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

1.
If both p and q belong to the set \( \{1, 2, 3, 4\} \), then how many equations of the form \( px^{2} + qx + 1 = 0 \) will have real roots?
A.
12
B.
10
C.
7
D.
6
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ANSWER :
C. 7
2.
What is the value of \( 1 - 2 + 3 - 4 + 5 - \ldots + 101 \)?
A.
51
B.
55
C.
110
D.
111
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ANSWER :
A. 51
3.
If A, B and C are subsets of a given set, then which one of the following relations is not correct?
A.
\( A \cup (A \cap B) = A \cup B \)
B.
\( A \cap (A \cup B) = A \)
C.
\( (A \cap B) \cup C = (A \cup C) \cap (B \cup C) \)
D.
\( (A \cup B) \cap C = (A \cap C) \cup (B \cap C) \)
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ANSWER :
A. \( A \cup (A \cap B) = A \cup B \)
4.
If the sum of first n terms of a series is \( (n + 12) \), then what is its third term?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
A. 1
5.
What is the value of k for which the sum of the squares of the roots of \( 2x^{2} - 2(k - 2)x - (k + 1) = 0 \) is minimum?
A.
−1
B.
1
C.
\( \frac{3}{2} \)
D.
2
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ANSWER :
C. \( \frac{3}{2} \)
6.
If the roots of the equation \( a(b - c)x^{2} + b(c - a)x + c(a - b) = 0 \) are equal, then which one of the following is correct?
A.
a, b and c are in AP
B.
a, b and c are in GP
C.
a, b and c are in HP
D.
a, b and c do not follow any regular pattern
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ANSWER :
C. a, b and c are in HP
7.
If \( \left| x^{2} - 3x + 2 \right| > x^{2} - 3x + 2 \), then which one of the following is correct?
A.
\( x \leq 1 \) or \( x \geq 2 \)
B.
\( 1 \leq x \leq 2 \)
C.
\( 1 < x < 2 \)
D.
x is any real value except 3 and 4
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ANSWER :
C. \( 1 < x < 2 \)
8.
A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio?
A.
\( m/n \)
B.
\( n/m \)
C.
\( m + (n/m) \)
D.
\( n + (m/n) \)
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ANSWER :
B. \( n/m \)
9.
If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that \( (A \cup B) \) can have?
A.
3
B.
6
C.
8
D.
9
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ANSWER :
B. 6
10.
What is the number of diagonals of an octagon?
A.
48
B.
40
C.
28
D.
20
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ANSWER :
D. 20
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