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

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NDA & NA Exam (I)- 2019 - Mathematics

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

11.
The common roots of the equations \( z^{3} + 2z^{2} + 2z + 1 = 0 \) and \( z^{1985} + z^{100} + 1 = 0 \) are
A.
\( -1, \omega \)
B.
\( 1, \omega^{2} \)
C.
\( -1, \omega^{2} \)
D.
\( \omega, \omega^{2} \)
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ANSWER :
D. \( \omega, \omega^{2} \)
12.
If \( C(20, n + 2) = C(20, n - 2) \), then what is n equal to?
A.
8
B.
10
C.
12
D.
16
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ANSWER :
B. 10
13.
There are 10 points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?
A.
90
B.
45
C.
40
D.
30
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ANSWER :
B. 45
14.
The equation \( px^{2} + qx + r = 0 \) (where p, q, r, all are positive) has distinct real roots a and b. Which one of the following is correct?
A.
\( a > 0, b > 0 \)
B.
\( a < 0, b < 0 \)
C.
\( a > 0, b < 0 \)
D.
\( a < 0, b > 0 \)
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ANSWER :
B. \( a < 0, b < 0 \)
15.
If \( A = \{\lambda, \{\lambda, \mu\}\} \), then the power set of A is
A.
\( \{\phi, \{\phi\}, \{\lambda\}, \{\lambda, \mu\}\} \)
B.
\( \{\phi, \{\lambda\}, \{\{\lambda, \mu\}\}, \{\lambda, \{\lambda, \mu\}\}\} \)
C.
\( \{\phi, \{\lambda\}, \{\lambda, \mu\}, \{\lambda, \{\lambda, \mu\}\}\} \)
D.
\( \{\{\lambda\}, \{\lambda, \mu\}, \{\lambda, \{\lambda, \mu\}\}\} \)
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ANSWER :
B. \( \{\phi, \{\lambda\}, \{\{\lambda, \mu\}\}, \{\lambda, \{\lambda, \mu\}\}\} \)
16.
Consider the following for the next 02 (two) items that follow:
In a school, all the students play at least one of three indoor games — chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.

What can be the minimum number of students in the school?
A.
123
B.
111
C.
95
D.
63
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ANSWER :
B. 111
17.
What can be the maximum number of students in the school?
A.
111
B.
123
C.
125
D.
135
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ANSWER :
B. 123
18.
If A is an identity matrix of order 3, then its inverse \( (A^{-1}) \)
A.
is equal to null matrix
B.
is equal to A
C.
is equal to 3A
D.
does not exist
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ANSWER :
B. is equal to A
19.
A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose?
A.
64
B.
36
C.
32
D.
4
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ANSWER :
D. 4
20.
From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?
A.
209
B.
210
C.
246
D.
242
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ANSWER :
C. 246
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