NDA & NA Exam (II)- 2024 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2024 - Mathematics

NDA & NA Exam (II)- 2024 - Mathematics Defence Questions

21.
If \( 4\sin^{-1} x + \cos^{-1} x = \pi \), then what is \( \sin^{-1} x + 4\cos^{-1} x \) equal to?
A.
\( \frac{\pi}{2} \)
B.
\( \pi \)
C.
\( \frac{3\pi}{2} \)
D.
\( 2\pi \)
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ANSWER :
C. \( \frac{3\pi}{2} \)
22.
What is \( \cot^{2}(\sec^{-1} 2) + \tan^{2}(\csc^{-1} 3) \) equal to?
A.
\( \frac{11}{12} \)
B.
\( \frac{11}{24} \)
C.
\( \frac{7}{24} \)
D.
\( \frac{1}{24} \)
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ANSWER :
B. \( \frac{11}{24} \)
23.
In a triangle ABC, \( \frac{a}{\cos A} = \frac{b}{\cos B} = \frac{c}{\cos C} \). What is the area of the triangle if a = 6 cm?
A.
\( 9\sqrt{3} \) square cm
B.
12 square cm
C.
\( 18\sqrt{3} \) square cm
D.
24 square cm
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ANSWER :
A. \( 9\sqrt{3} \) square cm
24.
The roots of the equation \( 7x^{2} - 6x + 1 = 0 \) are \( \tan\alpha \) and \( \tan\beta \), where \( 2\alpha \) and \( 2\beta \) are the angles of a triangle. Which one of the following is correct?
A.
The triangle is equilateral.
B.
The triangle is isosceles but not right-angled.
C.
The triangle is right-angled.
D.
The triangle is right-angled isosceles.
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ANSWER :
C. The triangle is right-angled.
25.
In a triangle ABC, \( \angle A = 75^{\circ} \) and \( \angle B = 45^{\circ} \). What is \( 2a - b \) equal to?
A.
c
B.
\( \sqrt{2}c \)
C.
2c
D.
\( 2\sqrt{2}c \)
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ANSWER :
B. \( \sqrt{2}c \)
26.
What is the number of solutions of the equation \( \cot 2x \cdot \cot 3x = 1 \) for \( 0 < x < \pi \)?
A.
Only one
B.
Only two
C.
Only four
D.
More than five
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ANSWER :
C. Only four
27.
What is the general solution of \( \cos^{100} x - \sin^{100} x = 1 \)?
where n is an integer.
A.
\( n\pi \)
B.
\( (2n + 1)\pi \)
C.
\( 2n\pi \)
D.
\( \frac{(2n + 1)\pi}{2} \)
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ANSWER :
A. \( n\pi \)
28.
In a triangle ABC, tan A + tan B + tan C = k. What is the value of cot A cot B cot C?
A.
0.5k
B.
\( \frac{1}{k} \)
C.
\( \frac{3}{k} \)
D.
\( \frac{1}{k^{3}} \)
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ANSWER :
B. \( \frac{1}{k} \)
29.
What is \( \sin 12^{\circ} \sin 48^{\circ} \) equal to?
A.
\( \frac{\sqrt{5} - 1}{4} \)
B.
\( \frac{\sqrt{5} + 1}{4} \)
C.
\( \frac{\sqrt{5} - 1}{8} \)
D.
\( \frac{\sqrt{5} + 1}{8} \)
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ANSWER :
C. \( \frac{\sqrt{5} - 1}{8} \)
30.
What is \( \frac{\cos 17^{\circ} - \sin 17^{\circ}}{\cos 17^{\circ} + \sin 17^{\circ}} \) equal to?
A.
\( \tan 34^{\circ} \)
B.
\( \cot 34^{\circ} \)
C.
\( \tan 62^{\circ} \)
D.
\( \cot 62^{\circ} \)
😑 View Answer Error
ANSWER :
D. \( \cot 62^{\circ} \)
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