NDA & NA Exam (I)- 2025 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2025 - Mathematics

NDA & NA Exam (I)- 2025 - Mathematics Defence Questions

31.
Consider the following for the next three (03) items that follow:
Let \( p = \sin 35^{\circ} \), \( q = \sin 25^{\circ} \) and \( r = \sin (-95^{\circ}) \).

What is \( (p + q + r) \) equal to?
A.
-1
B.
0
C.
\( 2\sin 5^{\circ} \)
D.
\( 2\cos 5^{\circ} \)
😑 View Answer Error
ANSWER :
B. 0
32.
What is \( (pq + qr + rp) \) equal to?
A.
\( -\frac{3}{4} \)
B.
0
C.
\( \frac{1}{4} \)
D.
\( \frac{3}{4} \)
😑 View Answer Error
ANSWER :
A. \( -\frac{3}{4} \)
33.
What is \( (p^{2} + q^{2} + r^{2}) \) equal to?
A.
\( \frac{1}{2} \)
B.
1
C.
\( \frac{3}{2} \)
D.
2
😑 View Answer Error
ANSWER :
C. \( \frac{3}{2} \)
34.
Consider the following for the next two (02) items that follow:
Let \( p = |\sin \alpha - \sin (\alpha - 90^{\circ})| \).

What is the minimum value of \( p \)?
A.
0
B.
\( \frac{1}{2} \)
C.
\( \frac{1}{\sqrt{2}} \)
D.
1
😑 View Answer Error
ANSWER :
A. 0
35.
What is the maximum value of \( p \)?
A.
1
B.
\( \sqrt{2} \)
C.
\( \sqrt{3} \)
D.
2
😑 View Answer Error
ANSWER :
B. \( \sqrt{2} \)
36.
Consider the following for the next three (03) items that follow:
The sides of a triangle ABC are AB = 3 cm, BC = 5 cm and CA = 7 cm.

Consider the following statements:
I. The triangle is obtuse-angled triangle.
II. The sum of acute angles of the triangle is also acute.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
C. Both I and II
37.
What is \( \angle B \) equal to?
A.
\( 60^{\circ} \)
B.
\( 105^{\circ} \)
C.
\( 120^{\circ} \)
D.
\( 150^{\circ} \)
😑 View Answer Error
ANSWER :
C. \( 120^{\circ} \)
38.
What is the area of the triangle?
A.
\( \frac{15\sqrt{3}}{4} \) square cm
B.
\( \frac{15\sqrt{3}}{2} \) square cm
C.
\( 15\sqrt{3} \) square cm
D.
\( 30\sqrt{3} \) square cm
😑 View Answer Error
ANSWER :
A. \( \frac{15\sqrt{3}}{4} \) square cm
39.
Consider the following for the next two (02) items that follow:
The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are \( 30^{\circ} \), \( 45^{\circ} \) and \( 60^{\circ} \) respectively. Let PQ = \( a \) and QR = \( b \).

What is PN equal to?
A.
\( \left(\frac{3-\sqrt{3}}{2}\right)a \)
B.
\( \left(\frac{3+\sqrt{3}}{2}\right)a \)
C.
\( \left(\frac{3-\sqrt{3}}{4}\right)a \)
D.
\( \left(\frac{3+\sqrt{3}}{4}\right)a \)
😑 View Answer Error
ANSWER :
B. \( \left(\frac{3+\sqrt{3}}{2}\right)a \)
40.
What is MN equal to?
A.
\( \left(\frac{3+\sqrt{3}}{2}\right)b \)
B.
\( \left(\frac{3-\sqrt{3}}{2}\right)b \)
C.
\( \left(\frac{3-\sqrt{3}}{4}\right)b \)
D.
\( \left(\frac{3+\sqrt{3}}{4}\right)b \)
😑 View Answer Error
ANSWER :
A. \( \left(\frac{3+\sqrt{3}}{2}\right)b \)
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