NDA & NA Exam (I)- 2021 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2021 - Mathematics

NDA & NA Exam (I)- 2021 - Mathematics Defence Questions

41.
What is the modulus of the complex number \( i^{2n+1}(-i)^{2n-1} \), where \( n \in \mathbb{N} \) and \( i = \sqrt{-1} \)?
A.
−1
B.
1
C.
\( \sqrt{2} \)
D.
2
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ANSWER :
B. 1
42.
If \( \alpha \) and \( \beta \) are the roots of the equation \( 4x^{2} + 2x - 1 = 0 \), then which one of the following is correct?
A.
\( \beta = -2\alpha^{3} - 2\alpha \)
B.
\( \beta = 4\alpha^{3} - 3\alpha \)
C.
\( \beta = \alpha^{3} - 3\alpha \)
D.
\( \beta = -2\alpha^{2} + 2\alpha \)
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ANSWER :
B. \( \beta = 4\alpha^{3} - 3\alpha \)
43.
If one root of \( 5x^{2} + 26x + k = 0 \) is reciprocal of the other, then what is the value of \( k \)?
A.
2
B.
3
C.
5
D.
8
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ANSWER :
C. 5
44.
In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?
A.
42
B.
35
C.
21
D.
20
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ANSWER :
C. 21
45.
What is the coefficient of the middle term in the expansion of \( (1 + 4x + 4x^{2})^{5} \)?
A.
8064
B.
4032
C.
2016
D.
1008
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ANSWER :
A. 8064
46.
What is \( C(n, 1) + C(n, 2) + \ldots + C(n, n) \) equal to?
A.
\( 2 + 2^{2} + 2^{3} + \ldots + 2^{n} \)
B.
\( 1 + 2 + 2^{2} + 2^{3} + \ldots + 2^{n} \)
C.
\( 1 + 2 + 2^{2} + 2^{3} + \ldots + 2^{n-1} \)
D.
\( 2 + 2^{2} + 2^{3} + \ldots + 2^{n-1} \)
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ANSWER :
C. \( 1 + 2 + 2^{2} + 2^{3} + \ldots + 2^{n-1} \)
47.
What is the sum of the coefficients of first and last terms in the expansion of \( (1+x)^{2n} \), where \( n \) is a natural number?
A.
1
B.
2
C.
\( n \)
D.
\( 2n \)
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ANSWER :
B. 2
48.
If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?
A.
−500
B.
−250
C.
500
D.
250
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ANSWER :
B. −250
49.
Consider the following statements:
1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.
2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
50.
How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
A.
5
B.
4
C.
3
D.
0
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ANSWER :
D. 0
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