NDA & NA Exam (II)- 2016 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2016 - Mathematics

NDA & NA Exam (II)- 2016 - Mathematics Defence Questions

21.
For the next two (02) items that follow:
Let \( ax^{3} + bx^{2} + cx + d = \begin{vmatrix} x+1 & 2x & 3x \\ 2x+3 & x+1 & x \\ 2-x & 3x+4 & 5x-1 \end{vmatrix} \), then

What is the value of c?
A.
−1
B.
34
C.
35
D.
50
😑 View Answer Error
ANSWER :
C. 35
22.
What is the value of a + b + c + d?
A.
62
B.
63
C.
65
D.
68
😑 View Answer Error
ANSWER :
B. 63
23.
For the next two (02) items that follow:
The interior angles of a polygon of n sides are in AP. The smallest angle is \( 120^{\circ} \) and the common difference is \( 5^{\circ} \).

How many possible values can n have (for a convex polygon)?
A.
One
B.
Two
C.
Four
D.
Infinitely many
😑 View Answer Error
ANSWER :
A. One
24.
What is the largest interior angle of the polygon?
A.
\( 160^{\circ} \) only
B.
\( 195^{\circ} \) only
C.
Either \( 160^{\circ} \) or \( 195^{\circ} \)
D.
Neither \( 160^{\circ} \) nor \( 195^{\circ} \)
😑 View Answer Error
ANSWER :
A. \( 160^{\circ} \) only
25.
If \( m = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \) and \( n = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \), then what is the value of the determinant of \( m \cos\theta - n \sin\theta \)?
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
26.
If \( f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then which of the following are correct?
1. \( f(\theta) \times f(\phi) = f(\theta + \phi) \)
2. The value of the determinant of the matrix \( f(\theta) \times f(\phi) \) is 1.
3. The determinant of f(x) is an even function.
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
😑 View Answer Error
ANSWER :
D. 1, 2 and 3
27.
Which of the following are correct in respect of the system of equations \( x + y + z = 8 \), \( x - y + 2z = 6 \) and \( 3x - y + 5z = k \)?
1. They have no solution, if \( k = 15 \).
2. They have infinitely many solutions, if \( k = 20 \).
3. They have unique solution, if \( k = 25 \).
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
😑 View Answer Error
ANSWER :
A. 1 and 2 only
28.
If \( A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} \) and \( B = \begin{bmatrix} 2 & 3 \\ -1 & -2 \end{bmatrix} \), then which of the following is/are correct?
1. \( AB(A^{-1}B^{-1}) \) is a unit matrix.
2. \( (AB)^{-1} = A^{-1}B^{-1} \)
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 :
D. Neither 1 nor 2
29.
If \( x^{\ln\left(\frac{y}{z}\right)} \cdot y^{\ln(xz)^{2}} \cdot z^{\ln\left(\frac{x}{y}\right)} = y^{4 \ln y} \) for any \( x > 1 \), \( y > 1 \) and \( z > 1 \), then which of the following is correct?
A.
ln y is the GM of ln x, ln x, ln x and ln z
B.
ln y is the AM of ln x, ln x, ln x and ln z
C.
ln y is the HM of ln x, ln x, ln x and ln z
D.
ln y is the AM of ln x, ln x, ln z and ln z
😑 View Answer Error
ANSWER :
B. ln y is the AM of ln x, ln x, ln x and ln z
30.
If the number 235 in decimal system is converted into binary system, then what is the resulting number?
A.
\( (11110011)_{2} \)
B.
\( (11101011)_{2} \)
C.
\( (11110101)_{2} \)
D.
\( (11011011)_{2} \)
😑 View Answer Error
ANSWER :
B. \( (11101011)_{2} \)
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