Page 8 - ECAT Past Paper 2006

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MATHEMATICS

Q.31 If x,y ∈R , then x+iy is purely imaginary if:
A) x≠0, y=0 B) x=0 , y≠0 (Correct)
C) x=0 , y=0 D) x≠0, y≠0
Explanation:-
Let z=a+bi
1) Purely Imaginary , x=0 , y≠0
2) Purely Real, ) x≠0, y=0
Q.32 A-B is a subset of ______ if B⊆A
A) ∅ B) B
C) AUB (Correct) D) A∩B
Explanation:-
Using the Venn Diagram, AUB satisfies..

√
Q.33 If x= 2 + √2 + √2 + ⋯ . . +∞ then x=?
A) 0 B) 2 (Correct)
C) 1 D) None of these
Explanation:-
Using the trick:-
xn=k(k+1)
In this case 1*2=k(k+1)
So x=2
1 +
Q.34 |1 + |=?
1 +
A) a+b+c B) -1
C) 0 (Correct) D) ab+bc+ca
Explanation:-
1 +
=|1 + |
1 +
:.C2+C1
1 + + +
=|1 + + + |
1 + + +
:.Taking Common from C2
1 1 +
= + + |1 1 + |
1 1 +
:.As Two columns are same so that using the property of determinant will be zero.
+
Q.35 Q = + Then find value of B?

+ − +
A) 2/3 B) ¼
C) 1/3 (Correct) D) ½
Explanation:-