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

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

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

1.
The sum of the first \( k \) terms of a series \( S \) is \( 3k^{2} + 5k \). Which one of the following is correct?
A.
The terms of \( S \) form an arithmetic progression with common difference 14.
B.
The terms of \( S \) form an arithmetic progression with common difference 6.
C.
The terms of \( S \) form a geometric progression with common ratio \( \frac{10}{7} \).
D.
The terms of \( S \) form a geometric progression with common ratio \( \frac{11}{4} \).
😑 View Answer Error
ANSWER :
B. The terms of \( S \) form an arithmetic progression with common difference 6.
2.
The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If \( r \neq 1 \) is the common ratio, then what is the number of possible real values of \( r \)?
A.
One
B.
Two
C.
Three
D.
More than three
😑 View Answer Error
ANSWER :
B. Two
3.
If one root of the equation \( x^{2} - kx + k = 0 \) exceeds the other by \( 2\sqrt{3} \), then which one of the following is a value of \( k \)?
A.
3
B.
6
C.
9
D.
12
😑 View Answer Error
ANSWER :
B. 6
4.
If \( x + \frac{5}{y} = 4 \) and \( y + \frac{5}{x} = -4 \), then what is \( (x + y) \) equal to?
A.
0
B.
1
C.
4
D.
5
😑 View Answer Error
ANSWER :
A. 0
5.
If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?
A.
-3
B.
-2
C.
2
D.
3
😑 View Answer Error
ANSWER :
A. -3
6.
If \( p, 1, q \) are in AP and \( p, 2, q \) are in GP, then which of the following statements is/are correct?
I. \( p, 4, q \) are in HP.
II. \( \frac{1}{p}, \frac{1}{4}, \frac{1}{q} \) are in AP.
Select the correct 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 :
C. Both I and II
7.
If \( x = (1111)_{2} \), \( y = (1001)_{2} \) and \( z = (110)_{2} \), then what is \( x^{3} - y^{3} - z^{3} - 3xyz \) equal to?
A.
\( (1111001)_{2} \)
B.
\( (1001111)_{2} \)
C.
\( (10)_{2} \)
D.
\( (0)_{2} \)
😑 View Answer Error
ANSWER :
D. \( (0)_{2} \)
8.
If
\( \Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & k \end{vmatrix} \)
and \( A, B, C, D, G \) are the cofactors of the elements \( a, b, c, d, g \) respectively, then what is \( bB + cC - dD - gG \) equal to?
A.
0
B.
1
C.
\( \Delta \)
D.
\( -\Delta \)
😑 View Answer Error
ANSWER :
A. 0
9.
Consider the following statements in respect of the determinant
\( \Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix} \)
I. \( \Delta \) is positive if \( k > 0 \).
II. \( \Delta \) is negative if \( k < 0 \).
III. \( \Delta \) is zero if \( k = 0 \).
How many of the statements given above are correct?
A.
None
B.
One
C.
Two
D.
All three
😑 View Answer Error
ANSWER :
B. One
10.
If
\( \begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i-1 \\ -1 & -1-i & 1 \end{vmatrix} = A + iB \)
where \( i = \sqrt{-1} \), then what is \( A + B \) equal to?
A.
-10
B.
-6
C.
0
D.
6
😑 View Answer Error
ANSWER :
B. -6
Prev Next page