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

• f (x) = x cot x

(a) Linear function
(b) Quadratic function
(c) Even function
(d) Odd function

(a) e³
(b) e1/³
(c)  1/e³
(d) -1/e³

• =

(a)
(b)        
(c)
(d) None of these

• =

(a) -2xSinx2
(b) 2xSinx2
(c)- Sinx2/2x
(d) -2SinxCosx

• =

(a)
(b) 2x          
(c) 2
(d) -2x

(a) 1/x
(b) 1/x
(c) x
(d) 1/

• =

(a) 1/x
(b) 1/
(c)  
(d)

(a)
(b)
(c) 5Sec(5x)+c
(d) 5tan(5x)+c

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

• x(cosx+sinx)dx=

(a) e^xCosx+c
(b) e^xSinx+c
(c)-e^xCosx+c
(d) –e^xSinx+c

(a)-2
(b) -1
(c) 0
(d) 2

• The solution of differential equation  is:

(a)y=Ce^-x
(b) y=e^-x
(c) y=e^x
(d) none of these

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

(a) 3
(b) -3
(c) -7
(d) 7

• The point of Concurrency of the medians of a triangle is called its:

(a) Centroid
(b) In-centre
(c) Circum centre
(d) Ortho centre

• Two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are parallel if:

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

• 2x + 3y <0 is:

(a) An equation
(b) Inequality
(c) Identity
(d) Non identity

• Center of the circle with equation x² + y² -6x + 4y +13= 0 is:

(a) (3 , -2)
(b) (-3 , 2)
(c) (-3 , -2)
(d) (3 , 2)

• The latus rectum of a parabola y² = 4ax is:

(a) x = - a
(b) y = - a
(c) x = a
(d) y = a

• For a vector v = ai + bj + ck, projection of v  along k is:

(a) a
(b) b
(c) c
(d) a+ b+ c

• j . k x i=

(a) I
(b) j
(c) k
(d) l

(Subjective Part)
SECTION-I

2.Attempt any Eight Parts.

• Evaluate Lim
  x
• Determine that function is even or odd if = x3 + x.
• Define continuity of function at a point.
• if  = x2, then find  by definition.
• Diff.  w.r.t x
• If x= + and y=  + 1 then find dy/dx.
• Find dy/dx if y=x cos y.
• If y= ex2=1 then find
• Find  if = In (ex + e-x)
• If y = cos (ax + b) then find y2.
• By Maclaurin's series prove that ex =1+ x+ x2/2!+….
• Define increasing and decreasing function.

3. Attempt any Eight Parts.         

• Evaluate
• Evaluate
• Evaluate   
• Evaluate  
• Evaluate
• Evaluate
• Evaluate  dx
• Find the area between the x-axis and the curve y=x2 + 1,from x=1, x=2.
• Solve the differential equation y dx + x dy = 0.
• Show that y = cx - 1, is the solution of differential equation x=1+y.
• Define objective function.
• Graph the feasible region of following inequality 2x - 36.

4. Attempt any Nine Parts.          

• Transform the equation 5x - 12y + 39 = 0 into intercept form.
• By means of slopes, show that the Points (a,2b), (c, a+b), (2c-a,2a) are collinear.
• Check whether the given Point lies above or below the given line.
  P(-7,6) ; 4x + 3y - 9 = 0.
• Find the angle from the line with slope  to the line with slope
• Find the equations of lines represented by 20x2 + 17xy - 24y2 = 0
• Find the centre and radius of the circle 4x2 +4y2 - 8x +12y - 25 = 0 .
• Find the length of the tangent from the point P(-5,10) to the circle 5x2 +5y2 +14x+12y-10= 0 .
• Find the coordinates of foci and vertices of the ellipse 25x2+9y2 = 225.
• Find the foci and eccentricity of the hyperbola - =1
• If u = 2i + 3j +4k, v = 4i + 6j+ 2k, w = -6i -9j-3k then find |u – v- w|
• If cos ,cos  and cos are direction consines of a vector, then Prove cos 2 + cos2 + cost =1 .
• Find a unit vector perpendicular to the place containing the vector a= i + j, b=i - j
• Find the volume of the parallelepiped determined by:
  u= i +2j- k, v = i - 2j+3k, w = i -7 j -4k

SECTION-II

Attempt any THREE questions. Each questions carries 19 mark.
5.(a)  = (-x+9)3  . Find and verify

(b) Prove that y.+x=0 if x= , y=

6. (a) Evaluate: dx

(b) Find ‘h’ such that the points A(h,1); B(2,7) and C(-6,-7) are the vertices of a right triangle with right angle at the vertex A.

7. (a) Evaluate:  dx.

(b) Graph the feasible region of the following system of linear inequalities. Also find corner points 2x – 3y  6 2x+3y  12, x  0,  0.

8.(a) Find coordinates region of the following system of line 2x + 3y=6 with the circle x2+y2 -2x-2y-39=0

(b) Prove that in any triangle ABC b2= c2 +a2 -2ca cos.

9. (a) Find an equation of the parabola whose focus is F(-3,4) and directrix line is 3x – 4y +5=0.

(b) Find the volume of the tetrahedron with vertices A(0, 1, 2), B(3, 2, 1) C(1, 2, 1) and D (5, 5, 6).