NDA & NA Exam (II)- 2015 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2015 - Mathematics

NDA & NA Exam (II)- 2015 - Mathematics Defence Questions

31.
For the next three (03) items that follow:
Consider the expansion of \( (1 + x)^{2n+1} \).

If the coefficients of \( x^{r} \) and \( x^{r+1} \) are equal in the expansion, then r is equal to
A.
n
B.
\( \frac{2n-1}{2} \)
C.
\( \frac{2n+1}{2} \)
D.
n + 1
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ANSWER :
A. n
32.
The average of the coefficients of the two middle terms in the expansion is
A.
\( {}^{2n+1}C_{n+2} \)
B.
\( {}^{2n+1}C_{n} \)
C.
\( {}^{2n+1}C_{n-1} \)
D.
\( {}^{2n}C_{n+1} \)
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ANSWER :
B. \( {}^{2n+1}C_{n} \)
33.
The sum of the coefficients of all the terms in the expansion is
A.
\( 2^{2n-1} \)
B.
\( 4^{n} - 1 \)
C.
\( 2 \times 4^{n} \)
D.
None of the above
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ANSWER :
C. \( 2 \times 4^{n} \)
34.
The \( n^{th} \) term of an A.P. is \( \frac{3+n}{4} \), then the sum of first 105 terms is
A.
270
B.
735
C.
1409
D.
1470
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ANSWER :
D. 1470
35.
A polygon has 44 diagonals. The number of its sides is
A.
11
B.
10
C.
8
D.
7
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ANSWER :
A. 11
36.
If p, q, r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in
A.
Arithmetic progression
B.
Geometric progression
C.
Harmonic progression
D.
None of the above
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ANSWER :
B. Geometric progression
37.
For the next two (02) items that follow:
Consider a triangle ABC satisfying \( 2a\sin^{2}\left(\frac{C}{2}\right) + 2c\sin^{2}\left(\frac{A}{2}\right) = 2a + 2c - 3b \).

The sides of the triangle are in
A.
G.P.
B.
A.P.
C.
H.P.
D.
Neither in G.P. nor in A.P. nor in H.P.
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ANSWER :
B. A.P.
38.
\( \sin A, \sin B, \sin C \) are in
A.
G.P.
B.
A.P.
C.
H.P.
D.
Neither in G.P. nor in A.P. nor in H.P.
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ANSWER :
B. A.P.
39.
If \( p = \tan\left(-\frac{11\pi}{6}\right) \), \( q = \tan\left(\frac{21\pi}{4}\right) \) and \( r = \cot\left(\frac{283\pi}{6}\right) \), then which of the following is/are correct?
1. The value of \( p \times r \) is 2.
2. p, q and r are in G.P.
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
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ANSWER :
B. 2 only
40.
The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is
A.
1140
B.
3420
C.
6840
D.
8000
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ANSWER :
D. 8000
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