IIT JAM Mathematics Practice Test- 18 - Mathematics MCQ

Consider the set E = , then

For what value of x, the infinite series,  converges?

Consider two  sets,  then

The Series  is,

{a_n} is a sequence of real no.'s satisfying  then

If  then  is,

Let 
Then which of the following is true?

The radius of convergence of the power series ∑ a_nsⁿ where  is 

If f(x) = 3x - 2 and (gof)^-1 (x) = x - 2, then function g(x) is

Let f : R → R be a differentiable function such that f(e) =  e and  for all x ∈ R and y ∈ R. Let g(x) = logx f(x) for all x > 0, then g'(e) is equal to 

Which of the following is convergent series?

The internal of convergence of the power series,

Let F : R → R be a differentiable function such that  then

Let f : (-1, 1) →  be defined as f(x) =  for x ≠ 0 and f(0) = 2.
If f(x) =  is the Taylor's expressing of f for all x in (-1,1) then  is,

The series  converges if,

If f(x) = (x²-1) |x²-3x+2| + cos (|x|), then set of points of non-differentiability is 

A function f : R → R, defined by f(x) =  
If T = {f(x) ; x ∈ R}, then the inverse function 

For which region, the series  is convergent?

If f(x) = (x²-4) | x³ -6x² + 11x - 6| +  then the set of point at which the function f(x) is not differentiable is,

Let A be a proper subset of R, given as  Then which of the following is true for A?

The Seqⁿ {x_n}, where x_n =  converges to,

Let {a_n} be a sequence of real number's defined as  If{a_n} is convergent then it converge to 

The series  is :

Let {a_n} be a sequence of real numbers with a₁ > 0, a₂ > 0 and  If a₁ = 1 and a₂ = 2 then the sequence {a_n} converge to?

Sum of the series  is

Let {a_n} be an increasing seqⁿ of positive real numbers such that the series  is divergent. Let ... then  is equal to