Sargodha Board
( Inter Part- II)
(Session 2015)
Mathematics
(Objective)
Paper (1)
Time Allowed:- 30 minutes
 Maximum Marks: 20
 Note: You have four choices 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 will. Cutting or filling two or more circles will result in zero mark in that question. Write PAPER CODE, which is printed on this question paper, on the both sides of the Answer Sheet and fill bubbles accordingly, otherwise the student will be responsible for the situation. Use of Ink Remover or white correcting fluid is not allowed

• x = a Secθ ; y = btanθ are parametric equations of curve

(A)- 
(B) + 
(C) - 
(D)+     

• …………….  equals

(A)1
(B) •1
(C) 0
(D) 2

• equals ex

(A) e^-x
(B) e^x
(C) xe^x
(D) xe^x-1

• Derivative of cot x w.r.t x equals

(A) Sec²x
(B)-Sec²x
(C) Cosec²x 
(D) - Cosec²x 

•  (Cosh2x) equals

(A) Cosh 2x
(B) Sinh 2x
(C)2Cosh 2x
(D) 2Sinh 2x

•  () Equal

  (A) - 
(B) 
(C) 
(D)

• equals

(A)sin 2x
(B) cos 2x
(C) –sin 2x
(D)-cos 2x

• dx is equal to

(B)
(C)
(D)

•  equals

(A)–Sinx
(B) –Cosx
(C)Sinx
(D) Cosx

• dx is equal to

(A)e^x+1
(B)e^x-1
(C)e^1-x
(D) e^x

• dx equal

(A)  (tan-1+ x)
(B)  (Cot-1x
(C)     (tan-1+ x2)
(D)  (Cot-1x2)      

• equals

 (A) 3/10
(B)
(C) 2
(D)                             

•   is equal to

(A)  
(B) 
(C)  
(D) 0

• Lines represented by ax²+ 2hxy + by²= 0 will be perpendicular if

(A) h²-ab=0
(B) h²+ab = 0
(C) a + = 0
(D) a -b= 0

• The point of intersection, of lines 2x- 3y=1and 2x-4y=3 equals

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

• Corner points of feasible region of inequalities are also called

(A) Constraints
(B) Variables
(C) Decision Variable
(D) Vertices

• The equation of directrix of =1 is

(A) y = ±
(B) x= ±
(C) y = ±
(D) x = ±

• The centre of circle with (-3 , 2) and (5 , -6) as ends of diameter is equal to

(A) (-1 , -3)
(B) (1, 2)
(C) (1 , -2)
(D) (-1 2)

• For non zeros vectors and : [x] equals

(A) ab Sinθ 
(B) ab Sinθn
(C) ab Cosθ 
(D) ab Cosθn

• If u=[1, 2,-1];v=[3.-2.-1]then =|u+v| 
  

(A) 1
(3) 2 
(C) 3
(D) 4

Mathematics (Subjective)
(Session 2015)Paper (1)
Time Allowed: 2.30 hours
(Inter Part -II) Group-I
Maximum Marks: 80

Section-I

2.Answer briefly any eight parts from the followings:

• Find the domain and range of the function g(x) = |x - 3|
• Evaluate
• Define continuous function
• If y=  , Find
• Find if x = I –t², y = 3t²-2t³
• Prove that(Sin-1 x)=
• Differentiate Sin x w.r.t Cot x                              
• Differentiate y = ax w.r. t x
• Find  if y =n (tan hx)
• Find y" if x= a Cosθ, y=a Sinθ
• Prove that e^x+h=e^x [l+h++……….]
• Define stationary points.

3. Answer briefly any Eight parts from the followings:

• Using differentials find when   -nx
• Evaluate
• Evaluate dx
• dx
• Evaluatetan-1x dx
• Evaluatex dx
• 
• Evaluate dx
• dx
• Solve[Siny+y Cos y] dy=[x(2]dx
• Indicate the solution set of linear inequality by shading 3x+7y4
• Define convex and feasible region.

4. Answer briefly any Nine parts from the following

• Find the distance between the points A(-8,3) , B(2,-1)
• Show that points A(-3 , 6), B(3,2) and C(6,0) are collinear.
• Find an equation of line through (-5 . -3) having slope undefined.
• Find straight lines from the equation 10x2-23xy-5y2=0
• Find an equation of the line through (-4 , 7) and parallel to the line 2x -7y + 4 = 0
• Find equation of tangent and normal to circle x²+y² =25 at (4,3)
• Define focal chord of parabola
• Define position vector:
• Find foci of hyperbola 25x² - 16y²=400
• If A(-1,1),B(2,0),C(-l,3) and D(-2,2)  are four points then find the sum of vectors and
• Find a vector whose magnitude is 4 and parallel to 2i - 3j +6k
• Show that vectors  =3i- j-2k and = i+2j - k are perpendicular.
• If =3i- j+5k = 4i +3j-2k and= 2i+5 j + k then find

Section-2

Note: Attempt any three questions.                                                                                 

5.(a) Find values of m, n, so that the function f(x) is continuous at x = 3 where

f (x)=
(b) Differentiaie y = Sin  from the first principe

6.(a) Evaluate dx
(b) Find joint-equation of line through (0.0) perpendicular to ax²+2hxy+by²=0

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

8.(a) Find an equation of the circle passing through A (3,-1), B( 0,1)and having centre at 4x - 3y -3=0
(b) Prove by vector method that Cos (α + β)=CosαCosβ –Sinα Sinβ

9.(a) Find the equation of the ellipse when Foci (±3 , 0) and the minor axis of length 10
(b) Find the volume of the Tetrahidron with the vertices ( 0,1,2 ), ( 3 , 2 , 1 ) ( 1,2 ,1) , (5,5,6)