CDS Exam (I)- 2024- Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2024- Elementary Mathematics

CDS Exam (I)- 2024- Elementary Mathematics Defence Questions

21.
If \( p = \sqrt[3]{\left(a + \sqrt{a^{2} + b^{3}}\right)} + \sqrt[3]{\left(a - \sqrt{a^{2} + b^{3}}\right)} \), then what is \( p^{3} + 3bp \) equal to?
A.
-2a
B.
a
C.
2a
D.
3a
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ANSWER :
C. 2a
22.
A plank of wood 4.25 m long and 3.4 m wide is to be cut into square pieces of equal size. How many square pieces of largest size can be cut from the plank, if no wastage is allowed?
A.
20
B.
90
C.
400
D.
500
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ANSWER :
A. 20
23.
What is the HCF of \( x^{4} - 13x^{2}y^{2} - 300y^{4} \), \( x^{3} - 4x^{2}y - 4xy^{2} - 5y^{3} \) and \( x^{3} - 125y^{3} \)?
A.
x - 5y
B.
x + 5y
C.
\( x^{2} + 5xy + 25y^{2} \)
D.
1
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ANSWER :
A. x - 5y
24.
If HCF of 768 and \( x^{6}y^{2} \) is 32xy for natural numbers \( x \geq 2, y \geq 2 \), then what is the value of (x + y)?
A.
5
B.
7
C.
9
D.
11
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ANSWER :
A. 5
25.
What is the smallest natural number n such that \( (n + 1) \times n \times (n - 1) \times (n - 2) \times \ldots 3 \times 2 \times 1 \) is divisible by 910?
A.
91
B.
90
C.
13
D.
12
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ANSWER :
D. 12
26.
The expression \( 555^{777} + 777^{555} \) is divisible by which of the following?
1. 2
2. 3
3. 37
Select the correct answer using the code given below:
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
27.
Consider the following statements:
1. If \( \frac{3m^{3} + 2m^{2} + 5m + n}{m} \) is not an integer, where m and n are integers, then n is not divisible by m.
2. \( 5\left(8^{m}\right) + 2^{3m} \) is divisible by 48 for all whole numbers m.
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. 1 only
28.
The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers?
A.
12
B.
18
C.
24
D.
28
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ANSWER :
C. 24
29.
50 men can complete a work in 40 days. They begin the work together but a batch of 5 men left after each period of 10 days. What is the time to complete the work?
A.
45 days
B.
50 days
C.
55 days
D.
60 days
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ANSWER :
B. 50 days
30.
If \( x = \frac{1}{2 + \frac{3}{4 + \frac{5}{6 + \frac{7}{8 + \frac{9}{10}}}}} \), then which one of the following is correct?
A.
\( 0 < x < 0.5 \)
B.
x = 0.5
C.
\( 0.5 < x < 1.0 \)
D.
\( x > 1.0 \)
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ANSWER :
A. \( 0 < x < 0.5 \)
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