NDA & NA Exam (I)- 2022 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2022 - Mathematics

NDA & NA Exam (I)- 2022 - Mathematics Defence Questions

41.
Consider all the subsets of the set \( A = \{1, 2, 3, 4\} \). How many of them are supersets of the set \( \{4\} \)?
A.
6
B.
7
C.
8
D.
9
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ANSWER :
C. 8
42.
Consider the following statements in respect of two non-empty sets \( A \) and \( B \):
1. \( x \notin (A \cup B) \Rightarrow x \notin A \) or \( x \notin B \)
2. \( x \notin (A \cap B) \Rightarrow x \notin A \) and \( x \notin B \)
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 :
A. 1 only
43.
Consider the following statements in respect of two non-empty sets \( A \) and \( B \):
1. \( A \cup B = A \cap B \) iff \( A = B \)
2. \( A \Delta B = \phi \) iff \( A = B \)
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
C. Both 1 and 2
44.
Consider the following statements in respect of the relation \( R \) in the set \( \mathbb{N} \) of natural numbers defined by \( xRy \) if \( x^{2} - 5xy + 4y^{2} = 0 \):
1. \( R \) is reflexive
2. \( R \) is symmetric
3. \( R \) is transitive
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
1 and 2 only
D.
1, 2 and 3
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ANSWER :
A. 1 only
45.
Consider the following statements in respect of any relation \( R \) on a set \( A \):
1. If \( R \) is reflexive, then \( R^{-1} \) is also reflexive
2. If \( R \) is symmetric, then \( R^{-1} \) is also symmetric
3. If \( R \) is transitive, then \( R^{-1} \) is also transitive
Which of the above statements are correct?
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
46.
What is the principal argument of \( \frac{1}{1 + i} \), where \( i = \sqrt{-1} \)?
A.
\( -\frac{3\pi}{4} \)
B.
\( -\frac{\pi}{4} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{3\pi}{4} \)
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ANSWER :
B. \( -\frac{\pi}{4} \)
47.
What is the modulus of
\( \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{200} \)?
A.
\( \frac{1}{4} \)
B.
\( \frac{1}{2} \)
C.
1
D.
\( 2^{200} \)
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ANSWER :
C. 1
48.
Consider the following statements:
1. \( \frac{n!}{3} \) is divisible by 6, where \( n > 3 \)
2. \( \frac{n!}{3} + 3 \) is divisible by 7, where \( n > 3 \)
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
D. Neither 1 nor 2
49.
In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?
A.
14
B.
21
C.
35
D.
42
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ANSWER :
B. 21
50.
In the expansion of \( \left(x + \frac{1}{x}\right)^{2n} \), what is the \( (n + 1) \)th term from the end (when arranged in descending powers of \( x \))?
A.
\( C(2n, n)x \)
B.
\( C(2n, n - 1)x \)
C.
\( C(2n, n) \)
D.
\( C(2n, n - 1) \)
😑 View Answer Error
ANSWER :
C. \( C(2n, n) \)
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