RAWALPINDI·BOARJJ 2013
PAPER MATHEMATICS
PARt-II
Time:30Min.
(Objective Part)
Marks:20
Note:  You have four choice for each objective type question as A,B,C and D.  The choice which you think is correct ; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or fill in two or circles will result in zero mark in that question.

•   (loga x)is equal to:

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

•  (tan-1 x + cot-1 x) is equal to
  

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

• ʃ dx is equal to :
  

(a) In |x sin x| +c
(b) In |x sin² x| +c
(c) In|ex cos² x| +c
(d) In |xcos² x| +c

• ʃ  is equal to :
  

(a) tan^-1+c
(b) cot^-1+c
(c) sin^-1+c
(d) In |x ++ c

• If f (x) =2x+1, then +fof (x)is equal to:
  

(a) 4x +1
(b) 4x+3
(c) 4x – 3
(d) 4x -1

• Lim  is equal to:
  

(a) 1 nx
(b) 1 na
(c) 1
(d) 0

• is equal to:
  

(a)
(b)  
(c)
(d) In(ax+b)

• is called:
  

(a) Product rule
(b) Power rule
(c) Chain rule
(d) Quotient rule

• (sin)is equal to :
  

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

• The circle x² +y² +gx +2fy +c=0 passes through origin if:
  

(a) c = 0
(b) c = 1
(c) c = -1
(d) c = f + g

• Parabola y²4ax , a > 0 opens:
  

(a) Upward
(b) Downward
(c) Right side
(d) Left side

• u x v is equal to :
  

(a) u vsinθ
(b) v x u
(c) u vcosθ
(d) –v x u

• Volume of paralell piped with u , v, w
  

(a) u . v x w
(b) ( u . v x w)
(c) ( u . v x w)
(d) ( u . v x w)

•  :

(a)
(b)
(c)
(d) π

• If dx =4then value of K is:
  

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

• (cos x- sin x) dx is equal to:
  

(a) e^-x cos x +c
(b) e^-x sinx +c
(c) e^x sinx +c
(d) e^x cosx +c

• Solution of ydx +xdy = 0 is:
  

(a) xy =c
(b) In=c
(c) X+y =c
(d) =c

• The intercept from of straight line is :
  

(a) y =mx +c
(b) =1
(c) y-y₁ =m (x – x₁)
(d) x cosa +ysin a=p

• The point of intersection of medians of a triangle is:
  

(a) Centroid
(b) Orthocentre
(c) Circumcentre
(d) Incentre

• Ax+ by<c is linear inquality in variables:
  

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

Time : 3:10 Hours
(Subjective Part)
Marks: 83
Section –II

2. Attempt any EIGHT Short Question.  (8x2=16)

• Define an implicit function. Give an example.
  
• Evaluate :  :
  
• Find the derivative of f(x) = x2 by definition.
  
• Find if y =
  
• Differentiate x.3+ 2x -3/2 +3 w.r.t.’x’
  
• Differentiate sin x.w.r.cotx.
  
• Find , if x =1 – t2 , y = 3t2 – 2t3 viii. Find , if xy +y2  = 2
  
• If tan y(1 +tanx) = 1-tanx, show that  = -1.
  
• Find f’ (x) , if f (x) = x3e1/x (x  0).
  
• Find  , y = sinh-1
  
• Find  , if x = y sin y.

3. Attempt any EIGHT short question. (8x2 = 16)

• Evaluate  dx.
  
• Evaluate  dθ
  
• Evaluate  In xdx.
  
• Evaluate  dx
  
• Evaluate  dx
  
• Evaluate  dx
  
• Evaluate  (cosx+sin x) dx
  
• Find the anti –derivative of :
  
• Evaluate  - dx.
  
• Evaluate the definite integral
  
• Define corner point .
  
• Find the solution set of linear inequality. 3x+7y21

4. Attempt any SIX short question.                              (6 x 2 = 12)

• Find the distance between A (-8,3) and 8 (2,-1).
  
• Define latusrectum of the parabola.
  
• The two points P and O' are given in xy co-ordinate system.
  
• Find xy-cordinate of  P referred to the co-ordinate axex O'X  and O'Y, where P (-2,6) and O' (-3,2)
  
• Find the slope and inclination of the line joining the points (-2,4) and (5,11).
  
• Find equations of lines represented by10x2-23xy-5y2=·O.'
  
• Find an equation of a line through(-4,-6)and perpendicular to a line have slo.pe  .
  
• Find an equation of the circle with centre at (5,-2) and radius 4.
  
• Find centre and foci of the ellipse x2+4y2=16.
  
• Write down equation of the tangent to the circle x2+y2 =25 at (4.3).
  
• If v =3i+j+2k and w=5i-j+3k then find |3v+w|.
  
• Find the cosine of the angle  between u and  v where u=3i + j-k and v=2i-j+k
  
• If a=i +J and b = i –j then compute the cross product a x b
  
• Find vector from the point A to the origin  .where  = 4i -2j  and B is the point(-2,5).
  

Attempt any THREE question.

5.(a) Evaluate
(b) If x= a (+sinand y=(1+cos show that +a = 0
6. (a) Evaluate .
(b) Find the point which is equidistant from the points A(5,3), B(2,2) and C(4,2). What is the radius of the circum circle of the triangle ABC?

7.(a)  - dθ.
(b) Maximize f(x,y) = 2x +5y subject to the constraints 2y-x

8.(a) Find a unit vector parallet to 3a – 2b +4c if a = 3 - -4 b = 2  - 4+ 3, c = +2 2 .
(b) Find an equation of the circle passing through A(-3,-1) , B(0,1) and having centre at 4x -3y -3 =0.

9.(a) Find an equation of parabola having focus F(-3,1), directrix x = 3
(b) Prove that in a triangle ABC, c² = a² +b² 2bc cos C.