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

31.
For the next three (03) items that follow:
In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.

The number of students who had taken only Physics is
A.
2
B.
3
C.
5
D.
6
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ANSWER :
A. 2
32.
The number of students who had taken only two subjects is
A.
7
B.
8
C.
9
D.
10
😑 View Answer Error
ANSWER :
C. 9
33.
Consider the following statements:
1. The number of students who had taken only one subject is equal to the number of students who had taken only two subjects.
2. The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects.
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 :
B. 2 only
34.
For the next three (03) items that follow:
In the expansion of \( \left(x^{3} - \frac{1}{x^{2}}\right)^{n} \), where n is a positive integer, the sum of the coefficients of \( x^{5} \) and \( x^{10} \) is 0.

What is n equal to?
A.
5
B.
10
C.
15
D.
None of the above
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ANSWER :
C. 15
35.
What is the value of the independent term?
A.
5005
B.
7200
C.
−5005
D.
−7200
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ANSWER :
C. −5005
36.
What is the sum of the coefficients of the two middle terms?
A.
0
B.
1
C.
−1
D.
None of the above
😑 View Answer Error
ANSWER :
A. 0
37.
For the next three (03) items that follow:
Given that \( C(n, r) : C(n, r+1) = 1 : 2 \) and \( C(n, r+1) : C(n, r+2) = 2 : 3 \).

What is n equal to?
A.
11
B.
12
C.
13
D.
14
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ANSWER :
D. 14
38.
What is r equal to?
A.
2
B.
3
C.
4
D.
5
😑 View Answer Error
ANSWER :
C. 4
39.
What is \( P(n, r) : C(n, r) \) equal to?
A.
6
B.
24
C.
120
D.
720
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ANSWER :
B. 24
40.
The complete solution of \( 3\tan^{2} x = 1 \) is given by (where \( n \in Z \))
A.
\( x = n\pi \pm \frac{\pi}{3} \)
B.
\( x = n\pi + \frac{\pi}{3} \) only
C.
\( x = n\pi \pm \frac{\pi}{6} \)
D.
\( x = n\pi + \frac{\pi}{6} \) only
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ANSWER :
C. \( x = n\pi \pm \frac{\pi}{6} \)
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