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

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NDA & NA Exam (I)- 2016 - Mathematics

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

21.
What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates \( x = \frac{1}{2} \) and x = 1?
A.
\( \frac{5}{12} \) square unit
B.
\( \frac{5}{6} \) square unit
C.
\( \frac{7}{6} \) square units
D.
2 square units
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ANSWER :
A. \( \frac{5}{12} \) square unit
22.
What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and \( x = \frac{3}{2} \)?
A.
\( \frac{5}{12} \) square unit
B.
\( \frac{7}{12} \) square unit
C.
\( \frac{2}{3} \) square unit
D.
\( \frac{11}{12} \) square unit
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ANSWER :
D. \( \frac{11}{12} \) square unit
23.
For the next two (2) items that follow:
Given that \( a_{n} = \int_{0}^{\pi} \frac{\sin^{2}\{(n+1)x\}}{\sin 2x} dx \)

Consider the following statements:
1. The sequence \( \{a_{2n}\} \) is in AP with common difference zero.
2. The sequence \( \{a_{2n+1}\} \) is in AP with common difference zero.
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
24.
What is \( a_{n-1} - a_{n-4} \) equal to?
A.
−1
B.
0
C.
1
D.
2
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ANSWER :
B. 0
25.
For the next two (2) items that follow:
Consider the equation \( x + |y| = 2y \).

Which of the following statements are not correct?
1. y as a function of x is not defined for all real x.
2. y as a function of x is not continuous at x = 0.
3. y as a function of x is differentiable for all x.
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
26.
What is the derivative of y as a function of x with respect to x for x < 0?
A.
2
B.
1
C.
\( \frac{1}{2} \)
D.
\( \frac{1}{3} \)
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ANSWER :
D. \( \frac{1}{3} \)
27.
For the next two (2) items that follow:
Consider the lines y = 3x, y = 6x and y = 9.

What is the area of the triangle formed by these lines?
A.
\( \frac{27}{4} \) square units
B.
\( \frac{27}{2} \) square units
C.
\( \frac{19}{4} \) square units
D.
\( \frac{19}{2} \) square units
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ANSWER :
A. \( \frac{27}{4} \) square units
28.
The centroid of the triangle is at which one of the following points?
A.
(3, 6)
B.
\( \left(\frac{3}{2}, 6\right) \)
C.
(3, 3)
D.
\( \left(\frac{3}{2}, 9\right) \)
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ANSWER :
B. \( \left(\frac{3}{2}, 6\right) \)
29.
For the next two (2) items that follow:
Consider the function \( f(x) = (x-1)^{2}(x+1)(x-2)^{3} \).

What is the number of points of local minima of the function f(x)?
A.
None
B.
One
C.
Two
D.
Three
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ANSWER :
C. Two
30.
What is the number of points of local maxima of the function f(x)?
A.
None
B.
One
C.
Two
D.
Three
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ANSWER :
B. One
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