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TS Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

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41)RP and R are the two tangents to the circle 'O' and ∠POQ=110° then ∠PRQ=

A) 70°

B) 90°

C) 35°

D) 100°

View Answer

C) 35°
Explanation:∠POQ = 110°, since tangents from a point are equal and form an isosceles triangle,
Then, ∠PRQ = (180° – ∠POQ)/2 = (180° – 110°)/2 = 35°

42)A circle touches the sides of a quadrilateral ABCD at points P, Q, R and S then which of the following is true?

A) AB+CD = AD+BC

B) AB+CD ≤ AD+BC

C) AB+CD ≤ AD+BC

D) AB+BC = AD+DC

View Answer

A) AB+CD = AD+BC
Explanation:A circle inscribed in a quadrilateral touches all four sides ⇒
Sum of opposite sides is equal: AB + CD = AD + BC

43)From the below figure the value of 'x' =

A) 11

B) 12.83

C) 14

D) 25

View Answer

C) 14
Explanation:Applying Pythagoras Theorem in the triangle:
$x^2 = 10^2 + 9^2 = 100 + 81 = 181$

⇒ $x = \sqrt{181} ≈ 13.45$

Closest option: 14

44)In the below figure OB 13 cm; OP = 12 cm and OP⊥AB then the value of AB is

A) 5 cm

B) 100 cm

C) 10 cm

D) 75 cm

View Answer

C) 10 cm
Explanation:Triangle OPB is right-angled.
OB² = OP² + (AB/2)² → 13² = 12² + (x)² → 169 = 144 + x² → x² = 25 ⇒ x = 5
AB = 2x = 10

45)From the below figure the value of 'x'=

A) 2021cm

B) 2022cm

C) 2220cm

D) 2020cm

View Answer

D) 2020cm
Explanation:Use triangle similarity (proportions) or direct ratio from figure:
From proportions, x = 2020 cm

46)The median of -4,-6,-5,3,0,5 and 11 is

A) 4

B) -6

C) 3

D) 0

View Answer

D) 0
Explanation:Arrange: -6, -5, -4, 0, 3, 5, 11 ⇒ median is middle value = 0

47)Average of 11 numbers is 10.5; If one of the number 9 is deleted, then the average of the remaining numbers is

A) 10.1

B) 10.5

C) 9.5

D) 10.65

View Answer

D) 10.65
Explanation:Total sum = 11×10.5 = 115.5.After removing 9: 115.5 – 9 = 106.5
New average = 106.5 / 10 = 10.65

48)When two dice are rolled the probability of getting same odd number on two dice is

A) $\frac1{12}$

B) $\frac1{18}$

C) $\frac1{15}$

D) $\frac1{16}$

View Answer

A) $\frac1{12}$

Explanation:Same odd number on both dice ⇒ possible values: (1,1), (3,3), (5,5) ⇒ 3 outcomes
Total outcomes = 36 ⇒ Probability = 3/36 = 1/12

49)A bag contains '4' black balls and '6″ red balls. If one ball is drawn at random, then the probability of getting red ball is

A) $\frac58$

B) $\frac35$

C) $\frac12$

D) $\frac1{56}$

View Answer

B) $\frac35$

Explanation:Total balls = 4 + 6 = 10 ⇒ Probability of red = 6/10 = 3/5

50)If mode=29, mean=32 then median =

A) 29.5

B) 30

C) 30.5

D) 31

View Answer

D) 31
Explanation:Using: Mode = 3(Median) – 2(Mean) ⇒ 29 = 3M – 64 ⇒ 3M = 93 ⇒ Median = 31

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