NDA & NA Exam (II)- 2017 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2017 - Mathematics

NDA & NA Exam (II)- 2017 - Mathematics Defence Questions

1.
If \( x + \log_{10}(1 + 2^{x}) = x \log_{10} 5 + \log_{10} 6 \), then x is equal to
A.
2, −3
B.
2 only
C.
1
D.
3
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ANSWER :
C. 1
2.
The remainder and the quotient of the binary division \( (101110)_{2} \div (110)_{2} \) are respectively
A.
\( (111)_{2} \) and \( (100)_{2} \)
B.
\( (100)_{2} \) and \( (111)_{2} \)
C.
\( (101)_{2} \) and \( (101)_{2} \)
D.
\( (100)_{2} \) and \( (100)_{2} \)
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ANSWER :
B. \( (100)_{2} \) and \( (111)_{2} \)
3.
The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 − y columns. Both AB and BA exist. What are the values of x and y respectively?
A.
8 and 3
B.
3 and 4
C.
3 and 8
D.
8 and 8
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ANSWER :
C. 3 and 8
4.
If \( S_{n} = nP + \frac{n(n-1)}{2}Q \), where \( S_{n} \) denotes the sum of the first n terms of an AP, then the common difference is
A.
P + Q
B.
2P + 3Q
C.
2Q
D.
Q
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ANSWER :
D. Q
5.
The roots of the equation \( (q - r)x^{2} + (r - p)x + (p - q) = 0 \) are
A.
\( \frac{r-p}{q-r} \), \( \frac{1}{2} \)
B.
\( \frac{p-q}{q-r} \), 1
C.
\( \frac{q-r}{p-q} \), 1
D.
\( \frac{r-p}{p-q} \), \( \frac{1}{2} \)
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ANSWER :
B. \( \frac{p-q}{q-r} \), 1
6.
If E is the universal set and \( A = B \cup C \), then the set \( E - (E - (E - (E - (E - A)))) \) is the same as the set
A.
\( B' \cup C' \)
B.
\( B \cup C \)
C.
\( B' \cap C' \)
D.
\( B \cap C \)
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ANSWER :
C. \( B' \cap C' \)
7.
If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then \( A \cap (B \cap C) \) is equal to
A.
A
B.
B
C.
C
D.
{x : x is a multiple of 100}
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ANSWER :
C. C
8.
If \( \alpha \) and \( \beta \) are the roots of the equation \( 1 + x + x^{2} = 0 \), then the matrix product \( \begin{bmatrix} 1 & \beta \\ \alpha & \alpha \end{bmatrix} \begin{bmatrix} \alpha & \beta \\ 1 & \beta \end{bmatrix} \) is equal to
A.
\( \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \)
B.
\( \begin{bmatrix} -1 & -1 \\ -1 & 2 \end{bmatrix} \)
C.
\( \begin{bmatrix} 1 & -1 \\ -1 & 2 \end{bmatrix} \)
D.
\( \begin{bmatrix} -1 & 1 \\ -1 & 2 \end{bmatrix} \)
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ANSWER :
B. \( \begin{bmatrix} -1 & -1 \\ -1 & 2 \end{bmatrix} \)
9.
If |a| denotes the absolute value of an integer, then which of the following are correct?
1. \( |ab| = |a||b| \)
2. \( |a + b| \leq |a| + |b| \)
3. \( |a - b| \geq ||a| - |b|| \)
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
10.
How many different permutations can be made out of the letters of the word ‘PERMUTATION’?
A.
19958400
B.
19954800
C.
19952400
D.
39916800
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ANSWER :
A. 19958400
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