Bahawalpur 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

• If f = xy is a function, then x is called:

(A) Domain        
(B) Range
(C) Function      
(D) Dependent Variable

• x is equal to:

(A) e^-1      
(B) e         
(C) e²
(D) e³

• (ax + b)ⁿ is equal to:

(A) n (ax^n-1+ b)   
(B) n (ax+ b)^n-1   
(C) nax^n-1
(D) na (ax + b)^n-1

• tan^-1x =……………….:

(A)
(B)
(C)    
(D)

• If y = e^2x, then y² is equal to:

(A) e^2x      
(B) 4e^2x    
(C) 2e^2x    
(D) 8e^2x

•  Cos h x is equal to:

(A) Sin h x           
(B) -Sin h x         
(C) Cosec h x      
(D) Cot h x

•  (In f (x)) is equal to:

(A)         
(B)
(C)
(D) f (x) . f’ (x)

• :

(A) -2Sin2x + C  
(B) 2Sin2x          
(C) -        
(D)   + C

(A) e^x-Cos x        
(B) e^x + Sin x + C
(C) e^x + Cos x + C          
(D) Cos x + C

(A) + C
(B) + C
(C)
(D) ax, Ina + C

(A) In (e^x+2) +C
(B) In (e^x + 3)     
(C) In (e^x - 2) + C
(D) In (e^x- 3) + C

• The distance between two points A (x₁ ,y₁ ), B(x₂, y₂)

(A) (x₂- x₁)²+ (y₂ – y₁)²
(B)
(C)
(D)

• Slope of the line passing though the points A(x₁, y₁) and B(x₂,y₂) is:

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

• Point Slope from the equation of line is:

(A) y = mx + c
(B) y + y₁ = m(x + x)
(C) y + y₁ = m (x + x₁)
(D) y –y₁ = m (x – x₁)

• General form of the equation of line is:

(A) ax - by + c = 0
(B) ax + by - c = 0
(C) ax + by + c = 0
(D) ax - by- c = 0

• ax + by < c is a linear inequality in:

(A) Four Variable
(B) Three Variable
(C) One Variable
(D) Two Variable

• x² + y² = r² is the equation of circle with centre:

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

• The length of the Latus Rectum of the Ellipse = is:

(A)
(B)
(C)
(D) 2ab

• The position vector of a point P (-1, 2, 3) is:

(A) +2+ 3
(B) +2+ 3
(C) -2-3
(D) -2-3

•  is equal to:

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

Bahawalpur Board 2017
INTERMEDIATE
PART-II (12th CLASS)
Mathematics (NEW SCHEME)
TIME ALLOWED: 2.10 Hours
MAXIMUM MARKS: 60
SUBJECTIVE
SECTION-I

1. Attempt any Eight of the following. All carry equal marks.

• Determine whether the given unction is Odd or Even f(x) =
  
• Define Limit of function f.
  
• Find Domain and Range of function g (x) = 1 x -3
  
• Find Derivative of  at x = 8.
  
• Differentiate w.r.t. x
  
• Find  if x = 1- t² and y = 3t²- 2t³.
  
• Find  if y2+ x2- 4x = 5.
  
• Differentiate between w.r.t x x² Sec 4x.
  
• Differentiate in (x² + 2x) w.r.t. x.
  
• Findif x=y Sin y.  
  
• Find if y =
  
• State Maclaurin's series Expansion.     

3. Write short answers to any Eight questions.

• Find y if y =  when x changes from 4 to 4.41.   
  
• Evaluate          
  
• Evaluate        
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Solve  
  
• Graph the Solution Set of x + 2y <6.
  
• Indicate the Solution Set of x+ y 
  
• Evaluate  

4. Write short answers to any Nine questions.

• Find area of triangle whose vertices are A (1, 4), 8(2, -3), C (3, -10)
  
• Find pair of lines represented by 2x²+ 3xy-5y2² = 0
  
• Find equation of the line through (3,-2) and perpendicular to line with sloe
  
• Find equation of line through (3, -2) and (2, 7).
  
• Check whether the lines 3x-4y-3 = 0, 5x+ 12y + 1 = 0, 32x + 14y - 17 = 0 are concurrent or not.
  
• Find Centre and Radius of x²+ y²-6x + 4y + 13 = 0
  
• Find Focus and Vertex of the Parabola (x - 1)² = 8 (y + 2).
  
• Find the Centre and Foci of the Ellipse 25x² + 9y² = 225     
  
• Find Eccentricity and Foci of the Hyperbola
  
• Find Unit Vector and Direction Cosines of
  
• Find so that
  
• Find Projection of along if +-,
  
• Find the value of [ ].

(SECTION II)

5. (a). Prove that =
(b). If x=Sin, y=Sin m

6. (a). Evaluate  
(b). Find a joint equation of the Straight Lines through the origin perpendicular to the lines represented by x²+ xy - 6y²= 0  

7. (a) Evaluate
(b) Minimize f(x , y) = 2x +y Subject to the Constraints x +y 3    7x+5y 35; x0

8. (a) Write an equation of the Parabola with given elements Focus (-3 , 1) and Directrix x = 3
(b) Show that Mid-Point of Hypotenuse a right triangle is equidistant from its vertices.       

9. (a). Write Equation of the Tangent to the give conic at the indicated point. 3x² = -16y at the points whose ordinate is -3.
(b). Find Volume of the Tetrahedron whose vertices are A(2 , 1 , 8) , B(3 , 2 , 9) , C(2, 1, 4) and D(3 , 3, 10)