NDA & NA Exam (II)- 2019 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2019 - Mathematics

NDA & NA Exam (II)- 2019 - Mathematics Defence Questions

11.
What is the value of the determinant \( \begin{vmatrix} 1! & 2! & 3! \\ 2! & 3! & 4! \\ 3! & 4! & 5! \end{vmatrix} \)?
A.
0
B.
12
C.
24
D.
36
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ANSWER :
C. 24
12.
What are the values of x that satisfy the equation \( \begin{vmatrix} x & 0 & 2 \\ 2x & 2 & 1 \\ 1 & 1 & 1 \end{vmatrix} + \begin{vmatrix} 3x & 0 & 2 \\ x^{2} & 2 & 1 \\ 0 & 1 & 1 \end{vmatrix} = 0 \)?
A.
\( -2 \pm \sqrt{3} \)
B.
\( -1 \pm \sqrt{3} \)
C.
\( -1 \pm \sqrt{6} \)
D.
\( -2 \pm \sqrt{6} \)
😑 View Answer Error
ANSWER :
D. \( -2 \pm \sqrt{6} \)
13.
If \( x + a + b + c = 0 \), then what is the value of \( \begin{vmatrix} x + a & b & c \\ a & x + b & c \\ a & b & x + c \end{vmatrix} \)?
A.
0
B.
\( (a + b + c)^{2} \)
C.
\( a^{2} + b^{2} + c^{2} \)
D.
\( a + b + c - 2 \)
😑 View Answer Error
ANSWER :
A. 0
14.
If \( A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \), then the expression \( A^{3} - 2A^{2} \) is
A.
a null matrix
B.
an identity matrix
C.
equal to A
D.
equal to −A
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ANSWER :
A. a null matrix
15.
Let m and n \( (m < n) \) be the roots of the equation \( x^{2} - 16x + 39 = 0 \). If four terms p, q, r and s are inserted between m and n to form an AP, then what is the value of \( p + q + r + s \)?
A.
29
B.
30
C.
32
D.
35
😑 View Answer Error
ANSWER :
C. 32
16.
Under which one of the following conditions will the quadratic equation \( x^{2} + mx + 2 = 0 \) always have real roots?
A.
\( 2\sqrt{3} \leq m^{2} \leq 8 \)
B.
\( \sqrt{3} \leq m^{2} \leq 4 \)
C.
\( m^{2} \geq 8 \)
D.
\( m^{2} \leq \sqrt{3} \)
😑 View Answer Error
ANSWER :
C. \( m^{2} \geq 8 \)
17.
What is the value of \( \left(\frac{i + \sqrt{3}}{2}\right)^{2019} + \left(\frac{i - \sqrt{3}}{2}\right)^{2019} \)?
A.
1
B.
−1
C.
\( 2i \)
D.
\( -2i \)
😑 View Answer Error
ANSWER :
C. \( 2i \)
18.
If \( \alpha \) and \( \beta \) are the roots of \( x^{2} + x + 1 = 0 \), then what is \( \sum_{j=0}^{3} (\alpha^{j} + \beta^{j}) \) equal to?
A.
8
B.
6
C.
4
D.
2
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ANSWER :
D. 2
19.
In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what per cent of students play neither cricket nor football?
A.
10%
B.
15%
C.
20%
D.
25%
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ANSWER :
C. 20%
20.
If \( A = \{x : 0 < x < 2\} \) and B = {y : y is a prime number}, then what is \( A \cap B \) equal to?
A.
\( \phi \)
B.
\( \{1\} \)
C.
\( \{2\} \)
D.
\( \{1, 2\} \)
😑 View Answer Error
ANSWER :
A. \( \phi \)
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