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

______________ invented a symbolic way to write the statement "y is a function of x" as y= f(x)

• Leibniz A
• Newton B
• Euler C
• None of these D

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
• -1 D

• 2 A
• 4 B
• 8 C
• 12 D

A function F(x) is called even if

• F(x) = F (-x) A
• F(x) = F(-x) B
• F(x) = -F(x) C
• 2F(x) = 0 D

A rule that assigns to each elements x in X a unique element y in Y is called a ____________

• domain A
• range B
• function C
• none of these D

If the domain of the function f: x⟶ 2x³+ 1 is {-1,2,3}, the range of the function is

• {3,2,5} A
• {1,3,9} B
• {-1,-2,-3} C
• {3,9,19} 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

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

• 3/7 A
• -2/5 B
• -7/5 C
• -7/3 D

• sin h x A
• cos h x B
• tan h x C
• cot h x D

Point (2,0) lies on trigonometric function f(x)=______;

• sinx A
• cosx B
• tanx C
• secx D

If f(x) = x³- 2x²+ 4x -1 then f(0) is

• 0 A
• 1 B
• -1 C
• none of these D

tan h x = _________

• 
  A
• 
  B
• 
  C
• 
  D

A function of the form p(x)/Q(x) is called:

• Rational function A
• Logarithmic function B
• Exponential function C
• Hyperbolic function D

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

• 0 A
• 1 B
• -1 C
• 2 D

The curve f(x,y) = 0 has a central symmetry if

• f(-x,-y)=f(x,y) A
• f(x,-y)=f(x,y) B
• f(-x,y)=f(x,y) C
• f(-x,-y)≠f(x,y) D

If f(x) = x + 1 then f(z²-1) is

• z² A
• z²+ 2 B
• z²- 2 C
• none of these D

If f(x) = x²-x then f(1) is

• 0 A
• 1 B
• 2 C
• 3 D

• 0 A
• -2 B
• 1 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

The function discontinuous at x = 0 is (1) tan x (II) cot x (III) sec x (iv)cosec x)

• I & III A
• I & IV B
• II & IV C
• II & III D

• One-one but not onto A
• One-one and onto B
• Onto but not one-one C
• Neither one-one nor onto D

• -2 A
• -1 B
• 1 C
• 2 D

• 0 A
• 1 B
• -1 C
• none of these D

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

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

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

If f(x) = (-x)²then f(-2) is

• 0 A
• 2 B
• -4 C
• 4 D

• 0 A
• 1 B
• 8 C
• ∞ D

• 2 A
• 6 B
• 
  C
• 
  D

f(x) = ax + b will be a constant function if

• a = 1 , b = 1 A
• a = 1 , b = 0 B
• 
  C
• 
  D