NDA & NA Exam (II)- 2019 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2019 - Mathematics

NDA & NA Exam (II)- 2019 - Mathematics Defence Questions

31.
Let a, b, c be in AP and \( k \neq 0 \) be a real number. Which of the following are correct?
1. ka, kb, kc are in AP
2. \( k - a, k - b, k - c \) are in AP
3. \( \frac{a}{k}, \frac{b}{k}, \frac{c}{k} \) are in AP
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
32.
How many two-digit numbers are divisible by 4?
A.
21
B.
22
C.
24
D.
25
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ANSWER :
B. 22
33.
Let \( S_{n} \) be the sum of the first n terms of an AP. If \( S_{2n} = 3n + 14n^{2} \), then what is the common difference?
A.
5
B.
6
C.
7
D.
9
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ANSWER :
C. 7
34.
If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?
A.
\( q^{2} = pr \)
B.
\( r^{2} = pq \)
C.
\( pqr = 1 \)
D.
\( 2q = p + r \)
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ANSWER :
A. \( q^{2} = pr \)
35.
What is the solution of \( x \leq 4, y \geq 0 \) and \( x \geq -4, y \leq 0 \)?
A.
\( x \geq -4, y \leq 0 \)
B.
\( x \leq 4, y \geq 0 \)
C.
\( -4 \leq x \leq 4, y = 0 \)
D.
\( -4 \leq x \leq 0, y = 0 \)
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ANSWER :
C. \( -4 \leq x \leq 4, y = 0 \)
36.
If \( x^{\log_{7} x} > 7 \) where \( x > 0 \), then which one of the following is correct?
A.
\( x \in (0, \infty) \)
B.
\( x \in \left(\frac{1}{7}, 7\right) \)
C.
\( x \in \left(0, \frac{1}{7}\right) \cup (7, \infty) \)
D.
\( x \in \left(\frac{1}{7}, \infty\right) \)
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ANSWER :
C. \( x \in \left(0, \frac{1}{7}\right) \cup (7, \infty) \)
37.
How many real roots does the equation \( x^{2} + 3|x| + 2 = 0 \) have?
A.
Zero
B.
One
C.
Two
D.
Four
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ANSWER :
A. Zero
38.
Consider the following statements in respect of the quadratic equation \( 4(x - p)(x - q) - r^{2} = 0 \), where p, q and r are real numbers:
1. The roots are real.
2. The roots are equal if \( p = q \) and \( r = 0 \).
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
39.
Let \( S = \{2, 4, 6, 8, \ldots, 20\} \). What is the maximum number of subsets does S have?
A.
10
B.
20
C.
512
D.
1024
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ANSWER :
D. 1024
40.
A binary number is represented by \( (cdccddcccddd)_{2} \), where \( c > d \). What is its decimal equivalent?
A.
1848
B.
2048
C.
2842
D.
2872
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ANSWER :
D. 2872
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