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ECAT Mathematics Functions and Limits Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Functions and Limits

ECAT Math Functions and Limits Chapter Online Test

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

Page 1 of 2

1. Every elements of A x B is in form of

Ordered pair

Ordered triples

Singles

Subset

2. If y is expressed in terms of a variable x as y = f(x), then y is called

Explicit function

Implicit function

Linear function

Identity function

3. The set of 1st elements of all ordered pairs of a binary relation is called its

Range

Domain

Co – domain

None of these

4. If f : X → Y is a function, then the elements of X are called

Pre –images

Images

Constants

Ranges

5. If y = eˣ, then f⁻¹ (x)

Lnx

eˣ

Logx

1/eˣ

6. If y is an image of x under the function f, we write it as

X = f(x)

Y = f(x)

Y = x

7. The domain of f(x) = 2 + √x – 1 ∀ x ϵ R is

[-1, ∞)

[1, ∞)

[2, ∞)

None of these

8. The function f(x) = ax² + bx + c has maximum value if

a > 0

a < 0

a > 1

a > 2

9. If graph of a function f has hole, jump or break then f is

Continuous function

Discontinuous

Constant

None of these

10. If : x – -x² is a function then,

-4

-2

11. If f : x → (-x²) is a function, then f(2) =

-4

-2

12. The function f (x) = x²–1/x+1 is undefined at

x = 0

x = 1

x = – 1

None of these

13. If f : x → x + 3 is a function, then f(3) =

14. Polynomial function will be linear function if degree is

15. If f : x – 2x²+5x–1/x+3 is a function, then f(0) =

– 1/3

– 1/4

– 1/5

16. For y = tanx, Range =

17. If f : x → tanx is a function, then f (π) =

-1

– ½

18. If f : x → x + 1 is a function, then f(t² – 1) =

t + 1

t² + 1

t²

19.

20. f(x) = x² – 4x + 1 is

Trigonometric function

Logarithmic function

Exponential function

Algebraic function

21.

22. f(x) = log x is

Trigonometric function

Logarithmic function

Exponential function

Algebraic function

23.

24. The graph of a linear function is

Parabola

Ellipse

Hyperbola

Straight line

25. Let variable t take in succession the value 4, 4 1/2, 4 2/3, 4 ¾, …………. then t →

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26. The linear function f(x) = ax + b is an identity function if

a = 0, b = 1

a = 1, b = 0

a = 1, b = 1

a = 0, b = 0

27.

28. The function f : x → 1 is

Constant function

Cubic function

Quadratic function

Identity function

29.

30.

31. If A = {1, 2, 3, ………. 100} how many distinct relations can be established

2¹⁰⁰

2ⁿ

2¹⁰⁰ⁿ

32. The range of f(x) = [x] is

33.

34.

35. sinh⁻¹ x =

In(x + √x²+1)

In(x + √x² – 1)

½ In(1+x/1–x)

½ In(x+1/x–1)

36. If f(x) = 3x+1/2x–1 then f[f⁻¹ (3)]= ?

3/2

4/3

None of these

37. coth⁻¹ x =

In(x + √x²+1)

In(x + √x² – 1)

½ In(1+x/1–x)

½ In(x+1/x–1)

38. The domain of function h(x) = √x²–4 is

Real

R – {2}

R – {2, 2}

None of these

39. cosech⁻¹

In(1/x + √1+x²/|x|)

In(1/x + √1–x²/|x|)

½ In(1+x/1–x)

In(x + √x²+1)

40. If f (x) = 2x + 3, g (x) = x² then g of (x) = ?

2x² – 1

4x² + 4x

4x + 3

(2x + 3)²

41. The term function was introduced by a mathematician

German

French

Swiss

English

42. If f(x) = x³ + 2x² – 1 = then f(1+h)–f(1)/h =

h² – 5h + 7

h² + 5h + 7

h² + 5h – 7

43. If A is the area of the circle and C is its circumference C, then A =

1/8π C²

1/4π C²

1/2π C²

π C²

44. The volume of a cube of side length 2 is

2 cubic units

4 cubic units

8 cubic units

16 cubic units

45. The area of a square of side length 2 is

2 square units

4 square units

8 square units

16 square units

46. Domain of √4x–x² =

R – [0, 4]

R – (0, 4)

(0, 4)

[0, 4]

47. X = acos θ, y = btan θ are parametric equations of

Circle

Parabola

Ellipse

Hyperbola

48. The period of the function f(x) = sin √x is

2π

π/2

None of these

49. The period sin² θ is

π²

2π

π/2

50. The period of the function f(x) = 2sin x = 3 Cos 2x is

2π

π/2

None of these

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Functions and Limits Online Test

ECAT Math Functions and Limits

ECAT Math Functions and Limits Chapter Online Test

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ECAT Math Functions and Limits

ECAT Math Functions and Limits Chapter Online Test

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