SAHIWAL Board 2017
INTERMEDIATE
PART-II (12th 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)
(B)
(C)
(D)  

(A)        
(B)        
(C)
(D)

•  is equal to:

(A)      
(B)     
(C)
(D)  

• = for n-1

(A)
(B)
(C)
(D)

(A)
(B)
(C)
(D)

(A)  
(B)         
(C) 2
(D) 2

• The derivative of at x = a is:

(A)      
(B)
(C)
(D)

• If f(x) = , then  (8) =

(A)
(B)
(C)
(D) 3

(A) (x)   
(B) (a)
(C)
(D)

•  where is measure in: 0

(A) Degree         
(B) Radian          
(C) Minutes        
(D) Second

• If f(x) = x², then domain of  is: 

(A) Real number           
(B) Integer         
(C) Rational number
(D) Irrational number

• Projection of  along is:

(A)
(B)
(C)
(D)

• is equal to:

(A)           
(B)           
(C) 1         
(D) 0

• The parabola y²= 4ax, a >0 opens:

(A) Right 
(B) Left    
(C) Upward        
(D) Downward

• Equation of circle with centre at origin and radius is:

(A) x²+y²=
(B) x²+ y²= 5       
(C) x²+ y²= 25    
(D) (x -3)²+ y²= 5

• (0,0) is the solution of inequality:

(A) 7x+ 2y> 3     
(B) x- 3y> 0
(C) x+2y<6         
(D) x+ 3y> 0

• If my and m₂ are slopes of two perpendicular lines, then:

(A) m₁ m₂+1 =0 
(B) m₁ m₂-1=0   
(C) m₁= m₂
(D) m₁= -m₂

• The distance between the points (0,0) and (1, 2) is:

(A) 0
(B) 1
(C) 2
(D)

• The x-component of appoint P(x,y) is called:

(A) ordinate
(B) Abscissa
(C) Coordinate
(D) Distance from origin

(A) In sec x + c
(B) In cosec x + c
(C) In sin x + c
(D) in cot x

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

SECTION-I

2. Write short answers to any Eight questions.

• Define identity function.
  
• Prove that Cosh2x –Sinh2 x = 1.
  
• Express the  in terms of e.
  
• Find if y=
  
• Differentiate Sin3x with respect to Cos2x.
  
• Differentiate tan3 Sec2 with respect to.
  
• Find  if y = Cosh-1 (Sec x) 0x.
  
• Find (x) if
  
• Find  ify=In(9-x2).
  
• Find  if x3-y3=a3
  
• Find if  Cos, Sin .
  
• Determine the Intervals in which  is increasing or decreasing = sin x

3. Write short answers to any Eight questions.

• Use differential to calculate Cos 29°.
  
• Evaluate
  
• Evaluate  
  
• Evaluate
  
• Evaluate          
  
• Evaluate       
  
• Evaluate
  
• Evaluate
  
• Find area below y = 3,, above x - axis between x =1 to x = 4
  
• Solve
  
• Find corner points of 2x - 3y6, 2x + 3y 12, x 0.
  
• Define objective function and linear programming.

4. Write short answers to any Nine questions.

• Convert the equation 4x + 7y — 2 = 0 in two intercepts form.
  
• Check whether the point (-2, 4) lies above or below the line 4x + 5y — 3 = 0.
  
• Find an equation of each of the lines represented by 20x2+ 17xy -24y2= 0
  
• Find the equation of the line through (-6, 5) with slope 7.
  
• Find an equation of the horizontal line through (7, 9).
  
• Find an equation of the circle with centre at (5, -2) and radius 4.
  
• Find the focus and vertex of the parabola (x—1)2=8(y+2).
  
• Find the centre and eccentricity of the ellipse 9x2+y2= 18
  
• Find the centre and vertices of the hyperbola
  
• Find a and b so that the vectors 3—+4 and a+-2 are parallel.
  
• Find a vector perpendicular to each of the vectors a =2—+ , 4+2-.
  
• Define work done by a force.
  
• Define scalar triple produce of three vectors

SECTION II

5. (a). Show that.   
(b). Differentiate w.r.t Sin-1

6. (a). Evaluate
(b). Find h such that the point A (,-1), B (0, 2) and C(4,-2) are vertices of right triangle with right angle at the vertex A.

7. (a). Evaluate tdt.
(b). Maximize 2x + 5y subject to the constraints 2y —x 8,x y4,x0,y.

8. (a). Find equation of circle passing thorough A (3, -1), B (0, 11) and having centre at 4x — 3y — 3 = 0
(b). Prove that the angle in a semicircle is a right angle.

9. (a). Find an equation of ellipse having the vertices (-1, 1), (5, 1) and Foci (4, 1) and (0, 1).
(b). Find volume of the parallelepiped for which given vectors are three edges.
,