NDA & NA Exam (II)- 2021 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2021 - Mathematics

NDA & NA Exam (II)- 2021 - Mathematics Defence Questions

11.
If
\( A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix} \)
where \( a \in \mathbb{N} \), then what is \( A^{100} - A^{50} - 2A^{25} \) equal to, where \( I \) is the identity matrix?
A.
\( -2I \)
B.
\( -I \)
C.
\( 2I \)
D.
\( I \)
😑 View Answer Error
ANSWER :
A. \( -2I \)
12.
If
\( \begin{vmatrix} a & -b & a-b-c \\ -a & b & -a+b-c \\ -a & -b & -a-b+c \end{vmatrix} - kabc = 0 \)
\( (a \neq 0, b \neq 0, c \neq 0) \)
then what is the value of \( k \)?
A.
−4
B.
−2
C.
2
D.
4
😑 View Answer Error
ANSWER :
A. −4
13.
What is \( \sum_{r=1}^{8n+7} i^{r} \) equal to, where \( i = \sqrt{-1} \)?
A.
−1
B.
1
C.
\( i \)
D.
\( -i \)
😑 View Answer Error
ANSWER :
A. −1
14.
If \( z = x + iy \), where \( i = \sqrt{-1} \), then what does the equation \( z\bar{z} + |z|^{2} + 4(z + \bar{z}) - 48 = 0 \) represent?
A.
Straight line
B.
Parabola
C.
Circle
D.
Pair of straight lines
😑 View Answer Error
ANSWER :
C. Circle
15.
Which one of the following is a square root of \( 2a + 2\sqrt{a^{2} + b^{2}} \), where \( a, b \in \mathbb{R} \) and \( i = \sqrt{-1} \)?
A.
\( \sqrt{a + ib} + \sqrt{a - ib} \)
B.
\( \sqrt{a + ib} - \sqrt{a - ib} \)
C.
\( 2a + ib \)
D.
\( 2a - ib \)
😑 View Answer Error
ANSWER :
A. \( \sqrt{a + ib} + \sqrt{a - ib} \)
16.
If \( \sin \theta \) and \( \cos \theta \) are the roots of the equation \( ax^{2} + bx + c = 0 \), then which one of the following is correct?
A.
\( a^{2} + b^{2} - 2ac = 0 \)
B.
\( -a^{2} + b^{2} + 2ac = 0 \)
C.
\( a^{2} - b^{2} + 2ac = 0 \)
D.
\( a^{2} + b^{2} + 2ac = 0 \)
😑 View Answer Error
ANSWER :
C. \( a^{2} - b^{2} + 2ac = 0 \)
17.
If \( C(n, 4), C(n, 5) \) and \( C(n, 6) \) are in AP, then what is the value of \( n \)?
A.
7
B.
8
C.
9
D.
10
😑 View Answer Error
ANSWER :
A. 7
18.
How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word ‘LUCKNOW’?
A.
240
B.
200
C.
150
D.
120
😑 View Answer Error
ANSWER :
A. 240
19.
Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct?
1. The number of straight lines that can be drawn by joining any two of these points is 380.
2. The number of triangles that can be drawn by joining any three of these points is 1140.
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 :
B. 2 only
20.
How many terms are there in the expansion of
\( \left(\frac{a^{2}}{b^{2}} + \frac{b^{2}}{a^{2}} + 2\right)^{21} \)
where \( a \neq 0, b \neq 0 \)?
A.
21
B.
22
C.
42
D.
43
😑 View Answer Error
ANSWER :
D. 43
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