NDA & NA Exam (II)- 2025 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2025 - Mathematics

NDA & NA Exam (II)- 2025 - Mathematics Defence Questions

31.
For the following two (02) items:
Consider the equation
\( abx^{2} + bcx + ca = cax^{2} + abx + bc \)

If the roots of the equation are equal, then which one of the following is correct?
A.
\( ac = b^{2} \)
B.
\( a + c = 2b \)
C.
\( \frac{1}{a} + \frac{1}{c} = \frac{1}{2b} \)
D.
\( \frac{1}{a} + \frac{1}{c} = \frac{2}{b} \)
😑 View Answer Error
ANSWER :
D. \( \frac{1}{a} + \frac{1}{c} = \frac{2}{b} \)
32.
If the roots of the equation are equal, then \( a, b, c \) are in
A.
AP
B.
GP
C.
HP
D.
None of the above
😑 View Answer Error
ANSWER :
C. HP
33.
For the following two (02) items:
Let \( (6 + 10 + 14 + \ldots \) up to \( m \) terms) = \( (1 + 3 + 5 + 7 + \ldots \) up to \( n \) terms), where \( m < 25 \) and \( n < 25 \).

What is the relation between \( m \) and \( n \)?
A.
\( n^{2} = m(m + 1) \)
B.
\( n^{2} = m(m + 2) \)
C.
\( n^{2} = 2m(m + 1) \)
D.
\( n^{2} = 2m(m + 2) \)
😑 View Answer Error
ANSWER :
D. \( n^{2} = 2m(m + 2) \)
34.
How many values of \( m \) are possible?
A.
None
B.
One
C.
Two
D.
More than two
😑 View Answer Error
ANSWER :
C. Two
35.
For the following two (02) items:
There are 8 points on a plane out of which 4 points are collinear.

How many triangles can be formed by joining these points?
A.
56
B.
54
C.
53
D.
52
😑 View Answer Error
ANSWER :
D. 52
36.
How many quadrilaterals can be formed by joining these points?
A.
70
B.
69
C.
53
D.
None of the above
😑 View Answer Error
ANSWER :
C. 53
37.
For the following two (02) items:
Let \( f(x) = ax^{2} + bx + c \) be a quadratic polynomial such that \( f(1) = f(4) = 2 \). Further, 2 is a root of \( f(x) = 0 \).

What is the other root of \( f(x) = 0 \)?
A.
1
B.
2
C.
3
D.
Cannot be determined
😑 View Answer Error
ANSWER :
C. 3
38.
What is \( (a + b + c) \) equal to?
A.
0
B.
1
C.
2
D.
Cannot be determined
😑 View Answer Error
ANSWER :
C. 2
39.
For the following two (02) items:
Let
\( A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix} \)

What is the value of the determinant of the matrix \( A^{4} \)?
A.
0
B.
1
C.
\( \cos 4\theta - \sin 4\theta \)
D.
\( \cos^{2} 4\theta - \sin^{2} 4\theta \)
😑 View Answer Error
ANSWER :
B. 1
40.
What is \( [adj A]^{-1} \) equal to?
A.
\( -A \)
B.
\( -A^{T} \)
C.
\( A \)
D.
\( A^{T} \)
😑 View Answer Error
ANSWER :
C. \( A \)
Prev Next page