NDA & NA Exam (I)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2014 - Mathematics

NDA & NA Exam (I)- 2014 - Mathematics Defence Questions

1.
Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct?
A.
The relation is an equivalence relation on X.
B.
The relation is symmetric but neither reflexive nor transitive.
C.
The relation is reflexive but neither symmetric nor transitive.
D.
None of the above
😑 View Answer Error
ANSWER :
B. The relation is symmetric but neither reflexive nor transitive.
2.
Consider the following relations from A to B where \( A = \{u, v, w, x, y, z\} \) and \( B = \{p, q, r, s\} \).
1. \( \{(u,p), (v,p), (w,p), (x,q), (y,q), (z,q)\} \)
2. \( \{(u,p), (v,q), (w,r), (z,s)\} \)
3. \( \{(u,s), (v,r), (w,q), (u,p), (v,q), (z,q)\} \)
4. \( \{(u,q), (v,p), (w,s), (x,r), (y,q), (z,s)\} \)
Which of the above relations are not functions?
A.
1 and 2
B.
1 and 4
C.
2 and 3
D.
3 and 4
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ANSWER :
C. 2 and 3
3.
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^{2} + bx + c = 0 \), where \( a \neq 0 \), then \( (a\alpha + b)(a\beta + b) \) is equal to
A.
ab
B.
bc
C.
ca
D.
abc
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ANSWER :
C. ca
4.
Let S denote set of all integers. Define a relation R on S as ‘aRb if \( ab \geq 0 \) where \( a, b \in S \)’. Then R is
A.
reflexive but neither symmetric nor transitive relation
B.
reflexive, symmetric but not transitive relation
C.
an equivalence relation
D.
symmetric but neither reflexive nor transitive relation
😑 View Answer Error
ANSWER :
B. reflexive, symmetric but not transitive relation
5.
The roots of the equation \( 2a^{2}x^{2} - 2abx + b^{2} = 0 \) when \( a < 0 \) and \( b > 0 \) are
A.
sometimes complex
B.
always irrational
C.
always complex
D.
always real
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ANSWER :
C. always complex
6.
What is the sum of the two numbers \( (11110)_{2} \) and \( (1010)_{2} \)?
A.
\( (101000)_{2} \)
B.
\( (110000)_{2} \)
C.
\( (100100)_{2} \)
D.
\( (101100)_{2} \)
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ANSWER :
A. \( (101000)_{2} \)
7.
Let N denote the set of all non-negative integers and Z denote the set of all integers. The function \( f: Z \rightarrow N \) given by \( f(x) = |x| \) is
A.
one-one but not onto
B.
onto but not one-one
C.
both one-one and onto
D.
neither one-one nor onto
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ANSWER :
B. onto but not one-one
8.
If P and Q are two complex numbers, then the modulus of the quotient of P and Q is
A.
greater than the quotient of their moduli
B.
less than the quotient of their moduli
C.
less than or equal to the quotient of their moduli
D.
equal to the quotient of their moduli
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ANSWER :
D. equal to the quotient of their moduli
9.
Let \( z = x + iy \) where x, y are real variables and \( i = \sqrt{-1} \). If \( |2z - 1| = |z - 2| \), then the point z describes
A.
a circle
B.
an ellipse
C.
a hyperbola
D.
a parabola
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ANSWER :
A. a circle
10.
The sum of an infinite GP is x and the common ratio r is such that \( |r| < 1 \). If the first term of the GP is 2, then which one of the following is correct?
A.
\( -1 < x < 1 \)
B.
\( -\infty < x < 1 \)
C.
\( 1 < x < \infty \)
D.
None of the above
😑 View Answer Error
ANSWER :
C. \( 1 < x < \infty \)
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