# IIT JAM Mathematics Test Series 2023 : Real Analysis – Function and Their Properties

Practice IIT JAM Mathematics Test Series for Free only On www.examflame.com and take your preparation to the another level. In the Series of Tests for IIT JAM 2023 this is the test of topic Function and Their Properties of the Chapter Real Analysis. These Questions are prepared as per the Latest Syllabus of IIT JAM Mathematics 2023 . Practicing mock tests/Test series, you will get an idea about how and which type of Question will ask in the Examination. It also boost your confidence level. Also Solve IIT JAM Mathematics Previous Year Question Paper. And Don’t Forget to Shore with Your Friends.

## IIT JAM Mathematics Test Series 2023 : Real Analysis – Function and Their Properties

Q1. The number of distinct real roots of the equation x9+x7+x5+x3+x+1=0 is

(a) 1
(b) 3
(c) 5
(d) 9

Q2. Limit of the function (1-1/n2)n where n → ∞ is equal to

(a) 1
(b) e-1/2
(c) e-2
(d) e-1

Q3. Consider the functions f, g : Z→ Z defined by f(n) = 3n + 2 and g(n) = n2 – 5

(a) Neither f  and g is a one-to-one function
(b) Ths function f is one-to-one, but not g
(c) Ths function g is one-to-one, but not f
(d) Both f and g are one-to-one functions

Q4. Let a,b,c,d be rational number with ad – bc ≠ 0. Then the function f : R\Q → R defined by f(x) = (ax+b)/(cx+d)

(a) onto but not one-one
(b) one-one but not onto
(c) neither one-one nor onto
(d) both one-one and onto

Q5. Let f:(0,∞) → R be the function defined by f(x) = ex/xx. Then the limit of f(x) where x→∞

(a) does not exist
(b) exists and is 0
(c) exists and is 1
(d) exists and is e

Q6. The correct value of limit of the f(x) = x/√(1-cosx) where x→0

(a) does not exist
(b) is √2
(c) is  -√2
(d) is 1/√2

Q7. If X and Y are two non-empty finite sets and f:X→Y and g:Y→X are mappings such that g o f : X→X is a surjective (i.e, onto) map, then

(a) f must be one-to-one
(b) f must be onto
(c) g must be one-to-one
(d) X and Y must have the same number of elements

Q8. Let P(x) be a non-constant polynomial such that P(n) = P(-n) for all n∈N. Then P'(0)

(a) Equals 1
(b) Equals 0
(c) Equals -1
(d) Can not be determined from the given data

Q9. If f(x) = 1/(1-x) , g(x) = f[f(x)] and h(x) = f[g(x)], then what is f(x)g(x)h(x) equal to ?

(a) -1
(b) 0
(c) 1
(d) 2

Q10. What is the value of Limit of f(x) = (xy – yx)/(xx – yy) ?

(a) (1+lny)/(1-lny)
(b) (1-lny)/(1+lny)
(c) (-1+lny)/(1+lny)
(d) (-1-lny)/(1-lny)

Q11. If D is the set of all real x such that f(x) = 1 – e(1-x)/x is positive, then what is D equal to ?

(a) (-∞,0) ∪ (1,∞)
(b) (-∞,0) ∪ [1,∞)
(c) (1,∞)
(d) (-∞,1)

Q12. Assertion (A) : ex cannot be expressed as sum of even and odd functions.
Reason (R) : ex is neither even nor odd function

(a) Both A and R are individually true but R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

Q13. Let f:R→R define g:R→R by g(x) = f(x)[f(x) + f(-x)]. Then

(a) g is even for all f
(b) f is odd for all f
(c) g is even if f is even
(d) g is even if f is odd

Q14. The limit of function  f(x) = (4x + 5x)1/x where x → ∞ is equal to

(a) 4
(b) 5
(c) e
(d) 5e

Q15. Which one of the following function is not well defined ?

(a) √(1 + sinx)
(b) √(5sec2x – 4)
(c) √(3 – cos2x)
(d) √(x4 + x2 + 1/100)

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