2nd Year Math Notes Chapter 3

Handwritten notes of 2nd Year Math Notes Chapter 3 written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of 2nd Year Math Chapter 3 Notes 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 3 mcqs for Intermediate part-II students.
  • 1. a_0+a_1 x+a_2 x^2+⋯+a_n x^n+⋯ is
    • (a) Maclaurin’s series (b) Taylor Series (c) Power Series (d) Bionomial Serie
    • 2. A function f(x) is such that , at a point x=c , f^' (x)>0 at x=c , then f is said to be
    • (a) Increasing (b) decreasing (c) constant (d) 1-1 function
    • 3. A function f(x) is such that , at a point x=c , f^' (x)<0 at x=c , then f is said to be
    • Increasing (b) decreasing (c) constant             (d) 1-1 function
    • Important 2nd year math ch 3 mcqs for Intermediate part-II students.
    • 4. A function f(x) is such that , at a point x=c , f^' (x)=0 at x=c , then f is said to be
    • (a) Increasing (b)  decreasing             (c) constant (d) 1-1 function
    • 5. A stationary point is called ______ if it is either a maximum point or a minimum point 
    • (a) Stationary point (b) turning point       (c) critical point (d) point of inflexion
    • 6. If f^' (c) does not change before and after x=c , then this point is called___:
    • (a) Stationary point (b)  turning point (c) critical poin     (d) point of inflexion 
    • Important 2nd year maths chapter 3 mcqs solved for Intermediate part-II students.
    • 7. Let  f be a differentiable function such that f^' (c)=0 then if f^' (x) changes sign from -iv to     +iv  i.e., before and after x=c , then it occurs relative ____at x=c
    • (a) Maximum (b)   minimum    (c)  point of inflexion      (d)  none
    • 8. Let  f be a differentiable function such that f^' (c)=0 then if f^' (x)  does not change sign  i.e., before and after x=c , then it occurs ____at x=c
    • (a) Maximum (b) minimum (c) point of inflexion         (d) none
    • 9. Let f be differentiable function in neighborhood of c and f^' (c)=0 then f(x) has relative maxima at c if 
    • (a) f^'' (c)>0 (b) f^'' (c)<0             (c) f^'' (c)=0              (d) f^'' (c)≠0
    • Important 2nd year maths chapter 3 mcqs for Intermediate part-II students.
    • 10. If ∫〖f(x)dx=φ(x)+c〗 ,then f(x) is called 
    • (a) Integral (b) differential             (c) derivative               (d) integrand
    • 11. Inverse of ∫〖….dx〗 is:
    • (a) d/dx    (b)      dy/dx               (c)     d/dy    (d)    dx/dy
    • 12. Differentials are used to find:
    • (a) Approximate value (b) exact value (c) Both (a) and (b)          (d) None of these
    • Important 2nd year maths chapter 3 mcqs with answers for Intermediate part-II students.
    • 13. xdy+ydx=
    • (a) d(x+y)      (b)  d(x/y)               (c) d(x-y)             (d)    d(xy)
    • 14. If  dy=cosxdx then dx/dy=
    • (a) sinx       (b)   cosx                 (c)   cscx (d)  secx 
    • 15. If ∫〖f(x)dx=φ(x)+c〗 ,then f(x) is called 
    • (a) Integral        (b) differential                 (c) derivative (d) integrand 
    • 16. If y=f(x), then differential of y is
    • (a) dy=f^' (x)            (b)   dy=f^' (x)dx       (c) dy=f(x)dx             (d) dy/dx
    • 17. The inverse process of derivative is called:
    • (a) Anti-derivative (b) Integration (c) Both (a) and (b)          (d) None of these
    • 18. If n≠1, then ∫〖(ax+b)^n dx=〗
    • (a) (n(ax+b)^(n-1))/a+c (b)   (n(ax+b)^(n+1))/n+c (c)   (ax+b)^(n-1)/(n+1)+c (d)   (ax+b)^(n+1)/(a(n+1))+c  
    • 19. ∫〖sin⁡(ax+b)dx〗=
    • (a) (-1)/a  cos⁡(ax+b)+c    (b) 1/a  cos⁡(ax+b)+c      (c) a cos⁡(ax+b)+c (d)-a cos⁡(ax+b)+c
    • 20. ∫〖e^(-λx) dx=〗
    • (a) λe^(-λx)+c (b) –λe^(-λx)+c (c) e^(-λx)/λ+c (d)   e^(-λx)/(-λ)+c
    • Important 2nd year math chapter 3 important questions for Intermediate part-II students.
    • Find dy in y=x^2+2x when x changes from 2 to 1.8 . 
    • If xy+x=4, find dx/dy by using differentials.
    • Using differentials find dx/dy □( ) xy-ln⁡x=c. 
    • Important 2nd year math chapter 3 examples for Intermediate part-II students.
    • Use differential to approximate the value of cos⁡29^∘
    • Show that the points A(3,1),B(-2,-3) and C(2,2) are vertices of an isosceles triangle.
    • Find the mid-point of the line segment joining the vertices A(-8,3),B(2,-1).
    • Important 2nd year math chapter 3 important long questions for Intermediate part-II students.
    • Show that the vertices (-1,2) , B(7,5),C(2,-6) are vertices of a right triangle.
    • Find the points trisecting the join of A(-1,-4) and B(6,2).
    • Important 2nd year math exercise 3.1 solution pdf for Intermediate part-II students.
    • Find h such that (-1,h) , B(3,2),and C(7,3) are collinear.
    • Important 2nd year math chapter 3 for Intermediate part-II students.
    • Describe the location in the plane of point P(x,y) for whcih x=y.
    • Important 2nd year math exercise 3.1 solved for Intermediate part-II students.
    • The point C(-5,3) is the centre of a circle and P(7,-2) lies on the circle. What is the radius of the circle?
    • Find the point three-fifth of the way along the line segment from A(-5,8) to B(5,3).
    • Important 2nd year maths chapter 3 exercise 3.1 for Intermediate part-II students.
    • Important 2nd year maths chapter 3 exercise 3.2 for Intermediate part-II students.
    • Important 2nd year maths chapter 3 exercise 3.3 for Intermediate part-II students.
    • Important 2nd year maths chapter 3 exercise 3.4 for Intermediate part-II students.

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