Federal Board HSSC-II (2012)
MATHEMATICS
Time: 25 Minutes    Marks: 20
SECTION — A (Marks 20)

• The term_____was recognized by a German Mathematician Leibniz to describe the dependence of one quantity on another.
  A Limit      
  B.Function
  C.Domain 
  D.Range
  
•          
  A. 0             
  B.-1
  C.1             
  D. None of these
  
• Y = e2x is called a/an_____function.
  A. Linear    
  B. Quadratic
  C. Rational      
  D. Exponential
  
• The minimum value of a function occurs when its derivative is 

1. Equal to zero
2. Greater than zero
3. Less than zero
4. Equal to one

• The slope of the tangent line to the graph of f at (x, f(x)) is________      
  A.   f'(x)   
  B.    f(x)
  C.    y     
  D.    x
  
•   The derivative of 6x3 w.r.t. x2 is
  A. 18x2    
  B.  Zero
  C. 9x2     
  D. 9x
  
• (= ________
  A.  aInx. lnx          
  B.  aInx.
  C. 
  D.  None of these
  
•   =___________
  A.  [Inf(x)]+c
  B.  Inf(x) + c
  C. Inf(x) + x + c      
  D. -Inf(x) + c
  
• (lnx). =  
  A.  + c    
  B.  (lnx)2 + c
  C.  +c
  D. None of these
  
•  cosecxdx =__________        
  A  In|secx + tanxl + c
  B.  InIcosecx + cotx| + c
  C. InIcosecx - cotxl + c
  D. -cosecx. cotx + c
  
• The centroid of a ∆ABC divides each median in the ratio__________   
  A. 1:2       
  B. 1:1
  C. 1:3       
  D.  2:1
  
• If "P" divides the line AB in the ratio 3:3, then coordinates of "P" are_______.
A. (,)

B.(,)
C. (,)
D.(,)

• The slope of a vertical line is_______.    
  A. 
  B.1
  C.0 
  D. 2

• If slope of = slope of , then points A, B, C are   
  A.  Non-collinear           
  B.  Coplanar
  C.  Non-coplanar
  D. Collinear
  
  
•   The feasible solution which maximizes or minimizes the objective function is called the______
  A.  Feasible solution
  B.  Simple solution
  C. Optimal solution
  D. None of these
  
  
• Radius of a circle is given by_________    
  A.  
  B. 
  C.   
  D. 
  
  
• Directices of ellipse : + =1,a > b are
  A.  x=   
  B.  y=   
  C.  x = +c    
  D.  x = +c
  
  
• Vertex of parabola (y - 2)2 = 10(x + 3) is     
  A.  (0, 0)      
  B.  (-2, 3)
  C. (2, -3)    
  D. (3, -2)
  
• If a x b = 0 and a. b = 0, then   
  A.a and b axe parallel
  B. aand b are perpendicular
  C.  a  b , b0
  D.  Either a = 0 or b = 0
  
• If P (2, 3) and Q (6, =2), then =
  A.   4ȋ— 5ĵ    
  B.   -4ȋ +5ĵ
  C.   4ȋ + 5ĵ  
  D.   5ȋ — 4ĵ
  

MATHEMATICS HSSC-II
Time allowed: 2:35 Hours  
Total Marks: 80
Note: Attempt any ten parts from Section 'B' and any five questions from Section on the separately provided answer book. Use supplementary answer sheet i.e. Sheet-B if required. Write your answers neatly and legibly.
SECTION - B (Marks 40)

• Determine whether the given function "f" is  Even or Odd:
• f(x) = X2/3 + 6
• Simplify: limx-0      , x> 0
• If y =  prove that 2x+y=2
• Find  if x = y. siny
• Find the extreme values for:
  f(x) = 5 + 3x - x3
• Evaluate: sin2x dx
• Evaluate:  x3. lnx dx
• Evaluate:  (2t - 1)3 dt
• Find the equation of a line through (-4, -6) and perpendicular to a line having slope
• The vertices of a triangle are A( - 2, 3), B(-4, 1) and C(3, 5). Find coordinates of the centroid.
• Find the centre and radius of the circle 5x2 + 5y2 + 14x + 12y- 10 = 0
• Show that the circles x2 + y2 + 2x - 2y - 7 = 0 and x2 + y2 6x + 4y + 9 = 0 touch externally.
• Find Focus and Vertex of the parabola: (x - 1)2 = 8(y + 2)
• If v = 3ȋ - 2ĵ + 2Ќ and w = 5ȋ -ĵ + 3Ќ , then find |3v + 3w|.

SECTION - C (Marks 40)
Note: Attempt any FIVE questions. All questions carry equal marks.        (5 x 8 = 40)
Q.3     Prove that  = loge a
Q.4   Show that =if =tan-1
Q.5     Evaluate: dx
Q. 6 The points (4, -2), (-2, 4) and (5, 5) are vertices of a triangle Find In-centre of the triangle.
Q. 7 Graph the feasible region of the system of linear inequalities and find the corner points: 5x + 7y35, x - 2y 4, x > 0, y > 0
Q. 8 Find the centre, foci, eccentricity and directices of the ellipse whose equation is: 25x2 + 9y2 = 225
Q. 9 Prove by vector method that: sin(α + β) sina 'cos13 + cosα sinβ