NDA & NA Exam (II)- 2022 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2022 - Mathematics

NDA & NA Exam (II)- 2022 - Mathematics Defence Questions

21.
If \( d \) is the common difference of A, and \( D \) is the common difference of B, then which one of the following is always correct?
A.
\( D > d \)
B.
\( D < d \)
C.
\( 7D < 12d \)
D.
None of the above
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ANSWER :
A. \( D > d \)
22.
Directions (Qn. 22-24): Consider the following for the next three (03) items that follow:
Consider the binomial expansion of \( (p + qx)^{9} \).

What is the value of \( q \) if the coefficients of \( x^{3} \) and \( x^{6} \) are equal?
A.
\( p \)
B.
\( 9p \)
C.
\( \frac{p}{3} \)
D.
\( p^{2} \)
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ANSWER :
A. \( p \)
23.
What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of \( x \))?
A.
\( pq \)
B.
\( p/q \)
C.
\( 4p/5q \)
D.
\( 1/(pq) \)
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ANSWER :
B. \( p/q \)
24.
Under what condition the coefficients of \( x^{2} \) and \( x^{4} \) are equal?
A.
\( p : q = 7 : 2 \)
B.
\( p^{2} : q^{2} = 7 : 2 \)
C.
\( p : q = 2 : 7 \)
D.
\( p^{2} : q^{2} = 2 : 7 \)
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ANSWER :
B. \( p^{2} : q^{2} = 7 : 2 \)
25.
Directions (Qn. 25-27): Consider the following for the next three (03) items that follow:
Consider the word ‘QUESTION’.

How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed?
A.
36
B.
144
C.
576
D.
864
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ANSWER :
D. 864
26.
How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?
A.
288
B.
576
C.
1152
D.
2304
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ANSWER :
C. 1152
27.
How many 8-letter words with or without meaning, can be formed so that all consonants are together?
A.
5760
B.
2880
C.
1440
D.
720
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ANSWER :
B. 2880
28.
Directions (Qn. 28-30): Consider the following for the next three (03) items that follow:
Let \( \Delta \) be the determinant of a matrix \( A \), where \( A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \) and \( C_{11}, C_{12}, C_{13} \) be the cofactors of \( a_{11}, a_{12}, a_{13} \) respectively.

What is the value of \( a_{11}C_{11} + a_{12}C_{12} + a_{13}C_{13} \)?
A.
0
B.
1
C.
\( \Delta \)
D.
\( -\Delta \)
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ANSWER :
C. \( \Delta \)
29.
What is the value of \( a_{21}C_{11} + a_{22}C_{12} + a_{23}C_{13} \)?
A.
0
B.
1
C.
\( \Delta \)
D.
\( -\Delta \)
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ANSWER :
A. 0
30.
What is the value of
\( \begin{vmatrix} a_{21} & a_{31} & a_{11} \\ a_{23} & a_{33} & a_{13} \\ a_{22} & a_{32} & a_{12} \end{vmatrix} \)?
A.
0
B.
1
C.
\( \Delta \)
D.
\( -\Delta \)
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ANSWER :
D. \( -\Delta \)
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