NDA & NA Exam (II)- 2026 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2026 - Mathematics

NDA & NA Exam (II)- 2026 - Mathematics Defence Questions

41.
What is the LCM of \( (11110)_{2} \), \( (10100)_{2} \) and \( (11011)_{2} \)?
A.
\( (1000001100)_{2} \)
B.
\( (1000011100)_{2} \)
C.
\( (1000111100)_{2} \)
D.
\( (1000011101)_{2} \)
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ANSWER :
B. \( (1000011100)_{2} \)
42.
What is the coefficient of \( x^{2n} \) in the expansion of the following?
\( (1 + x)^{2n}\left(1 + \frac{1}{x}\right)^{2n} \)
A.
1
B.
\( 2n(2n - 1)(2n - 2) \ldots (n + 1)n \)
C.
\( 4n(4n - 1)(4n - 2) \ldots (2n + 1)(2n) \)
D.
Such term does not exist
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ANSWER :
A. 1
43.
Consider the following statements in respect of the expansion of \( (x^{2} + x^{-2} + 2)^{4} \):
I. The number of terms in the expansion is 5.
II. One of the coefficients in the expansion has a maximum value equal to 70.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
B. II only
44.
Consider the following relations from A to B, where A = {1, 3, 5} and B = {2, 4, 6, 8}:
I. {(1, 2), (3, 2), (3, 6), (5, 8)}
II. {(3, 4), (5, 8), (1, 6), (3, 2)}
III. {(1, 2), (3, 6)}
IV. {(1, 6), (3, 2), (5, 2)}
Which of the above is/are function(s) from A to B?
A.
I, III and IV
B.
IV only
C.
II and IV
D.
III only
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ANSWER :
B. IV only
45.
If \( x^{2} - 2x \cos \theta + 1 = 0 \), then what is the magnitude of x?
A.
−1
B.
0
C.
1
D.
\( \sqrt{2} \)
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ANSWER :
C. 1
46.
Consider the following statements in respect of sets A and B:
I. If \( x \in A \) and \( A \subseteq B \), then \( x \in B \).
II. If \( A \subseteq B \) and \( x \notin B \), then \( x \notin A \).
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
47.
A research group conducted a survey of 500 consumers and reported that 370 consumers preferred product X and 240 consumers preferred product Y. What is the least number that must have preferred both the products?
A.
90
B.
100
C.
110
D.
Cannot be determined due to insufficient data
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ANSWER :
C. 110
48.
The Cartesian product \( A \times A \) has 25 elements among which are found (3, 1), (6, 2), (5, 3). Which of the following statements is/are correct?
I. It is possible to determine other elements of \( A \times A \).
II. \( (5, 5) \in A \times A \) and \( (1, 3) \notin A \times A \).
Select the answer using the code given below.
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
A. I only
49.
Consider the following statements in respect of a relation R from a set A to a set B:
I. The set B is called codomain of the relation R.
II. The range of the relation is always equal to codomain of the relation R.
III. The domain of the relation R must be equal to the set A.
Which of the statements given above is/are correct?
A.
I only
B.
III only
C.
I and II
D.
I and III
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ANSWER :
A. I only
50.
Consider the following system of linear inequalities:
\( x - y \leq 3 \) and \( x + y \geq 5 \)
The solution of the inequalities lies in
A.
first quadrant only
B.
second quadrant only
C.
both first quadrant and second quadrant only
D.
all the four quadrants
😑 View Answer Error
ANSWER :
C. both first quadrant and second quadrant only
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