MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (101 to 120)

Total Questions: 20

1. Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?

Correct Answer: (b) 1/5
Solution:

2. The frequency curve (assuming unimodal) corresponding to the data obtained in an experiment is skewed to the left. What conclusion can be drawn from the curve?

Correct Answer: (d) Mode > Median > Mean
Solution:Since frequency curve has left skewed so, In this case mode is the greatest and mean is the lowest hence. option (d) is correct.

3. The variance of five positive observations is 3.6. If four of the observations are 2, 2, 4, 5 then what is the remaining observation?

Correct Answer: (c) 7
Solution:

4. What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4?

Correct Answer: (d) 102
Solution:

5. What is the coefficient of mean deviation of 21, 34, 23, 39, 26, 37, 40, 20, 33, 27 (taken from mean)?

Correct Answer: (b) 0.22
Solution:

6. What is the mean of the values?

The algebraic sum of the deviations of a set of values x₁, x₂, ,x₃,____xₙ measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140.

Correct Answer: (d) 99
Solution:Here, (x₁ - 100) + (x₂ - 100)+_____+(xₙ - 100) = -20
hence(x₁ + x₂ + x₃ +______xₙ) - 100x = -20
or x₁ + x₂ + x₃ +______xₙ = 100n - 20                      .....(i)
and accoding to question for same set
x₁ + x₂ + x₃ +______xₙ = 92n + 140                          .....(ii)
from (i) and (ii)

8n = 160 ⇒ n = 20
from (i) x₁ + x₂ + x₃ +______xₙ = 1980
mean = (100 × 20 -20) /20 = 99

7. What is the algebraic sum of the deviations of the same set of values measured from 99?

The algebraic sum of the deviations of a set of values x₁, x₂, ,x₃,____xₙ measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140.

Correct Answer: (a) 0
Solution:Here, (x₁ - 100) + (x₂ - 100)+_____+(xₙ - 100) = -20
hence(x₁ + x₂ + x₃ +______xₙ) - 100x = -20
or x₁ + x₂ + x₃ +______xₙ = 100n - 20                      .....(i)
and accoding to question for same set
x₁ + x₂ + x₃ +______xₙ = 92n + 140                          .....(ii)
from (i) and (ii)

Acc to question
(x₁ + x₂ + x₃ +______xₙ) - 99n
⇒ 1980 - 99 × 20 = 0

8. If the algebraic sum of the deviations of the same set of values measured from y is 180, then what is the value of y?

The algebraic sum of the deviations of a set of values x₁, x₂, ,x₃,____xₙ measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140.

Correct Answer: (c) 90
Solution:Here, (x₁ - 100) + (x₂ - 100)+_____+(xₙ - 100) = -20
hence(x₁ + x₂ + x₃ +______xₙ) - 100x = -20
or x₁ + x₂ + x₃ +______xₙ = 100n - 20                      .....(i)
and accoding to question for same set
x₁ + x₂ + x₃ +______xₙ = 92n + 140                          .....(ii)
from (i) and (ii)

Acc to question.
(x₁ + x₂ + x₃ +______xₙ) -20y = 180
or 20y = 1800 ⇒ y = 90

9. What is the mean of the marks?

The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3.

Correct Answer: (d) 79
Solution:

10. What is the median of the marks?

The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3.

Correct Answer: (b) 79
Solution:Median = Middle term of A.P = (51 + 1 / 2)ᵗʰ term = 26ᵗʰ term
T₂₆ = 4 + 25 × 3 = 79