(Mathematics-Part-3) NDA/NA Solved Paper 2017-I

Total Questions: 20

1. The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations?

Correct Answer: (d) 45
Solution:

New variance = k² (old variance)
=3²x5=9×5=45

2. The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21,21, 18 and 20. What is the mean if the incorrect observations are omitted?

Correct Answer: (b) 20
Solution:

3. A committee of two persons is contituted from two men and two women. What is the probability that the committee will have only women?

Correct Answer: (a) 1/6
Solution:

4. A question is given to three students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 pectively. What is the probability that the question will be solved?

Correct Answer: (c) 3/4
Solution:

5. The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the number of boys in the class?

Correct Answer: (a) 50
Solution:

6. For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilites P(A|B) and P(B|A) are respectively

Correct Answer: (b) 2/5,1
Solution:

7. A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary?

Correct Answer: (b) 1/4
Solution:

8. If two regression lines between height (x) and weight (y) are 4y - 15x + 410 = 0 and 30x - 2y - 825 = 0, then what will be the correlation coefficient between height and weight?

Correct Answer: (b) 1/2
Solution:

9. In an examination, 40% of candidates got second class. When the data are represented by a pie chart, what is the angle corresponding to second class?

Correct Answer: (c) 144°
Solution:

First, convert 40% into fraction
40%=40/100=2/5
Angle =2/5x360 =144°

10. Consider the following statements:

Statement 1 : Range is not a good measure of dispersion.
Statement 2 : Range is highly affected by the existence of extreme values.
Which one of the following is correct in respect of the above statements?

Correct Answer: (a) Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
Solution:

Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1