SAHIWAL BOARD 2015
INTER
PART-II
Mathematics
(Session: 2015)
Time: 20Minutes
(OBJECTIVE)
Marks: 20
Note: - Write answers to the questions on objective answer sheet provided, four possible answers A, B, C & D to each question are given. Which answer you consider correct, fill the corresponding circle A, B, C or D given in front of each question with Marker or pen ink on the answer sheet provided.

  1.  (±2, 0)
  2.  (±3, 0)
  3.  (0, ±3)
  4.  (0, ±2)
  1.             
  2.  
  4.  
  1.  (0,4)
  2.  (0,-4)
  3.  (0,16)
  4.  (0,-16)
  1. 6     
  2. 8
  3. 9     
  4. 4
  3.  
  4.  
  1. 3
  2. 4
  3. 5

  1. m1.m2=1
  2.  m1.m2=-1
  3.  m1-m2=0
  4.  m1+m2=1
  1. ex/x
  2. ex.ln x
  3. xex
  4. x.ln x
  1. 1
  2. 2
  3.  
  4.  
  3.  
  4.  
  1. tan-1x
  2. tanx-2
  3. cot-1x-2
  4. cot-1x
  1. Ln
  2. ln x
  4.  
  1. ln sec x
  2. ln cos x
  3. ln sin x
  4. -ln sin x
  1. tan x
  2. tan x/2
  3. cot x/2
  4. cot x
  1. esinx.cos x
  2. -esinx.cos x
  3. ecosx.sin x
  4. -ecosx.sin x
  1. cos2x
  2.  2cos2x
  3.  
  4.  
  1.  Sin h x
  2. -sin h x
  3.  cosh x
  4.  -cosh x
  1.  1-x
  2.  1+x
  1. sinh x
  2. –sinh
  3. cosh x
  4. -cosh x

SAHIWAL BOARD2015
Mathematics
(Session: 2015)
Time: 2:10Hours
(SUBJECTIVE)
Marks: 80
Note: Section I is compulsory. Attempt any three questions from Section II and any Two parts from Section III.
SECTION-I

2. Write short answers to any Eight questions.

  1. Prove the identity sin h 2x = 2sin h x cos h
  2. Evaluate:
  3. Express in terms of e,
  4. Find  by definition if
  5. Differentiate: w.r.t x
  6. Differentiate: (1 + x2)n w,r.t x2.
  7. Differentiate: sin3x w.r.t cos2x
  8. Find  if y x=cos y
  9. Find  if y =
  10. Find y2 if y = x2e-x
  11. By Maclaurin's series prove that e2x= 1 + 2x ++ ……..
  12. Find the interval in which f is increasing or decreasing, f (x) = sin x ;  x

3. Write short answers to any Eight questions.

  1. Using differential find  in the ay - In x = c
  2. Using differentials to approximate the value of
  3. Evaluate:  
  4. Evaluate:
  5. Evaluate:
  6. Evaluate
  7. Evaluate
  8. Find the area between the x-axis  and the curve, y = 4x-x2
  9. Evaluate :
  10. Solve the differential equation xdy+y(x-1)dx=0
  11. Graph the solution set 3y - 4 in xy - plane.
  12. What is an objective function?

4. Write short answers to any Nine questions.

  1. Show that the points A (0,2), B (,-1) and C (0,-2) are vertices of a right triangle
  2. Find the points trisecting the join of A (-1, 4) and B (6,2).
  3. Find slope and angle of inclination of line joining the points (4,6) and (4,8).
  4. Find equation of line through the point (2, -9) and the intersection of the
  5. lines 2x + 5y-8= 0 and 3x- 4y- 6 = 0
  6. Vertices of triangle are A (-2, 3), B)-4, 1) and C (3,5). Find coordinates of centroid.
  7. Find centre and radius of circle x2 + y2- 6x + 4y + 13 = 0
  8. Write equations of tangents from (2, 3) to the circle x2+ y2=9
  9. Find focus and directrix of parabola y2 = 8x
  10. Find centre, foci and eccentricity of the ellipse x2 + 4y2= 16
  11. Find a unit vector in the direction
  12. Find a so that  
  13. If - , =.Find projection of a along b.
  14. If -2 and -3+5 are coplanar

SECTION-III

Q.5.
(a) Define continuous function Discuss the continuity of
(b) Find the derivative of with respect to x

Q.6.
(a) Evaluate:ln x dx
(b)  By means of slopes, show that the points lie on the same line (-1, -3) , (1,5) ,(2,9)

Q.7.
(a) Evaluate:
(b) Graph the feasible region of the following system of linear inequalities and find and the corner points.

Q.8.
(a)  Find the equation of the circle that passes through the points A(4,5), B(-4,-3), C(8,-3)
(b) Using vector method prove that in any triangle ABC c = a cos B + b cos A

Q.9.
(a) Find equation of the parabola having its focus at the origin and directrix parallel to the y - axis.
(b) Find volume of the tetrahedron with the vertices (0,1,2); (3,2,1), (1,2,1) and (5,5,61)