 14 m → vertical difference = 6 m
Wire makes 30° with ground:
$\sin 30° = \frac{6}{\text{hypotenuse}} ⇒ \frac{1}{2} = \frac{6}{x} ⇒ x = 12$

Correct Answer: 12 m

50)If three coins are tossed simultaneously, then the probability of getting at least two heads is

A) $\frac12$

B) $\frac23$

C) $\frac13$

D) $\frac32$

View Answer

A) $\frac12$

Explanation:Three coins tossed → total outcomes = 8
Favorable outcomes for at least 2 heads:
HHTHTHTHHHHH → 4 outcomes
$⇒ P = \frac{4}{8} = \frac{1}{2}$

Correct Answer: $\frac{1}{2}$

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