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

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Polycet Mock Test

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}
Let me know if you’d like these 10 answers in a summarized table.

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