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

41) Which of the following cannot be the probability of an event?

A) $\frac13$

B) 0.3

C) 33%

D) $\frac76$

View Answer

D) $\frac76$
Explanation:Probabilities are always between 0 and 1.
Options:
A. $\frac{1}{3} = 0.33$ Valid
B. 0.3 Valid
C. 33% = 0.33 Valid
D. $\frac{7}{6} = 1.166...$ Not valid
Answer: $\frac{7}{6}$

42) If a card is selected at random from a deck of 52 cards, then the probability of getting a red face card is

A) $\frac3{26}$

B) $\frac3{13}$

C) $\frac2{13}$

D) $\frac12$

View Answer

A) $\frac3{26}$
Explanation:Probability of red face card from a deck of 52 cards.
There are 6 red face cards (J, Q, K of ♥ and ♦).
So,
$P = \frac{6}{52} = \frac{3}{26}$

43) Two dice are thrown together, the probability of getting the same number on both dice is

A) $\frac12$

B) $\frac13$

C) $\frac16$

D) $\frac1{12}$

View Answer

C) $\frac16$
Explanation:Two dice → Same number (doubles): (1,1), (2,2), …, (6,6) = 6 outcomes
Total outcomes = 6 × 6 = 36
$P = \frac{6}{36} = \frac{1}{6}$

44) A box contains 3 blue, 2 white and 4 red balls. If a ball is drawn at random from the box, what is the probability that it will not be a white ball?

A) $\frac13$

B) $\frac49$

C) $\frac79$

D) $\frac29$

View Answer

C) $\frac79$
Explanation:Balls: 3 Blue + 2 White + 4 Red = 9 balls
Not white = 7 balls
$P = \frac{7}{9}$

45) The mean of 12 numbers is 19. If 4 is subtracted from each number, then the new mean is

A) 17

B) 23

C) 21

D) 15

View Answer

D) 15
Explanation:Mean = 19
If we subtract 4 from each, new mean = 19 − 4 = 15

46) If the mean of the following data is k(>0) then the value of k is

Marks
మార్కులు k 4 k 8 3

Frequency
పౌనఃపున్యం k 2k 3k 4k 5k

A) 10

B) 8

C) 5

D) 4

View Answer

C) 5
Explanation:Data:
Marks = k, 4, k, 8, 3
Frequencies = k, 2k, 3k, 4k, 5k
Mean:
$\text{Mean} = \frac{\sum (f \cdot x)}{\sum f} = k$
Numerator:
$k \cdot k + 4 \cdot 2k + k \cdot 3k + 8 \cdot 4k + 3 \cdot 5k = k^2 + 8k + 3k^2 + 32k + 15k = 4k^2 + 55k$
Denominator:
k + 2k + 3k + 4k + 5k = 15k
So,
$k = \frac{4k^2 + 55k}{15k} = \frac{4k + 55}{15} ⇒ 15k = 4k + 55 ⇒ 11k = 55 ⇒ k = \boxed{5}$

47) If a data has 25 observations (arranged in ascending order), then which of the following observations represents the median?

A) 12th

B) 13th

C) 14th

D) 15th

View Answer

B) 13th
Explanation:25 observations → Odd, so median is the 13th value.

48) If the mode and median of a frequency distribution are 5 and 10 respectively, then the mean is

A) 7.5

B) 10.5

C) 12.5

D) 25

View Answer

C) 12.5
Explanation:Use empirical formula:
$\text{Mode} = 3 × \text{Median} - 2 × \text{Mean} ⇒ 5 = 3(10) - 2 × \text{Mean} ⇒ 5 = 30 - 2 × \text{Mean} ⇒ 2 × \text{Mean} = 25 ⇒ \text{Mean} = \boxed{12.5}$

49) Which of the following cannot be determined graphically?

A) Mean

B) Median

C) Mode

D) None of these

View Answer

A) Mean
Explanation:Mean: Cannot be determined graphicallyMedian & Mode: Can be determined using ogive and histogram

50) If the mode of the data 2,4,6,7,5,6,7,2k+1,9,7,13 is 7, then the value of k is

A) 7

B) 3

C) 4

D) 2

View Answer

B) 3
Explanation:Data: 2, 4, 6, 7, 5, 6, 7, 2k+1, 9, 7, 13
Mode = 7 ⇒ 7 must occur most frequently.
Currently:
7 appears 3 times
We must make 2k + 1 = 7 so that 7 occurs one more time (4 times total, more than others)
2k + 1 = 7 ⇒ 2k = 6 ⇒ k = $\boxed{3}$
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