If the minimum and the maximum values of the functionf :&thi

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 Multiple Choice QuestionsMultiple Choice Questions

331.

If f : Z  Z is defined byf(x) = x2, if x is even0, if x is odd, then f is

  • Onto but not one-to-one

  • One-to-one but not onto

  • One-to-one and onto

  • Neither one-to-one nor onto


332.

1 + i1 - im2 = 1 + i1 - in3 = 1. m, n  N find HCF of m, n for least m & n

  • 4

  • 3

  • 6

  • 9


333.

limx01 - x + x1 + x - λ = L finite where * denotes the greatest integer function then find L

  • 0

  • 12

  • 1

  • 2


334.

The preposition p ~p  ~ q is equivalent to

  • q

  • ~ p  q

  • p  ~ q

  • ~ p  ~ q


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335.

Ler R1 and R2 be two relations defined as follows :

R= {(a, b)  R: a2 + b2  Q} and R2 = {(a, b) ∈ R2: a2 + b2 ∈ Q}, where Q is the set of all rational numbers, then

  • R1 is transitive but R2 is not transitive.

  • R2 is transitive but R1 is not transitive.

  • Neither R1 nor R2 is transitive

  • R1 and R2 are both transitive.


336.

Suppose f(x) is a polynomial of degree four, having critical points at – 1, 0, 1. If T = {x  R |f(x) = f(0)}, then the sum of squares of all the elements of T is :

  • 4

  • 6

  • 2

  • 8


337.

The function fx = π4 + tan-1x, x  112x - 1, x > 1  is :

  • continuous on R  {  1} and differentiable on R     1,  1

  • both continuous and differentiable on R   1

  • both continuous and differentiable on R  1

  • continuous on R  1 and differentiable on R   1, 1


338.

If 32sin2α - 1, 14 and 34 - 2sin2α are the first three terms of an A.P. for some α, then the sixth term of this A.P. is 

  • 81

  • 65

  • 66

  • 78


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339.

If the minimum and the maximum values of the function

f :π4, π2  R, defined by fθ =  - sin2θ - 1 - sin2θ1cos2θ - 1 - cos2θ11210 - 2

are m and M respectively, then the ordered pair (m, M) = : 

  • ( - 4, 4)

  • 0, 22

  • ( - 4, 0)

  • (0, 4)


C.

( - 4, 0)

C2  C2 - C1fθ =  - sin2θ - 11 - cos2θ - 1112 - 2 - 2= 4cos2θ - sin2θ= 4cos2θ, θ  π4, π2fθmax = M = 0fθmin = m = - 4


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340.

If x = 1 is a critical point of the function f(x) = (3x2 + ax –2 – a) ex, then

  • x = 1 and x = - 23 are local minima of f

  • x = 1 is a local maxima and x =  - 23is a local minima of f.

  •  x = 1 is a local minima and x = - 23 is a local maxima of f.

  • x = 1 and x =  - 23are local maxima of f.


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