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

31.
Consider the following numbers:
(I) \( \tan 22.5^{\circ} \)
(II) \( \cot 22.5^{\circ} \)
(III) \( \tan 22.5^{\circ} - \cot 22.5^{\circ} \)
How many of the above are irrational numbers?
A.
None
B.
Only one
C.
Only two
D.
All three
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ANSWER :
C. Only two
32.
If \( \frac{x}{\cos\theta} = \frac{y}{\cos\left(\theta - \frac{2\pi}{3}\right)} = \frac{z}{\cos\left(\theta + \frac{2\pi}{3}\right)} \), then what is x + y + z equal to?
A.
−1
B.
0
C.
1
D.
3
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ANSWER :
B. 0
33.
If \( p\tan(\theta - 30^{\circ}) = q\tan(\theta + 120^{\circ}) \), then what is \( \frac{p + q}{p - q} \) equal to?
A.
\( \sin 2\theta \)
B.
\( \cos 2\theta \)
C.
\( 2\sin 2\theta \)
D.
\( 2\cos 2\theta \)
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ANSWER :
D. \( 2\cos 2\theta \)
34.
Let P and Q be two non-void relations on a set A. Which of the following statements are correct?
I. P and Q are reflexive \( \Rightarrow P \cap Q \) is reflexive.
II. P and Q are symmetric \( \Rightarrow P \cup Q \) is symmetric.
III. P and Q are transitive \( \Rightarrow P \cap Q \) is transitive.
Select the correct answer using the code given below.
A.
I and II only
B.
II and III only
C.
I and III only
D.
I, II and III
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ANSWER :
D. I, II and III
35.
If A and B are two non-empty sets having 10 elements in common, then how many elements do A × B and B × A have in common?
A.
10
B.
20
C.
40
D.
100
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ANSWER :
D. 100
36.
What is the remainder when \( 7^{n} - 6n \) is divided by 36 for n = 100?
A.
0
B.
1
C.
2
D.
6
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ANSWER :
B. 1
37.
What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as circle and lines)?
A.
6
B.
10
C.
14
D.
16
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ANSWER :
C. 14
38.
In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is \( p^{2} : q^{2} \). Which one of the following is correct?
A.
The first term is equal to the common difference.
B.
The first term is equal to twice the common difference.
C.
The common difference is equal to twice the first term.
D.
The first term is equal to square of the common difference.
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ANSWER :
C. The common difference is equal to twice the first term.
39.
What is the number of real roots of the equation \( (x - 1)^{2} + (x - 3)^{2} + (x - 5)^{2} = 0 \)?
A.
None
B.
Only one
C.
Only two
D.
Three
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ANSWER :
A. None
40.
In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?
A.
60
B.
55
C.
40
D.
35
😑 View Answer Error
ANSWER :
A. 60
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