Sargodha Board 2017
INTERMEDIATE PART-I (11th CLASS)
Mathematics (NEW SCHEME)
TIME ALLOWED: 20 Minutes
MAXIMUM MARKS: 15
OBJECTIVE
Note: You have four chokes 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 circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not salve question on this sheet of OBJECTIVE PAPER.

Q.No.1

• A function I: XX of the form I(x) = X is called

(A) Linear fn.   
(B) Constant fa.
(C) Identity fn. 
(D) Even fn.

(A) 2
(B) 0       
(C)
(D)

• =

(A) 4x
(B) 4x^1/3
(C) x⁴
(D) 4x^-1/3

(A) f’(g(x))
(B) f(g’(x))
(C) f(g(x),g’(x)
(D) f’(g(x),g’(x)

(A) ax In a
(B)
(C) a^x In e
(D) -a^x In e

•  (tan h-1 x) =

(A)   
(B)
(C)
(D)

• Let " f " be differential function in neighbourhood of "c" where '(c)=0, then "f " has relative maxima at x = c if:

(A) f"(c)= 0      
(B) f"(c)>0       
(C) f" (c)< 0     
(D) f" (c)does not exist

• (x +)

(A) f’(x) dx      
(B) f(x)-f’ (x) dx
(C) f(x)+f’ (x) dx       
(D) -f’(x)-dx

(A) 
(B)
(C)       
(D)

• When the expression  involve in integration, we substitute:

(A) x= a coses
(B) x= a tan
(C) x= as sec 
(D) x= a sin

• Applying initial value conditions in solution of differential Equations, we substitute:

(A) General solution  
(B) Particular solution
(C) No solution
(D) Infinite solutions

• Location of Point P(x,y) for which x = y is in the quadrants:

(A) 1st and 3rd 
(B) 2nd and 4th
(C) 1st and 2nd
(D) 3rd and 4th

• Centroid of a ABC is a Point that divides each median in the ratio

(A) 1:1    
(B) 3:2    
(C) 2:1
(D) 2:3

• x cos  + y sin  = P is a Point that divides each median in the ratio:

(A) Slope – intercept  
(B) Two–intercepts
(C) Point–slope form
(D) Normal form

Two lines represented by ax²+2hxy+by²=0 are Perpendicular of:

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

• The solution set of an inequality ax + by <0 is

(A) Open half plane   
(B) Closed half plane
(C) Circle
(D) Parabola     

• Parabola having Equation x² = 4ay opens:

(A) Towards left
(B) Towards right      
(C) Upwards    
(D) Downwards

• Vertices of ellipse with equation x²+ 4y² = 16 are:

(A) (±4, 0)        
(B) (0, ± 4)       
(C) (±2, 0)        
(D) (0, ±2)

• The vectors  and  are parallel if angle between them is:

(A)    
(B)
(C)    
(D)

•   is formula to calculate:

(A) Areal of triangle   
(B) Area of Parallelogram
(C) Volume of Parallelepiped
(D) Volume of Tetrahedron

SARGODHA BOARD
Note: Section I is compulsory. Attempt any Three questions from Section II
and any Two parts from Section III.

2.       Write short answers to any Eight questions.

• Express the volume V of a cube as a function of the area A of its base.
  
• )= + 6,Determine whether the f (x) Is even or odd.
  
• Evaluate Lim
  
• Define the derivative w.r.t. x.   
  
• Differentiate w.r.t. x {x —5} {3— x}.
  
• Differentiate w.r.t. x -1  
  
• Find if y = x2 In  
  
• Find  if y = x esin x
  
• Find y₂ if y= (2x + 5)1/2
  
• What is the decreasing function.
  
• State the Maclarin's Series Expansion.
  
• Find if y= In

3. Write short answers to any Eight questions.

• Evaluate  
  
• Evaluate  
  
• Evaluate
  
• Evaluate
  
• Evaluate  
  
• Evaluate  
  
• Find  
  
• Find
  
• Solve  
  
• Evaluate
  
• Define feasible region and feasible solution.
  
• Define optimal solution.

4. Write short answers to any Nine questions.

• Find the point three-fifth of the way along the line segment form A(-5 , 8) to B(5 , 3).
  
• By mean of slopes show that Points (4, -5), (7, 5), (10, 15) are collinear.
  
• Find an equation of line through A(-6 , 5) having slope 7.
  
• Find equation of line through (5, -8) and perpendicular to the line with slope 3/5.   
  
• Find the distance from the point (6,-1) to the line 6x -4y + 9 = 0.
  
• Find the centre and radius of the circle with equation 4x2 + 4y5 - to + 12y -25 = 0.
  
• Find focus and vertex of x2= -16y
  
• Find eccentricity of ellipse = 1
  
• Define vertices and co-vertices of an ellipse.
  
• Find  so that vectors  = 2+ and  =  ++ 4are perpendicular.
  
• If  is a vector for which = 0 = 0 = 0 find.
  
• Find a unit vector perpendicular to both  = 2-6-3  =4+3- 
  
• Prove that x(+)+x(+)+ x()= 0

SECTION-----------II

Note: Attempt any three questions.

5. (a) Evaluate
(b) Differentiate cos  w.r.t x from first principle.    

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

7. (a) Solve the differential equation
(b) Graph the feasible region of the following system of linear inequalities also find comer points.

8-(a)  Find focus, vertex and directrix of ²
(b) Prove that the line segment joining the mid points of two sides of a triangle is parallel to the third side and half as long.

9. (a) Find the points of intersection of the conics 2and 2 .
(b) Prove that sin()= sin cos-cos sin by vectors method