SAHIWAL BOARD 2014
PAPER MATHEMATICS
PART-2
Time: 30
(Objective Part)
Mark20
Note:Four Answers are given against each column A, B, C & D. Select the write answer and onto separet answer sheet, fill the circle A, B, C or D with pen or marker in from of that question number.

•  (sinh ³x) equals:

(a) cosh ³x
(b) -cosh ³x
(C) 3cosh ³x
(d) Coshx

•  (2x ) equals:

(a) x^2x-1
(b) 2^x In 2                      
(c) In 2x
(d) X In 2        

• If f(x) =  , domain of ƒ equal to :

(a) (1, + ∞)
(b) (-1, - ∞)
(c) (-1, + ∞)
(d) (-∞, + ∞)

•  (-cot x) equals:

(a) sec² x
(b) cosec² x
(c) - cosec²x
(d) –sec² x

•  equals:

(a) zero
(b) -1                
(c)  I
(d) 2

• ʃcot xdx equals:          

(a) Insecx+c
(b) Incosecx+c
(c) In sin x + c
(d) In cot x + c

• ʃ xsin xdx equals:

(a) xsin x-cosx + c
(b) –xcosx + sinx + c
(c) Sin x - COS X + c
(d) sin x+cosx + c

•  (In3x) equals:

(a)
(b)                   
(c) 3x
(d)         

•        dx equals:

(a) tan x+c
(b) In cot x + c
(c) cot x+ c
(c) –In cot x + c

•  loga (2x) equals:

(a)  loga e
(b)  loga e    
(c)  loge e
(d)  Ina

• For b > 0 the point (x, y) is above the line a+ by +c =0 if:

(a) ax₁ + by₁ + c < 0 
(b) ax₁ + by₁ + c = 0
(c) ax₁+by₁+c>0
(d) ax₁-by₁-c<0

• The slope of line with inclination 300 is:

(a) zero
(b)
(c) 1
(d)

•  xdx equals:

(a) 5
(b) 4
(c) 2
(d) 1

•  equals:

(a) Inx + c
(b) In In In x + c
(c) x+c
(d) 40(In x) + c

•  (cos x +sin x)dx:

(a) ex cos x + c
(b) ex sin x+c
(c) ex tan x + c
(d)  ex cot x + c

• Projection of  = i - k along  = j + k is:

(a)  
(b)                     
(c)    
(d)

• J.K × I equals:

(a) i 
(b) j                    
(c) 1
(d) k

• For ellipse  +  = 1, a > b where (c,0) are foci :

(a)  =  +
(b)  =  -  
(c)   =  +
(d)  =  -    

• (2,1)isin the solution of inequality:

(a)  2x + y  6
(b) x-y > 1
(c) 3x + 5y < 7
(d) 2x+y 6

• The vertex of parabola y2  = -8(x- 3) is:

(a) (3,0)
(b) (2,1)             
(c) (3, 1)
(d) (0,1)

Time: 2:30 Hours
(Subjective Part)
Marks: 80
SECTION-I
2.Attempt any Eight Parts.16

• Find the domain and range of the function.
  G(x) =
• Evaluate:  
• Find the derivative of ƒ (x)= c by definition,
• Differentiate w.r.t. ‘x’ .
• Find   if xy + y² = 2.                
• Differentiate cot-1   w.r.t. 'x':
• Find f'(x) if ƒ(x) = x³ .
• Find  if y =  
• Find Y² if y = x². e-x
•   Determine the interval in which ƒ (x) = sin x is increasing for the domain X(-π, π).
• State  taylor’s  series
• Find  if y = sinh-1

3.Attempt any Eight Parts.16

• Using differentials to Find  if x² + 2y² = 16.
• Evaluate  dx.                   
• Evaluate  dx .
• Evaluate  .
• Evaluate   
•   Evaluate  
• Evaluate   dx
• lf  = 5,   = 3 then evaluate .
• Find the area above the x-axis and under the curve y = 5-x2 form x = -1 to x = 2 .
• Define order of a differential equation.
• State the theorem of linear programming.
• What is an objective function?

4. Attempt any Nine Parts.18

• Find the centrold of the triangle having vertices (-2, 3), (-4, 1) and (3, 5)
• Write down the translated coordiantes of a point in place by shifting origin at (h, k)
• Find an equation of the line having y-intercept -7 and slope-5.
• Check whether the point (-2,4) lies above or below the line
  4x+ 5y - 3 = 0.
• Find measure of the angle between the lines represented by
  X² - xy -6y² =0
• Find the centre and radian of the circle with given equation
  X² + y² + 12x = 10y = 0
• Find the focus and &directrix of the parabola y² = 8x.
  (viii)     Show that the equation 9x² -18x + 4y² +8y - 23 = 0
  Represents an ellipse.
• Find the equation of the ellipse with foci (±3,0) and minor axis of length 10.
• Find a scalar α  so that the vectors 2 +  + 5 and 3 + + are perpendicular.
• Find a unit Sector in the direction of the vector  = 2 -
• Calculate the projection of  along  when
   =  -  ,  =  +  .
• Find the value of 2  2. .

Section-II 

Attempt nay three question. Each questions carries 10 marks.
Q.5
(a) Evaluate    .
(b)Differentiate y = sin  w.r.t. ‘x’
Q.6
(a) Find   dx
(b) Find lines represented by 2x² +3xy – 5y² = 0

Q.7
(a) Evaluate θdθ .
(b) Find the solution set of inequalities x+ y  5 and x – y  1.

Q.8
(a) Find the equations of tangents drawn from point (-7,-2) to circle (X+1)2  + (y -2)2 = 26.
(b )Find cosine of angle  between  and  where  = 3 +  -  ,  = 2 -  +  .

Q.9
(a) The major axis of an ellipse in standard form lies along the x-axis and has length 4 .The distance between foci equals the length of the minor axis. Write an equation of the ellipse.
(b) Find volume of the tetrahedron with the vertices (0,1,2), (3,2,1), (1,2,1) and (5,5,6).