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

If a variable y dependents on a variable x in such a way that each value of x determines exactly one value of y, then we say that

• x is function of y A
• y is a function of x B
• y is independent variable C
• x is real valued function 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

For f(x) = x2, what is the value of f(a) +f (-a) in terms of a?

• 3a2 A
• 2a2 B
• 2a C
• -7a 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

• 0 A
• -2 B
• 1 C
• 4 D

The domain of y = cos-1 x is

• -∞ < x < ∞ A
• -1≤ x≤ 1 B
• x≤ -1 or x ≥ 1 C
• None of these D

A function in which the variable appears as exponent is called:

• An identity function A
• A logarithmic function B
• an exponential function C
• A rational function D

• 2 A
• 1 B
• 5 C
• 0 D

If f(x) = x²- x then f(-2) is

• 4 A
• 6 B
• 2 C
• 0 D

• 0 A
• 1 B
• -1 C
• none of these 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• -1 A
• 1 B
• 2 C
• -2 D

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

• 
  A
• 
  B
• 
  C
• 
  D

f(x) = 1 is

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

• 
  A
• 
  B
• 
  C
• 
  D

p(x) = 2x⁴- 3x³+ 2x - 1 is polynomial of degree

• 1 A
• 2 B
• 3 C
• 4 D

sec h x = ________

• 
  A
• 
  B
• 
  C
• 
  D

f(x) = C is

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

If y is an image of x under the function f, then we write

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

f(x) = x is

• trigonometric function A
• exponential function B
• quadratic function C
• identify function D

f(x) = 3x/x² + 1 is:

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

Composition of functions is

• Non-commutative (fg ≠ gf) A
• non-associative [8(fh) ≠(8f)h] B
• Commutative (fg = gf) C
• f of-1≠ 1 D

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

The function f(x) =|x| is a/an_______function

• Even A
• Odd B
• Both even as well as odd C
• Neither even nor odd D

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

• 3/4 A
• r B
• v C
• None of these D