NDA & NA Exam (I)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2014 - Mathematics

NDA & NA Exam (I)- 2014 - Mathematics Defence Questions

11.
A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?
A.
\( \frac{2}{5} \)
B.
\( \frac{1}{5} \)
C.
\( \frac{1}{10} \)
D.
None of the above
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ANSWER :
C. \( \frac{1}{10} \)
12.
For two variables x and y, the two regression coefficients are \( b_{yx} = -\frac{3}{2} \) and \( b_{xy} = -\frac{1}{6} \). The correlation coefficient between x and y is
A.
\( -\frac{1}{4} \)
B.
\( \frac{1}{4} \)
C.
\( -\frac{1}{2} \)
D.
\( \frac{1}{2} \)
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ANSWER :
C. \( -\frac{1}{2} \)
13.
The variance of numbers \( x_{1}, x_{2}, x_{3}, \ldots, x_{n} \) is V. Consider the following statements:
1. If every \( x_{i} \) is increased by 2, the variance of the new set of numbers is V.
2. If each number \( x_{i} \) is squared, the variance of the new set is \( V^{2} \).
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. 1 only
14.
What is the mean of the squares of the first 20 natural numbers?
A.
151.5
B.
143.5
C.
65
D.
72
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ANSWER :
B. 143.5
15.
p, q, r, s, t are five numbers such that the average of p, q and r is 5 and that of s and t is 10. What is the average of all the five numbers?
A.
7.75
B.
7.5
C.
7
D.
5
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ANSWER :
C. 7
16.
The cumulative frequency of the largest observed value must always be
A.
less than the total number of observations
B.
greater than the total number of observations
C.
equal to total number of observations
D.
equal to mid-point of the last class interval
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ANSWER :
C. equal to total number of observations
17.
It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternately is
A.
\( \frac{5}{12} \)
B.
\( \frac{5}{36} \)
C.
\( \frac{19}{27} \)
D.
\( \frac{5}{27} \)
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ANSWER :
B. \( \frac{5}{36} \)
18.
Out of 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is
A.
25200
B.
22500
C.
10080
D.
5040
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ANSWER :
A. 25200
19.
Let X denote the number of scores which exceed 4 in 18 tosses of a symmetrical die. Consider the following statements:
1. The arithmetic mean of X is 6.
2. The standard deviation of X is 2.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
20.
How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to start with A?
A.
6
B.
12
C.
24
D.
None of the above
😑 View Answer Error
ANSWER :
C. 24
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