NDA & NA Exam (II)- 2024 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2024 - Mathematics

NDA & NA Exam (II)- 2024 - Mathematics Defence Questions

1.
Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct?
(I) (ZY)X is defined and is a square matrix of order 3.
(II) Y(XZ) is defined and is a square matrix of order 2.
(III) X(YZ) is not defined.
Select the correct answer using the code given below.
A.
I and II only
B.
II and III only
C.
I and III only
D.
I, II and III
😑 View Answer Error
ANSWER :
D. I, II and III
2.
Consider the following statements:
(I) The set of all irrational numbers between 12 and 15 is an infinite set.
(II) The set of all odd integers less than 1000 is a finite set.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
A. I only
3.
How many 4-digit numbers are there having all digits as odd?
A.
625
B.
400
C.
196
D.
120
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ANSWER :
A. 625
4.
If \( \omega \neq 1 \) is a cube root of unity, then what is \( (1 + \omega - \omega^{2})^{100} + (1 - \omega + \omega^{2})^{100} \) equal to?
A.
\( 2^{100}\omega^{2} \)
B.
\( 2^{100}\omega \)
C.
\( 2^{100} \)
D.
\( -2^{100} \)
😑 View Answer Error
ANSWER :
D. \( -2^{100} \)
5.
Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?
A.
Both A and B are null matrices.
B.
Either A or B is a null matrix.
C.
B is a null matrix if A is a non-singular matrix.
D.
Both A and B are singular matrices.
😑 View Answer Error
ANSWER :
C. B is a null matrix if A is a non-singular matrix.
6.
In the expansion of \( (1 + x)^{p}(1 + x)^{q} \), if the coefficient of \( x^{3} \) is 35, then what is the value of (p + q)?
A.
5
B.
6
C.
7
D.
8
😑 View Answer Error
ANSWER :
C. 7
7.
If p times the \( p^{th} \) term of an AP is equal to q times the \( q^{th} \) term \( (p \neq q) \), then what is the \( (p + q)^{th} \) term equal to?
A.
0
B.
p + q
C.
pq
D.
pq(p + q)
😑 View Answer Error
ANSWER :
A. 0
8.
Let \( p = \ln(x) \), \( q = \ln(x^{3}) \) and \( r = \ln(x^{5}) \), where x > 1. Which of the following statements is/are correct?
(I) p, q and r are in AP.
(II) p, q and r can never be in GP.
Select the correct answer using the code given below.
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
9.
If \( Z = \frac{1}{3}\begin{vmatrix} i & 2i & 1 \\ 2i & 3i & 2 \\ 3 & 1 & 3 \end{vmatrix} = x + iy \); \( i = \sqrt{-1} \), then what is modulus of Z equal to?
A.
1
B.
\( \sqrt{2} \)
C.
2
D.
3
😑 View Answer Error
ANSWER :
B. \( \sqrt{2} \)
10.
What is the value of the sum \( \sum_{n=1}^{20} (i^{n-1} + i^{n} + i^{n+1}) \), where \( i = \sqrt{-1} \)?
A.
\( -2i \)
B.
0
C.
1
D.
\( 2i \)
😑 View Answer Error
ANSWER :
B. 0
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