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If X = {4n - 3n-1 : n ε N} and Y = {9(n-1):n εN}; where N is the set of natural numbers,then X U Y is equal to
N
Y-X
X
Y
D.
Y
We have X = {4n - 3n-1 : n ε N}
X = {0,9,54,243,.....} [put n = 1,2,3....]
Y = {9(n-1):n ε N}
Y = {0,9,18,27,......}[Put n = 1,2,3....]
It is clear that
X ⊂ Y
Therefore, X U Y = Y
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If z is a complex number such that |z|≥2, then the minimum value of 
is equal to 5/2
lies in the interval (1,2)
is strictly greater than 5/2
is strictly greater than 3/2 but less than 5/2
B.
lies in the interval (1,2)
|z| ≥2 is the region on or outside circle whose centre is (0,0) and the radius is 2.
Minimum 
is distance of z, which lies on circle |z| = 2 from 
therefore, minimum 
= Distance of 
from (-2,0)
Hence, minimum value of 
lies in the interval (1,2)
If a ε R and the equation - 3(x-[x]2 + 2(x-[x] +a2 = 0(where,[x] denotes the greatest integer ≤ x) has no integral solution, then all possible value of lie in the interval
(-1,0) ∪ (0,1)
(1,2)
(-2,-1)
(-∞,-2) ∪ (2, ∞)
A.
(-1,0) ∪ (0,1)
Given a ε R and equation is
-3{x-[x]}2 + 2{x-[x] +a2 = 0
Let t = x - [x], then equation is
-3t2 +2t+ a2 = 0
⇒ 
∵ t = x - [x] = {X}
∴ 0≤ t≤1
Taking positive sign, we get
⇒ 
⇒ 1+3a2 <4
⇒ a2-1 <0
⇒(a+1)(a-1) <0
a ε (-1,1)
For no integral solution of a, we consider the interval (-1,0) ∪ (0,1)
Let α and β be the roots of equation px2 +qx r =0 p ≠0. If p,q and r are in AP and 
= 4, then the value of |α- β| is
D.
If the coefficients of x3 and x4 in the expansion of (1+ax+bx2)(1-2x)18 in powers of x are both zero, then (a,b) is equal to
D.
In expansion of (1+ax+bx2)(1-2x)18,
Coefficient of x3 = Coefficient of x3 in (1-2x)18
+Coefficient of x2 in a(1-2x)18
+Coefficient of x in b(1-2x)18
= - 
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Mock Test Series
