Multiple Choice QuestionsConsider the following relations:
R = {(x, y)| x, y are real numbers and x = wy for some rational number w}; S = {(m/p, p/q)| m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then
R is an equivalence relation but S is not an equivalence relation
neither R nor S is an equivalence relation
S is an equivalence relation but R is not an equivalence relation
S is an equivalence relation but R is not an equivalence relation
If α and β are the roots of the equation x2 – x +1 =0, then α2009 + β2009 =
-2
-1
1
1
C.
1
The quadratic equation ax2 + bx +c = 0 has roots α and β,
Then α + β = - b/a, α β = c/a
Also, if ax2+ bx +c = 0
Then, 
We know that 1,ω, ω2 are cube roots of unity.
1+ω + ω2 = 0 (ω2 = 1)
and 
Since α and β are roots of the equations
x2-x+1 = 0
⇒ α + β = 1 , α β =1
x = ω2, or -ω
α = -ω2, then β =-ω
or α = -ω, then β =-ω2, (where ω3 = 1)
Hence, α2009 + β2009 =(-ω)2009 + (-ω2)2009
= - [(ω3)669. ω2 + (ω3)1337.ω]
= - [ω2 + ω]
= -(-1) = 1
A person is to count 4500 currency notes. Let a denote the number of notes he counts in the nth minute. If a1 = a2 = ... = a10 = 150 and a10, a11, ...are in an AP with common difference -2, then the time taken by him to count all notes is
24 min
34 min
125 min
125 min
The equation of the tangent to the curve y = x +4/x2, that is parallel to the x-axis, is
y= 0
y= 1
y= 2
y= 2
Let p(x) be a function defined on R such that 
= 1, p'(x) p'(1-x),for all x∈[0,1] p(0) = 1 and p(1) = 41. Then 
equals
√41
21
41
41
Let S be a non empty subset of R. Consider the
following statement:
P: There is a rational number x∈S such that x > 0.
Which of the following statements is the negation of the statement P?
There is a rational number x∈S such that x ≤ 0.
There is no rational number x∈ S such that x≤0.
Every rational number x∈S satisfies x ≤ 0.
Every rational number x∈S satisfies x ≤ 0.
Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0 ≤α,β ≤ π/4. Then tan 2α is equal to
25/16
56/33
19/12
19/12
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
5/2
11/2
6
6
For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is
there is a regular polygon with r/R = 1/2
there is a regular polygon with 
there is a regular polygon with r/R = 2/3
there is a regular polygon with r/R = 2/3
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