NDA & NA Exam (II)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2014 - Mathematics

NDA & NA Exam (II)- 2014 - Mathematics Defence Questions

11.
Consider the following statements:
1. Determinant is a square matrix.
2. Determinant is a number associated with a square matrix.
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 :
B. 2 only
12.
If A is an invertible matrix, then what is \( \det(A^{-1}) \) equal to?
A.
det A
B.
\( \frac{1}{\det A} \)
C.
1
D.
None of the above
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ANSWER :
B. \( \frac{1}{\det A} \)
13.
From the matrix equation \( AB = AC \), where A, B, C are the square matrices of same order, we can conclude \( B = C \) provided
A.
A is non-singular
B.
A is singular
C.
A is symmetric
D.
A is skew-symmetric
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ANSWER :
A. A is non-singular
14.
If \( A = \begin{pmatrix} 4 & x+2 \\ 2x-3 & x+1 \end{pmatrix} \) is symmetric, then what is x equal to?
A.
2
B.
3
C.
−1
D.
5
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ANSWER :
D. 5
15.
If \( \begin{vmatrix} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{vmatrix} = 0 \), then which one of the following is correct?
A.
\( \frac{a}{b} \) is one of the cube roots of unity
B.
\( \frac{a}{b} \) is one of the cube roots of −1
C.
a is one of the cube roots of unity
D.
b is one of the cube roots of unity
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ANSWER :
B. \( \frac{a}{b} \) is one of the cube roots of −1
16.
The function \( f: N \rightarrow N \), N being the set of natural numbers, defined by \( f(x) = 2x + 3 \) is
A.
injective and surjective
B.
injective but not surjective
C.
not injective but surjective
D.
neither injective nor surjective
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ANSWER :
B. injective but not surjective
17.
What is \( \frac{(1+i)^{4n+5}}{(1-i)^{4n+3}} \) equal to, where n is a natural number and \( i = \sqrt{-1} \)?
A.
2
B.
2i
C.
−2i
D.
i
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ANSWER :
A. 2
18.
What is the number of ways in which one can post 5 letters in 7 letter boxes?
A.
\( 7^{5} \)
B.
\( 3^{5} \)
C.
\( 5^{7} \)
D.
2520
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ANSWER :
A. \( 7^{5} \)
19.
What is the number of ways that a cricket team of 11 players can be made out of 15 players?
A.
364
B.
1001
C.
1365
D.
32760
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ANSWER :
C. 1365
20.
A and B are two sets having 3 elements in common. If \( n(A) = 5 \), \( n(B) = 4 \), then what is \( n(A \times B) \) equal to?
A.
0
B.
9
C.
15
D.
20
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ANSWER :
D. 20
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