SAHIWAL BOARD 2016
PAPER MATHEMATICS PART-II
Time: 30 Minutes
(Objective Part)
Marks:20
Note: Four Answers are given against each column A,B,C & D. Select the write answer and only separate answer sheet, fill the circle A, B ,C or D with pen or marker in front of that question number.

• If

(A) In a   
(B)   
(C)x                                                   
(D).Ina

• (Cosh x) is equal to:

(A) sinh x   
(B) -sinhx                         
(C) cosech x                            
(D) coth x

• Differential of y is denoted by:

(A) d        
(B)                                    
(C)dy                                         
(D) dx

• ∫-sinxdx is equal to:

(A) Sin x    
(B) cos x                                 
(C) –cos                     
(D) -sinx

• dx is equal to:
  

(A)
(B)
(C)
(D)

• If f(x)= then  is equal to
  

(A)      
(B)                       
(C)                       
(D)

• cosh x is equal to:

(A)             
(B)                           
(C)                       
(D)

•  is equal to
  

(A)               
(B)                             
(C)                            
(D)

• 5f(x) is equal to :

(A) (x)                 
(B) 5                          
(C) 5(x)                          
(D) f(x)

•  is equal to:
  (A)                
  (B)                               
  (C)
  (D)
  
• x=5 is the solution of inequality.

(A) 2x-3>0                 
(B) 2x+3<0                                         
(C) x+4<0                            
(D)  x<0    

• The centre of the circle = 3 is equal to:
  

(A) (-1,-3)                  
(B) (-1,3)                                                 
(C) (1,-3)                               
(D) (1,3)

• Focus of the parabola =4ay is :

(A) (a,0)                   
(B)  (-a,0 )                                               
(C) (0,a)                                  
(D) (0,-a)

•  is equal to
  

(A)                             
(B)                                                     
(C) 1                                     
(D) 0

• If =2++4, then || is equal to :
  

(A)                         
(B) 5                                                        
(C) 25                                  
(D) 30

• +1)dx is equal to:

(A)             
(B)                                            
(C)                                 
(D)

• ∫(3x²+2x)dx is equal to :
  

(A) 6x+2                    
(B)x³+x²                         
(C) 3x+2                     
(D) +

• The distance of the point (3, -7) from the x-axis is :

(A) 7                             
(B) 3                                      
(C) -3                                                     
(D) -7

• The slope of the line with inclination 45° is:

(A) 0                             
(B)                                     
(C)1                                       
(D)

• A linear equation represents a:

(A) Circle                      
(B) Ellipse                            
(C) Parabola                       
(D) Straight Line

(Subjective Part)
Marks: 80

SECTION-I

2. Attempt any Eight Parts.

• Given that f(x)=-2+4x-1, find f
  
• Evaluate  
  
• Evaluate
  
• Find  if y=
  
• Differentiate y = w.r.t. x
  
• Differentiate w.r.t  x, cos + .
  
• Differentiate w.r.t  x, sin
  
• State Maclaurin's series expansion.
  
• Find y₂ if +  = .
  
• Define power series expansions of a function f (x)
  
• Find  if y = In
  
• Find if y = sinh 2x
  

3. Attempt any Eight Parts.

• Using differentials, find  if xy - In x = c.
  
• Evaluate: dx
  
• Evaluate: dx
  
• Evaluate:  
  
• Evaluate: dx
  
• Evaluate:  
  
• 
  
• Evaluate:
  
• Find the area below the curve y = 3 and above the x-axis between x = 1 and x = 4
  
• Solve the differential equation =  
  
• Define feasible region and feasible solution of system of linear inequalities.
  
• Indicate the solution region of the linear inequalities 2x-3y≤ 6, 2x+3y≤12
  

SECTION-II

Note:Attempt any THREE questions. Each questions carries 10 marks.

Q.No.5.
(a) If f(x)= Find the value of k so  that f is continuous at x = 2.
(b) Show that  = if

Q.No.6.
(a) Evaluate dx
(b) Find the equation of perpendicular bisector of the segment joining the points A (3,5) and B (9,8)

Q.No.7.
(a) Evaluate:  
(b) Graph the feasible region constrained by 2x-3y≤6,2x+y≥2, x+2y≤8,x≥,y≥ 0

Q.No. 8.
(a) Find an equation of the circle which passes through the points A(5,10) , B (6,9) , C (-2,3).
(b) Using vectors method prove that cos(α + β) = cosα cosβ -sinα sinβ

Q.No.9.
(a) Find focus, vertex, and directrix of parabola x² -4x-8y+4=0.
(b) Find the moment about A(1,1,1) of each of the concurrent forces -2-,3+2-k,5+2 where P (2,0,1) is their point of concurrency.