Sargodha Board 2012 Part II
Mathematics (Objective)
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. Cutting or filling two or more arks will result in zero mark in that question, Attempt as many questions as given in objective type question paper and leave others blank. Write the letter A, B, C or D in the column (write correct option) against each question If there is a contradiction in the bubble and hand written answer, bubble option will be considered corret.

A. 0
B. 2
C. 4
D.

• If y=f(x) then Notation was used for derivative by 
  

A. Lebnitz                           
B. Newton                      
C. Lagrange
D. Canchy

• If y=3x+4y+7=0 then
  

A.       
B.                                       
C. -                                                  
D.
 

A.

B.        

C.            

D.

• The expansion +……..is called 
  

A. Taylor Theorem    
B. Maclaum Theorem      
C. Binomial Theorem 
D. Fundamental Theorem

•  Let f be differentiable in neighborhood of c where =0 then f has relative maximum if
  

A.                     
B.                     
C.)         
D.

A.                 
B.    
C.       
D.

A. Sec x +c                        
B. Sec x tan x+c              
C. Ln(sec x + Tan x )+c    
D. Sec x+ Tan x +c

A. x                    
B.  
C.                          
D.

A. 0                                   
B. 1                                  
C.                                       
D.

• Area between x-axis and curve y=x2 from x=0 to x=1.is .
  

A. 0                                     
B. 1                                                      
C.       
D.

• What is order of differential equation
  

A. First order                 
B. 2nd order                                      
C. 3rd  order
D. 4th order

The condition for two lines 11.12 to bol r with slopes ml, m2 is

A. m₁= m₂
B. m₁m₂-1=0                                   
C. m₁m₂+1=0   
D. m₁+2m₂

The two lines ax² +.2hxy+by² =0 are imaginary if

A. h2> ab                          
B. h2< ab                                             
C. h2=ab   
D. None

X=5 is the solution of the Inequality

A. 2x-3>0                         
B. 2x+3<0                                         
C. x+4<0
D. x<0

• The centre of circle x²+y²+2gx+2fy+c=0 is
  

A. (h, k)                             
B. (-h,-k)                                             
C. (g, f)   
D. (-g,-f)

• The parabola x² =4ay (a>0) opens
  

A. Right side
B. Left side  
C. Up ward  
D. Down ward

• Length of Latus  Rectum of eillips

A.                                   
B.                                                       
C .    
D.

• Let u = 2i+3j and v=-i-j then u.v=
  

A. 6                                      
B. -6                                                     
C. 5                                      
D. -5

• 2ix2j.k=
  

A. 1                                    
B. 2                                                      
C. 3                                       
D. 4

Mathematics (Subjective)
Time Allowed: 2.30 hours 
paper-II
Section -

Answer briefly any EIGHT parts front the followings:-

• Find  if f(x)=Cosx and simplify
• If f(x)= find ‘c’ so that  exists.
• Define derivative of function f(x) at ‘x’.
• Find derivative of(x-5)(3-x) w.r.t. ‘x’
• Differentiate (1+x²)ⁿ w.r.t. x² 
• Prove that
• Find derivative of tanh(x²) w.r.t. ‘x’
• Find  if y=5
• Find
• Find y₂ if y=(2x+5)^3/2
• Expand  by Maclarin Series
• Find interval in which f(x)=x2+3x+2,x(-4,1) is increasing

Answer briefly any eight parts from the following

• Find  y and dy of y=x²+2x when x changes from 2 to 1.8
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Find the area below the curve y =3 and above the  x-axis between x=1 and x=4.
• Find the area below the curve y =3and above the x-axis betwe
• Solve the differential equation
• Graph the solution set of the linear inequality 2x > -3 in xy-plane.
•  Define feasible solution and optimal solution.

4 Answer briefly any NINE parts from the followings:

• Find the points trisecting the join of A(1,-4) B(6,2)
• Two points P & 0’ are given in xy-Coordinates system. Find the X,Y co-ordinates of P referred to the translated axes O’X & O’Y : P(3,2) , O’(1,3)
•  What do you mean by the constants used in
•  If 11⊥12; then show that m₁.m₂=-1.
•  Find the centre & radius of the circle x²-+y²+12x-10y=0
• Write down the equation of tangent to the circle.x²+y²=36 at (4,3)
•  Define ellipse.
• Find focus and vertex of the parabola y²=8x.
• Find the centre & Foci of the ellipse 4x²+y²=16
• Find the equation of Hyperbola having Foci (±5,0) vertex (3,0).
•  Find where  =-2i-7j , 6 ,=-i+j
• Find cosine of the angle between  and where ,
•  Find a unit vector ⊥to &;where = -i-j-k  ,

SECTION  II

Note: Attempt any three question

5. A.Evaluate  
B. If y=(Cos^-1x)², Prove that (I –x²)y₂-xy₁-2

6.A. Evaluate
B. Find the lines represented by 2x²+3xy-5y² = 0 and also find measure of angle between them.

7.A. Solve the differential equation.
B. Minimize Z=3x+y subjext to the constraints 3x+5y>15 ;x+6y>9
x>0  ; y>0

8.A. Find an equation of circle passing through A(-3,1) with radius 2 and centre at 2x-3y+3=0
B. If  find a unit vector parallel to 3

9.A. Find an equation of the Parabola with focus (2,5) , Directrix y =1
B. A force  + 31 acting at a point A (1, -2,1). Find the moment of force about the point B(2,0, -2).