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

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2026 - Mathematics

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

41.
Let R be a relation on the set N of natural numbers defined by
R = {(x, y) : x, y \( \in \) N and \( x = y^{2} \)}.
Which of the following statements is/are correct?
I. R is symmetric relation
II. R is transitive relation
Select the answer using the code given below:
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
D. Neither I nor II
42.
For a given k, what is the minimum value of \( x^{2} + kx + k^{2} \)?
A.
0
B.
\( \frac{k^{2}}{4} \)
C.
\( \frac{3k^{2}}{4} \)
D.
\( \frac{k^{2}}{2} \)
😑 View Answer Error
ANSWER :
C. \( \frac{3k^{2}}{4} \)
43.
Consider the following statements:
I. \( \sqrt{x} + x + 1 = 0 \) has two irrational roots.
II. \( 5\sqrt{x} - x - 4 = 0 \) has two rational roots.
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 :
B. II only
44.
How many numbers greater than 1000 can be formed using the digits 0, 1, 2 and 3 (repetition of digits is not allowed)?
A.
24
B.
18
C.
15
D.
12
😑 View Answer Error
ANSWER :
B. 18
45.
If pth term of an AP is k, then what is the sum of pth term, \( (p + q)^{th} \) term and \( (p - q)^{th} \) term of the AP?
A.
2k
B.
3k
C.
4k
D.
5k
😑 View Answer Error
ANSWER :
B. 3k
46.
Directions (Next 5 Questions):
Let u be a positive integer and f be a real number lying between 0 and 1. Further, \( (\sqrt{2} + 1)^{10} = u + f \) and \( (\sqrt{2} - 1)^{10} = v \).

Consider the following statements:
I. \( (u + v + f) \) is an integer.
II. \( (f + v) \) is an integer.
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.
What is the multiplicative inverse of \( (\sqrt{2} + 1)^{20} \)?
A.
v
B.
\( v^{2} - 1 \)
C.
\( v^{2} \)
D.
\( v^{2} + 1 \)
😑 View Answer Error
ANSWER :
C. \( v^{2} \)
48.
What is the value of \( (v + f) \)?
A.
2
B.
1
C.
0.5
D.
0.25
😑 View Answer Error
ANSWER :
B. 1
49.
What is the value of u?
A.
9725
B.
6971
C.
6726
D.
6725
😑 View Answer Error
ANSWER :
D. 6725
50.
What is the value of uv?
A.
1
B.
2
C.
\( 0 < uv < 1 \)
D.
\( 1 < uv < 2 \)
😑 View Answer Error
ANSWER :
C. \( 0 < uv < 1 \)
Prev Next page