Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Consider 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

308 Views

2.

The Number of complex numbers z such that |z– 1| = |z + 1| = |z – i| equals 

  • 0

  • 1

  • 2

  • 2

149 Views

3.

If α and β are the roots of the equation x2 – x +1 =0, then α2009 + β2009 =

  • -2

  • -1

  • 1

  • 1

157 Views

4.

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

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5.

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 

162 Views

6.

Let p(x) be a function defined on R such that limit as straight x space rightwards arrow infinity of space fraction numerator straight f left parenthesis 3 straight x right parenthesis over denominator straight f left parenthesis straight x right parenthesis end fraction = 1, p'(x)  p'(1-x),for all x∈[0,1] p(0) = 1 and p(1) = 41. Then integral subscript 0 superscript straight x space straight p space left parenthesis straight x right parenthesis space dx equals

  • √41

  • 21

  • 41

  • 41

224 Views

7.

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.

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8.

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


B.

56/33

Cos (α + β) = 4/5 
⇒  (α + β) ∈ 1st quadrant
and sin (α - β) = 5/13
⇒  (α - β) ∈ 1st quadrant
⇒ 2α =(α + β) +  (α - β)
space tan space 2 straight alpha space equals space fraction numerator tan space left parenthesis straight alpha space space plus space straight beta right parenthesis space plus space tan space left parenthesis straight alpha space minus straight beta right parenthesis over denominator 1 minus tan space left parenthesis straight alpha space plus straight beta right parenthesis space tan left parenthesis straight alpha minus straight beta right parenthesis end fraction
space equals space fraction numerator begin display style 3 over 4 end style plus begin display style 5 over 12 end style over denominator 1 minus begin display style 3 over 4 end style. begin display style 5 over 12 end style end fraction space equals space 56 over 33

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9.

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

202 Views

10.

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 straight r over straight R space equals space fraction numerator 1 over denominator square root of 2 end fraction

  • there is a regular polygon with r/R = 2/3

  • there is a regular polygon with r/R = 2/3

190 Views

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