Mathematics
Paper II
(Objective Type) 2014
Time Allowed: 30 Minutes
Max. Marks: 20
(Group-I)
Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink. Cutting orfilling two or more circles will result in zero mark in that question.

•  dx is equal to

(A) +c              
(B)
(C)          
(D)

• The centre of circle (x + 3)2 + ( y - 2)2 =16 equals :
  

(A) (-3, 2)       
(B) (3 - 2)
(C) (3, 2)        
(D) (-3, -2)

• 2 (2 x ) equals :
  

(A) 0   
(B) 2
(C) 4   
(D) 6

•  equals:
  

(A) 0   
(B)
(C)   
(D)

• If f (x + h) = 2x+h, then f’(x) equals:

(A) 2x+h           
(B)
(C) 2x. n2     
(D)2x

• Anti derivative of cot x is equal to :
  

(A)  n cosx + c         
(B)  n sin x + c
(C) -n cosx + c        
(D) -nsinx + c

•  equals :
  

(A) 0               
(B) 1
(C) x + 2         
(D) x - 2

• Point (1,2) lies in the region of inequality :    

(A)2x+y>5     
(B)2x+y 5
(C)2x+y<3     
(D)2x+y<5

• Work done by a constant force  during displacement  is equal to :
  

(A)           
(B)
(C)  
(D)

• The eccentricity of  - x2 =1 equals :
  

(A)         
(B)
(C)        
(D)

• Slope of line perpendicular to line 2x - 3y + 1 = 0 is equal

(A)         
(B)
(C)           
(D)

• The differential co-efficient of e sin' equals :
  

(A) e^sinx.cosx    
(B) e^sinx .sin x
(C) sin x e^sinx-1
(D) sin xe^sinx+1

dx equals:

(A) e^-x.x     
(B) e^-x . +
(C) e^x. +c      
(D) e^-x.nx+c

 is equal to:

(A) sin x         
(B) cos x
(C) sinh x       
(D) cosh x

dx equals:

(A) n (nx) + c         
(B) nx + c
(C) n  + c            
(D) n  + c

Solution of y.dx + x.dy = 0 is equal to :

(A) x . y = Constant   
(B)  = Constant
(C) x + y = constant   
(D) x - y = constant

If y = ,then   equals:

(A) tan x         
(B) cot x
(C) - tan x       
(D) - cot x

X-co-ordinate of centroid of triangle ABC with A (-2 , 3) B (- 4, 1 ) : C (3, 5 ) equals :

(A) -1 
(B) 1
(C) 3   
(D) -3

 (tan x) is equal to:dx

(A)  cos x   
(B)
(C)    
(D)

 dx equals:

(A)  
(B)    
(C)
(D)

Inter Part-II
Lahore Board 2014.
Mathematics
Paper H (Essay Type)
Time Allowed: 2.30 hours
Max. Marks: 80
(Group-I)

(SECTION-I)

2.Write short answers to any EIGHT (8) questions :  16

• Express the perimeter P of square as a function of its area A.
  
• Evaluate  equals:
  
• Find the derivative of f (x) = C by definition.
  
• If y = x⁴ + 2x² + 2 prove that  =
  
• Find  if y²- xy –x² + 4 = 0
  
• Differentiate (1 + x²)n w.r.t. x²
  
• Find  if x = y sin y
  
• Find y² if y = n (x² - 9)
  
• Differentiate  w.r.t. x
  
• Find if y = x²;
  
• What is a stationary point?
  
• Determine the interval in which f (x) = x² + 3x + 2;x [- 4, 1 ] is increasing.
  

3. Write short answers to any EIGHT (8) questions :     I6

• Find y and dy if y= x²:when x=2 and dx = 0
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Show that
  
• Evaluate
  
• Solve the differential equation  = -y
  
• State the theorem of linear programming.
  
• What is a feasible solution?
  
• Find the area bounded by cosx from  x=- to x=
  

4. Write short answers to any NINE (9) Questions : 18

• Find equation of a line through (-4, 7) and parallel to the line 2x - 7y + 4 = 0
  
• Find equation of a line through (-6, 5) having slope = 7
  
• Find distance from the point P (6, -1) to the line 6x - 4y+ 9 = 0
  
• Find area of triangular region whose vertices are A (5, 3), B (-2, 2), C (4, 2)
  
• Find the angle from the line with slope  to the line with slope
  
• Find the equation of tangent to the circle x² + y² = 25 at(4, 3)
  
• Find the equation of parabola whose focus is (2 , 5) and directrix, is .y = 1
  
• Find foci and eccentricity of ellipse = 1
  
• Find eccentricity and foci of the asymptotes of hyperbolay =1
  
• Find vector from A to origin whose  = 4i - 2j and B (-2, 5)
  
• Find a vector whose magnitude is 2 and is parallel to –i+j+k
  
• Find a so that the vectors 2i + aj + 5k and 3i + j + αk are perpendicular.
  
• Find α so that are coplanar.
  

(SECTION-II)

Attempt any THREE questions.

5.(a) If find the value of k. so that f is continuous at x = 2
(b) Differentiate  w.r.t

6.(a) Evaluate
(b) Find an equation of the perpendicular bisector of the segment joining the points A (3, 5) and B (9, 8)  5

7.(a) Solve differential equation 1 + cos x tan y  = 0
(b) Minimize z = 2x+ y subject to the constraints x+y≥3 , 7x+ 5y≤35 ,x≥0 ,y≥0

8.(a) Write equations of tangent- lines to the circle x² + y² + 4x+ 2y = 0 drawn from the point P (-1, 2). Also find the tangential distance.  
(b) Prove by using vectors that the line segment joining the mid points of two sides of a triangle is parallel to the third side and half as long.          

9.(a) Show that the equation x² + 16x + 4y² - I6y + 76 = 0 represents an ellipse. Find its foci eccentricity, vertices and directrices.
(b) A focus magnitude 6 units acting parallel to 2 displaces the point of application from (1, 2, 3) to (5,3,7 ) find the work done.