ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 17 (Functions and Limits)

The period of the function f(x) = sin⁴x + cos⁴x is

• π A
• π/2 B
• 2π C
• None of these D

• 0 A
• 1 B
• 
  C
• none of these D

The range of y=x2 + 1 is the set of non-negative real numbers except

• 0≤ y < 1 A
• 0 < y < 1 B
• 0≤ y≤ 1 C
• 0 < y≤1 D

If the function y=2x -3, what is the preimage of 11?

• 11 A
• 7 B
• 5 C
• 2 D

• 0 A
• -2 B
• 1 C
• 4 D

f(x) = 3x⁴ -2x² + 7 is:

• an even function A
• an odd function B
• an even and implicit function C
• neither even nor a odd D

The area of circle of unit radius =

• 0 A
• 1 B
• 4 C
• π D

Which of the following function form 1 to itself are bi-jective

• F(x) = x + 3 A
• F(x) = x⁵ B
• F(x) = 3x + 2 C
• F(x) = x²+ x D

• 
  A
• 
  B
• 
  C
• 
  D

The value of x which is unchanged by the mapping in the function defined by f ; x⟶ x² + 5x -5 for x> 0 is

• 1 A
• 5 B
• -5 C
• -1 D

• 1/8 A
• 1/2 B
• 1/4 C
• 1/6 D

If x is an image of y under the function f. This can be written as

• y = f(x) A
• f(x) = 0 B
• x = f(y) C
• f(y) =0 D

f(x) = sin x + cos²x is

• trigonometric function A
• algebraic function B
• exponential function C
• logarithmic function D

If a tangent line touches the function y = f (x) in more than one point then y = f (x) is

• Periodic A
• Surjective B
• Bijective C
• Injective D

• 0 A
• 1 B
• -1 C
• none of these D

• 2 A
• 
  B
• -2 C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

The domain of f(x) = log x is

• [0,∞] A
• (0,∞) B
• [0,∞[ C
• [∞,∞] D

• -2 A
• -1 B
• 1 C
• 2 D

• quadratic function A
• constant function B
• trigonometric function C
• linear function D

x = secθ,y = tanθ are the parametric equations of

• Circle A
• Hyperbola B
• Ellipse C
• parabola D

• sin h x A
• cos h x B
• sec h x C
• cosec h x D

If y=f(x) is a function then x is called

• dependent variable A
• independent variable B
• constant C
• none of these D

For f(x) = x² + px +1, if f(3) = 3 then P =

• 3/7 A
• -2/5 B
• -7/5 C
• -7/3 D

A function from X to X is denoted as

• 
  A
• f : X to Y B
• 
  C
• f : Y to Y D

• f(x) = x² A
• f(x²) = x B
• f(x) = x C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 
  D

• range of f A
• domain of f B
• both (a) and (b) C
• none of these D

Which is not included in the domain of cos^-1x

• 0 A
• 1 B
• -1 C
• 2 D