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

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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