NDA & NA Exam (II)- 2016 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2016 - Mathematics

NDA & NA Exam (II)- 2016 - Mathematics Defence Questions

1.
Let S be a set of all distinct numbers of the form \( \frac{p}{q} \), where \( p, q \in \{1, 2, 3, 4, 5, 6\} \). What is the cardinality of the set S?
A.
21
B.
23
C.
32
D.
36
😑 View Answer Error
ANSWER :
B. 23
2.
If \( c > 0 \) and \( 4a + c < 2b \), then \( ax^{2} - bx + c = 0 \) has a root in which one of the following intervals?
A.
(0, 2)
B.
(2, 3)
C.
(3, 4)
D.
(−2, 0)
😑 View Answer Error
ANSWER :
A. (0, 2)
3.
If \( A = \{x \in R : x^{2} + 6x - 7 < 0\} \) and \( B = \{x \in R : x^{2} + 9x + 14 > 0\} \), then which of the following is/are correct?
1. \( A \cap B = \{x \in R : -2 < x < 1\} \)
2. \( A \setminus B = \{x \in R : -7 < x < 1\} \)
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 :
A. 1 only
4.
If A is a square matrix of order 3 and \( \det A = 5 \), then what is \( \det[(2A)^{-1}] \) equal to?
A.
\( \frac{1}{10} \)
B.
\( \frac{2}{5} \)
C.
\( \frac{8}{5} \)
D.
\( \frac{1}{40} \)
😑 View Answer Error
ANSWER :
D. \( \frac{1}{40} \)
5.
What is \( \omega^{100} + \omega^{200} + \omega^{300} \) equal to, where \( \omega \) is the cube root of unity?
A.
1
B.
\( 3\omega \)
C.
\( 3\omega^{2} \)
D.
0
😑 View Answer Error
ANSWER :
D. 0
6.
If \( Re\left(\frac{z-1}{z+1}\right) = 0 \), where \( z = x + iy \) is a complex number, then which one of the following is correct?
A.
\( z = 1 + i \)
B.
\( |z| = 2 \)
C.
\( z = 1 - i \)
D.
\( |z| = 1 \)
😑 View Answer Error
ANSWER :
D. \( |z| = 1 \)
7.
What is \( \begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \) equal to?
A.
\( \begin{bmatrix} ax + hy + gz & h + b + f & g + f + c \end{bmatrix} \)
B.
\( \begin{bmatrix} a & h & g \\ hx & by & fz \\ g & f & c \end{bmatrix} \)
C.
\( \begin{bmatrix} ax + hy + gz \\ hx + by + fz \\ gx + fy + cz \end{bmatrix} \)
D.
\( \begin{bmatrix} ax + hy + gz & hx + by + fz & gx + fy + cz \end{bmatrix} \)
😑 View Answer Error
ANSWER :
D. \( \begin{bmatrix} ax + hy + gz & hx + by + fz & gx + fy + cz \end{bmatrix} \)
8.
Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n?
A.
3
B.
4
C.
5
D.
6
😑 View Answer Error
ANSWER :
C. 5
9.
If \( z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^{107} + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{107} \), then what is the imaginary part of z equal to?
A.
0
B.
\( \frac{1}{2} \)
C.
\( \frac{\sqrt{3}}{2} \)
D.
1
😑 View Answer Error
ANSWER :
A. 0
10.
If both the roots of the equation \( x^{2} - 2kx + k^{2} - 4 = 0 \) lie between −3 and 5, then which one of the following is correct?
A.
\( -2 < k < 2 \)
B.
\( -5 < k < 3 \)
C.
\( -3 < k < 5 \)
D.
\( -1 < k < 3 \)
😑 View Answer Error
ANSWER :
D. \( -1 < k < 3 \)
Prev Next page