Chapter 1: Functions and Limits

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MCQ's with answers from chapter 1 Functions and Limits Mathematics book 2 for FSC pre engineering  for Board of Intermediate and Secondary education. Also For Entry Test Preparation for UET, NUST, PIEAS, GIKI, AIR, FAST, WAH University, other engineering Universities.



1)            The domain of binary relation  y2 = - 4x is,

A)      R
B)      Z
C)      R +
D)      Negative real numbers including zero.
Answer:                 D

2)            If S = {a, b, c} then the number of distinct relations on S is

A)      9
B)      29
C)      23
D)      92
Answer:                 B

3)            The domain of the binary relation 2x2 + 2y2 = 18 is

A)      R
B)      R+
C)      Z
D)      {- 3, 3}
Answer:                 D

4)            The range of the binary relation 4x2 + 9y2 = 36 is

A)      {- 2, 2}
B)      {– 3, 3}
C)      {- 2,  3}
D)      R
Answer:                 A

5)            If R1 = {(x, y) ½ x, y Î R and x >y} is a binary relation then its inverse is

A)      {(1, 2),  (2, 3)}
B)      {(2, 1),  (3, 2),  (4, 3)}
C)      {(x, y) ½ x = y}
D)      {(x, y) ½ x, y Î R and y > x}
Answer:                 D

6)            The graph of the binary relation y = x2 – 6x + 5 represents

A)      Line
B)      Circle
C)      Parabola
D)      Ellipse
Answer:                 C

7)            The graph of R1 = {(x, y) ½ x, y Î R and y > x} is

A)      Line
B)      Points on the line y = x
C)      All points below the line y = x
D)      All points above the line y = x
Answer:                 D
 

8)            If f (x) = ax + b, where a, b Î R, a ¹ 0, then f is called a

A)      Constant Function
B)      Linear Function
C)      Quadratic Function
D)      Polynomial Function
Answer:                 B

9)            The graph of a linear function represents a

A)      Circle
B)      Line
C)      Parabola
D)      Ellipse
Answer:                 B

10)          The equation having null set as its solution set is

A)      x = cos x
B)      x = ex
C)      x = sin x
D)      x = tan x
Answer:                 B

11)          The composition of two functions f and g is defined as (fog) (x) = f {g (x)}, for all x in the set

A)      Rg
B)      Dg
C)      Dg Ç Df
D)      Rg Ç Df
Answer:                 D

12)          If f(x) = x and g(x) = x2 then the value of (fog) (x) is

A)      x2
B)      x
C)      x3
D)      x4
Answer:                 A

13)          Let f: S ® T be a one – to – one function such that f(x1) = 6 and f(2) = 6 then the value of x1 is :
A)      6
B)      2
C)      3
D)      12
Answer:                 B

14)          Let f(x) = 5x + 3 then f is
A)      One – to – one function
B)      Onto function
C)      Constant function
D)      Both one-to-one and onto function
Answer:                 D

15)          Let : S ® S be an identity function and 2 Î S, then the value of f(2) is
A)                  2
B)                  – 2
C)                  3
D)                  ½
Answer:                 A

16)          Let g = {(1, 1), (2, 3), (3, 2), (4, 4)} be a function from S onto S, then the value of g–1  (2) is,
A)      2
B)      3
C)      4
D)      1
Answer:                 B

17)          Let f(x) = 5x + 1, x Î R then value of f–1 (6) is,

A)      31
B)      1
C)      6
D)      1/6
Answer:                 B

18)          If g(x) = 2x + 1 then the value of g2(1) is

A)      3
B)      9
C)      7
D)      8
Answer:                 C

20)          The graph of the function y = x and y = tan x intersect at the point

A)      x = p/4
B)      x = 0
C)      x = p/2
D)      x = p/3
Answer:                 B

21)          The solution set of the equation x = tan x is

A)      f
B)      {p/4}
C)      {1}
D)      {0}
Answer:                 D

22)          The solution set of 2x3 – 3x2 + 4x – 5 = 0 can have at the most,

A)      4 members
B)      3 members
C)      2 members
D)      5 members
Answer:                 B

23)          If f (x) = 2x2 – 1 and g(x) = 5x + 2 then value of f[g(2)] is

A)      312
B)      87
C)      287
D)      288
Answer:                 C


 






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