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

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NDA & NA Exam (II)- 2021 - Mathematics

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

1.
If \( x^{2} + x + 1 = 0 \), then what is the value of \( x^{199} + x^{200} + x^{201} \)?
A.
−1
B.
0
C.
1
D.
3
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ANSWER :
B. 0
2.
If \( x, y, z \) are in GP, then which of the following is/are correct?
1. \( \ln(3x), \ln(3y), \ln(3z) \) are in AP
2. \( xyz + \ln(x), xyz + \ln(y), xyz + \ln(z) \) are in HP
Select the correct answer using the code given below.
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
3.
If \( \log_{10} 2, \log_{10}(2^{x} - 1), \log_{10}(2^{x} + 3) \) are in AP, then what is \( x \) equal to?
A.
0
B.
1
C.
\( \log_{2} 5 \)
D.
\( \log_{5} 2 \)
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ANSWER :
C. \( \log_{2} 5 \)
4.
Let \( S = \{2, 3, 4, 5, 6, 7, 9\} \). How many different 3-digit numbers (with all digits different) from \( S \) can be made which are less than 500?
A.
30
B.
49
C.
90
D.
147
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ANSWER :
C. 90
5.
If \( p = (1111 \ldots \) up to \( n \) digits), then what is the value of \( 9p^{2} + p \)?
A.
\( 10^{n}p \)
B.
\( 2p \cdot 10^{n} \)
C.
\( 10^{n}p - 1 \)
D.
\( 10^{n}p + 1 \)
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ANSWER :
A. \( 10^{n}p \)
6.
The quadratic equation \( 3x^{2} - (k^{2} + 5k)x + 3k^{2} - 5k = 0 \) has real roots of equal magnitude and opposite sign. Which one of the following is correct?
A.
\( 0 < k < \frac{5}{3} \)
B.
\( 0 < k < \frac{3}{5} \) only
C.
\( \frac{3}{5} < k < \frac{5}{3} \)
D.
No such value of \( k \) exists
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ANSWER :
D. No such value of \( k \) exists
7.
If \( a_{n} = n(n!) \), then what is \( a_{1} + a_{2} + a_{3} + \ldots + a_{10} \) equal to?
A.
\( 10! - 1 \)
B.
\( 11! + 1 \)
C.
\( 10! + 1 \)
D.
\( 11! - 1 \)
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ANSWER :
D. \( 11! - 1 \)
8.
If \( p \) and \( q \) are the non-zero roots of the equation \( x^{2} + px + q = 0 \), then how many possible values can \( q \) have?
A.
Nil
B.
One
C.
Two
D.
Three
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ANSWER :
B. One
9.
If
\( \Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \)
then what is
\( \begin{vmatrix} 3d+5g & 4a+7g & 6g \\ 3e+5h & 4b+7h & 6h \\ 3f+5i & 4c+7i & 6i \end{vmatrix} \)
equal to?
A.
\( \Delta \)
B.
\( 7\Delta \)
C.
\( 72\Delta \)
D.
\( -72\Delta \)
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ANSWER :
D. \( -72\Delta \)
10.
If
\( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \)
are in HP, then which of the following is/are correct?
1. \( a, b, c \) are in AP
2. \( (b+c)^{2}, (c+a)^{2}, (a+b)^{2} \) are in GP
Select the correct answer using the code given below.
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
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