2nd Year Math Chapter 1 Notes

Important Handwritten 2nd Year Math Chapter 1 Notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of the 2nd year math notes chapter 1 pdf for the students of Mathematics of the intermediate and these are according to the paper patterns of all Punjab boards.

Summary and Contents:
Topics which are discussed in the notes are given below:
  • Important 2nd year math chapter 1 mcqs for Intermediate part-II students.
  • 1. If f(x)=x^2-2x+1 , then f(0) =
  • (a) -1 (b) 0            (c)  1           (d) 2
  • 2. When we say that f is function from set X to set Y, then X is called
  • (a) Domain of f     (b) Range of f        (c)  Codomain of f     (d)  None of these
  • 3. The term “Function” was recognized by______ to describe the dependence  of one quantity to another.
  • (a) Lebnitz (b)   Euler (c)   Newton (d)   Lagrange
  • 4. If f(x)=x^2 then the range of f is
  • (a) [0,∞)         (b) (-∞,0] (c)   (0,∞) (d)   None of these
  • 5. Cosh^2 x-Sinh^2 x=
  • (a) -1 (b)   0          (c)    1   (d)   None of these
  • Important 2nd year math ch 1 mcqs for Intermediate part-II students.
  • 6. cosechx is equal to
  • (a) 2/(e^x+e^(-x) ) (b)   1/(e^x-e^(-x) ) (c)   2/(e^x-e^(-x) )   (d)     2/(e^(-x)+e^x)
  • 7. The domain and range of identity function , I:X→X is
  • (a) X (b) +iv real numbers (c)    –iv real numbers    (d) integers
  • 8. The linear function f(x)=ax+b is constant function if
  • (a)   a≠0,b=1    (b)  a=1,b=0      (c)    a=1,b=1 (d) a=0   
  • 9. If f(x)=2x+3, g(x)=x^2-1 ,  then (gof)(x)=
  • (a) 2x^2-1 (b)  4x^2+4x (c)   4x+3   (d)   x^4-2x^2
  • Important 2nd year maths chapter 1 mcqs solved for Intermediate part-II students.
  • 10.If f(x)=2x+3, g(x)=x^2-1 ,  then (gog)(x)=
  • (a) 2x^2-1 (b)  4x^2+4x   (c)   4x+3 (d)   x^4-2x^2  
  • 11. The inverse of a function exists only if it is
  • (a) an into function (b) an onto function     (c) (1-1) and into function   (d) None of these
  • 12. If f(x)=2+√(x-1), then domain of f^(-1)=
  • (a) ]2,∞[     (b) [2,∞[    (c)   [1,∞[ (d)    ]1,∞[
  • 13. (lim)┬(x→∞)⁡〖e^x=〗
  • (a) 1 (b)  ∞ (c)  0 (d)   -1
  • Important 2nd year maths chapter 1 mcqs for Intermediate part-II students.
  • 14. (lim)┬(x→0)⁡〖sin⁡(x-3)/(x-3)=〗
  • (a) 1  (b) ∞ (c)    sin3/3 (d)  - 3
  • 15. ( lim)┬(x→0)⁡〖sin⁡(x-a)/(x-a)=〗
  • (a) 1 (b)   ∞ (c)     sina/a (d)   -3
  • 16. f(x)=x^3+x is :
  • (a) Even (b) Odd (c) Neither even nor odd     (d) None
  • 17. If f:X→Y is a function , then elements of x are called
  • (a) Images (b) Pre-Images (c) Constant    (d) Ranges
  • Important 2nd year maths chapter 1 mcqs with answers for Intermediate part-II students.
  • 18. (lim)┬(x→0)⁡〖(x/(1+x))=〗
  • (a) e (b) e^(-1)     (c) e^2 (d)   √e
  • 19. (lim)┬(x→0)⁡〖(a^x-1)/x〗  is equal to
  • (a) log_(e^x ) (b)  log_(a^x )        (c) a    (d) log_(e^a ) 
  • 20. (lim)┬(x→0)⁡〖(Sinx^°)/x=〗
  • (a)   π/(180°)          (b)    (180°)/π (c)  180 π     (d) 1
  • Important 2nd year math chapter 1 important questions for Intermediate part-II students.
  • Definition of Continous Funtion: A function is said to be continous at a number " C " if and only if following three conditions are satisfied. (i) f(c) is defined.
  • Important 2nd year math chapter 1 solution for Intermediate part-II students.
  • Definition of Discontinous Funtion: If one or more of these three conditons fail to hold at "c" then the function is said to be Discountinous at C.
  • Important 2nd year math chapter 1 examples for Intermediate part-II students.
  • Definition of The Left Hand Limit: Limit f(x) = L is read as the Limit of f(x) equal to L as x approches c from the left. i - e for all x sufficiently close to C, but less than C.
  • Important 2nd year math chapter 1 important long questions for Intermediate part-II students.
  • Definition of The Left Hand Limit: Limit f(x) = M is read as the limit for f(x)  is equal to M as x approches from the right i -> for all x sufficiently close to c, but greater then C.
  • Important 2nd year math exercise 1.1 solution pdf for Intermediate part-II students.
  • Definition of Odd function with example
  • Definition of Even function with example: "A function is said to be an even if (x) = f(x) for every number x in the domain of f." f(x) = x^2 and f(x) = cosx are even function.
  • Important 2nd year math chapter 1 for Intermediate part-II students.
  • Definition of Continuity: A function f is said to be continous at a number "c" if and only if  the following conditions are satisfied: f(x) is defined. Lim f(x) exists.
  • Important 2nd year math exercise 1.1 solved for Intermediate part-II students.
  • Definition of continuity and its conditions
  • State and Prove sandwich theorem
  • Find the domain and range of a function
  • Important 2nd year maths chapter 1 exercise 1.1 for Intermediate part-II students.
  • Important 2nd year maths chapter 1 exercise 1.2 for Intermediate part-II students.
  • Important 2nd year maths chapter 1 exercise 1.3 for Intermediate part-II students.
  • Important 2nd year maths chapter 1 exercise 1.4 for Intermediate part-II students.

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