NDA & NA Exam (I)- 2023 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2023 - Mathematics

NDA & NA Exam (I)- 2023 - Mathematics Defence Questions

41.
Directions (Qn. 41-42): Consider the following for the next two (02) items that follow:
Consider the function \( f(x) = |x - 2| + |3 - x| + |4 - x| \), where \( x \in \mathbb{R} \).

At what value of \( x \) does the function attain minimum value?
A.
2
B.
3
C.
4
D.
0
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ANSWER :
B. 3
42.
What is the minimum value of the function?
A.
2
B.
3
C.
4
D.
0
😑 View Answer Error
ANSWER :
A. 2
43.
Directions (Qn. 43-44): Consider the following for the next two (02) items that follow:
Consider the sum \( S = 0! + 1! + 2! + 3! + 4! + \ldots + 100! \)

If the sum \( S \) is divided by 8, what is the remainder?
A.
0
B.
1
C.
2
D.
Cannot be determined
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ANSWER :
C. 2
44.
If the sum \( S \) is divided by 60, what is the remainder?
A.
1
B.
3
C.
17
D.
34
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ANSWER :
D. 34
45.
Directions (Qn. 45-46): Consider the following for the next two (02) items that follow:
In a triangle PQR, P is the largest angle and \( \cos P = \frac{1}{3} \). Further the in-circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively such that the lengths PN, QL and RM are \( n, n + 2, n + 4 \) respectively where \( n \) is an integer.

What is the value of \( n \)?
A.
4
B.
6
C.
8
D.
10
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ANSWER :
C. 8
46.
What is the length of the smallest side?
A.
12
B.
14
C.
16
D.
18
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ANSWER :
D. 18
47.
Directions (Qn. 47-48): Consider the following for the next two (02) items that follow:
Given that \( \sin x + \cos x + \tan x + \cot x + \sec x + cosec x = 7 \)

The given equation can be reduced to
A.
\( \sin^{2} 2x - 44 \sin 2x + 36 = 0 \)
B.
\( \sin^{2} 2x + 44 \sin 2x - 36 = 0 \)
C.
\( \sin^{2} 2x - 22 \sin 2x + 18 = 0 \)
D.
\( \sin^{2} 2x + 22 \sin 2x - 18 = 0 \)
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ANSWER :
A. \( \sin^{2} 2x - 44 \sin 2x + 36 = 0 \)
48.
If \( \sin 2x = a - b\sqrt{c} \), where \( a \) and \( b \) are natural numbers and \( c \) is prime number, then what is the value of \( a - b + 2c \)?
A.
0
B.
14
C.
21
D.
28
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ANSWER :
D. 28
49.
Directions (Qn. 49-50): Consider the following for the next two (02) items that follow:
A quadratic equation is given by \( (3 + 2\sqrt{2})x^{2} - (4 + 2\sqrt{3})x + (8 + 4\sqrt{3}) = 0 \)

What is the HM of the roots of the equation?
A.
2
B.
4
C.
\( 2\sqrt{2} \)
D.
\( 2\sqrt{3} \)
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ANSWER :
B. 4
50.
What is the GM of the roots of the equation?
A.
\( \sqrt{2}(\sqrt{6} - \sqrt{3} + \sqrt{2} - 1) \)
B.
\( \sqrt{2}(\sqrt{6} + \sqrt{3} - \sqrt{2} - 1) \)
C.
\( (\sqrt{6} - \sqrt{3} + \sqrt{2} - 1) \)
D.
\( (\sqrt{6} + \sqrt{3} + \sqrt{2} - 1) \)
😑 View Answer Error
ANSWER :
A. \( \sqrt{2}(\sqrt{6} - \sqrt{3} + \sqrt{2} - 1) \)
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