NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I) & (II)- 2020 - Mathematics

NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Questions

41.
If A is a matrix of order \( 3 \times 5 \) and B is a matrix of order \( 5 \times 3 \), then the order of AB and BA will respectively be
A.
\( 3 \times 3 \) and \( 3 \times 3 \)
B.
\( 3 \times 5 \) and \( 5 \times 3 \)
C.
\( 3 \times 3 \) and \( 5 \times 5 \)
D.
\( 5 \times 3 \) and \( 3 \times 5 \)
😑 View Answer Error
ANSWER :
C. \( 3 \times 3 \) and \( 5 \times 5 \)
42.
If \( p^{2}, q^{2} \) and \( r^{2} \) (where \( p, q, r > 0 \)) are in GP, then which of the following is/are correct?
1. p, q and r are in GP.
2. \( \ln p, \ln q \) and \( \ln r \) are in AP.
Select the correct answer using the code given below.
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
43.
If \( \cot \alpha \) and \( \cot \beta \) are the roots of the equation \( x^{2} - 3x + 2 = 0 \), then what is \( \cot(\alpha + \beta) \) equal to?
A.
\( \frac{1}{2} \)
B.
\( \frac{1}{3} \)
C.
2
D.
3
😑 View Answer Error
ANSWER :
B. \( \frac{1}{3} \)
44.
The roots \( \alpha \) and \( \beta \) of a quadratic equation satisfy the relations \( \alpha + \beta = \alpha^{2} + \beta^{2} \) and \( \alpha \beta = \alpha^{2} \beta^{2} \). What is the number of such quadratic equations?
A.
0
B.
2
C.
3
D.
4
😑 View Answer Error
ANSWER :
D. 4
45.
What is the argument of the complex number \( \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \), where \( i = \sqrt{-1} \)?
A.
\( 240^{\circ} \)
B.
\( 210^{\circ} \)
C.
\( 120^{\circ} \)
D.
\( 60^{\circ} \)
😑 View Answer Error
ANSWER :
A. \( 240^{\circ} \)
46.
What is the modulus of the complex number \( \frac{\cos \theta + i \sin \theta}{\cos \theta - i \sin \theta} \), where \( i = \sqrt{-1} \)?
A.
\( \frac{1}{2} \)
B.
1
C.
\( \frac{3}{2} \)
D.
2
😑 View Answer Error
ANSWER :
B. 1
47.
Consider the proper subsets of \( \{1, 2, 3, 4\} \). How many of these proper subsets are superset of the set \( \{3\} \)?
A.
5
B.
6
C.
7
D.
8
😑 View Answer Error
ANSWER :
C. 7
48.
Let p, q and r be three distinct positive real numbers. If \( D = \begin{vmatrix} p & q & r \\ q & r & p \\ r & p & q \end{vmatrix} \), then which one of the following is correct?
A.
\( D < 0 \)
B.
\( D = 0 \)
C.
\( D > 0 \)
D.
\( D \geq 0 \)
😑 View Answer Error
ANSWER :
A. \( D < 0 \)
49.
What is the sum of the last five coefficients in the expansion of \( (1 + x)^{9} \) when it is expanded in ascending powers of x?
A.
256
B.
512
C.
1024
D.
2048
😑 View Answer Error
ANSWER :
A. 256
50.
Consider the following in respect of a non-singular matrix A of order 3:
1. \( A (adj(A)) = (adj(A)) A \)
2. \( |adj(A)| = |A| \)
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 :
A. 1 only
Prev Next page