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

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2016 - Mathematics

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

31.
Let f(x) and g(x) be twice differentiable functions on [0, 2] satisfying \( f''(x) = g''(x) \), \( f'(1) = 4 \), \( g'(1) = 6 \), \( f(2) = 3 \) and \( g(2) = 9 \). Then what is \( f(x) - g(x) \) at x = 4 equal to?
A.
−10
B.
−6
C.
−4
D.
2
😑 View Answer Error
ANSWER :
A. −10
32.
For the next two (2) items that follow:
Consider the curves \( y = |x - 1| \) and \( |x| = 2 \).

What is/are the point(s) of intersection of the curves?
A.
(−2, 3) only
B.
(2, 1) only
C.
(−2, 3) and (2, 1)
D.
Neither (−2, 3) nor (2, 1)
😑 View Answer Error
ANSWER :
C. (−2, 3) and (2, 1)
33.
What is the area of the region bounded by the curves and x-axis?
A.
3 square units
B.
4 square units
C.
5 square units
D.
6 square units
😑 View Answer Error
ANSWER :
C. 5 square units
34.
For the next two (2) items that follow:
Consider the function \( f(x) = \begin{vmatrix} x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^{2} & p^{3} \end{vmatrix} \), where p is a constant.

What is the value of \( f'(0) \)?
A.
\( p^{3} \)
B.
\( 3p^{3} \)
C.
\( 6p^{3} \)
D.
\( -6p^{3} \)
😑 View Answer Error
ANSWER :
D. \( -6p^{3} \)
35.
What is the value of p for which \( f''(0) = 0 \)?
A.
\( -\frac{1}{6} \) or 0
B.
−1 or 0
C.
\( -\frac{1}{6} \) or 1
D.
−1 or 1
😑 View Answer Error
ANSWER :
A. \( -\frac{1}{6} \) or 0
36.
For the next two (2) items that follow:
Consider a triangle ABC in which \( \cos A + \cos B + \cos C = \sqrt{3} \sin\frac{\pi}{3} \).

What is the value of \( \sin\frac{A}{2} \sin\frac{B}{2} \sin\frac{C}{2} \)?
A.
\( \frac{1}{2} \)
B.
\( \frac{1}{4} \)
C.
\( \frac{1}{8} \)
D.
\( \frac{1}{16} \)
😑 View Answer Error
ANSWER :
C. \( \frac{1}{8} \)
37.
What is the value of \( \cos\left(\frac{A+B}{2}\right) \cos\left(\frac{B+C}{2}\right) \cos\left(\frac{C+A}{2}\right) \)?
A.
\( \frac{1}{4} \)
B.
\( \frac{1}{2} \)
C.
\( \frac{1}{16} \)
D.
None of the above
😑 View Answer Error
ANSWER :
D. None of the above
38.
For the next two (2) items that follow:
Given that \( \tan\alpha \) and \( \tan\beta \) are the roots of the equation \( x^{2} + bx + c = 0 \) with \( b \neq 0 \).

What is \( \tan(\alpha + \beta) \) equal to?
A.
\( b(c-1) \)
B.
\( c(b-1) \)
C.
\( c(b-1)^{-1} \)
D.
\( b(c-1)^{-1} \)
😑 View Answer Error
ANSWER :
D. \( b(c-1)^{-1} \)
39.
What is \( \sin(\alpha + \beta) \sec\alpha \sec\beta \) equal to?
A.
b
B.
−b
C.
c
D.
−c
😑 View Answer Error
ANSWER :
B. −b
40.
For the next two (2) items that follow:
Consider the two circles \( (x-1)^{2} + (y-3)^{2} = r^{2} \) and \( x^{2} + y^{2} - 8x + 2y + 8 = 0 \).

What is the distance between the centres of the two circles?
A.
5 units
B.
6 units
C.
8 units
D.
10 units
😑 View Answer Error
ANSWER :
A. 5 units
Prev Next page