Gujranwala Board 2017
INTERMEDIATE (12th CLASS)
PART-II
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(x) = sin s + cos x, then f(x) + f(-x) is equal to:

(A)       2sinx 
(B)       2 cos x          
(C)       0         
(D)      -2 cos x

 is equal to:

(A) na
(B) 0
(C) 1
(D) α

• Derivative of (x³ +1)⁹ w.r.t x³ equals:

(A) 9(x³ + 1)⁸
(B) 27x² (x³+ 1)⁹
(C) 3x² (x³ + 1)⁸
(D) 27x² (x³+ 1)⁸

•  is equal to:

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

•  sec x is equal to:

(A) sec² x
(B) tan² x
(C)
(D) tan x sec x

•  is equal to:

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

• a^f(x) equals:

(A) a^f(x) f’(x)
(B) a^f(x) f’(x).a
(C) a^f(x) f’(x)na

• dx is equal to:

(A) 2 + c
(B) -2
(C) +c
(D) +c

• dx is equal to:

(A)
(B)
(C) + c
(D)

•  equals:

(A)
(B)
(C) +c
(D) +c

•  equals:

(A) + c
(B) -+ c
(C) + c
(D) +c

• Slope of line parallel to x-axis is:

(A) -1
(B) 0
(C) 1
(D) 90°

• The mid-point divides the line segment in the ratio:

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

• The lines a₁x+ b₁y + c₁ = 0, a₂x +b₂y+c₂ = 0 are perpendicular if and only if:

(A) a₁b₂+ a₂b₁ = 0
(B) a₁a₂ - b₁b₂ = 0
(C) a₁a₂ + b₁b₂ = 0
(D) a₁b₂ = a₂b₂

• The point of intersection of altitudes of a triangle is:

(A) centroid
(B) orthocenter
(C) e-center
(D) circumcentre

• The feasible solution that maximizes or minimizes the objective function is:

(A) solution
(B) optimal solution
(C) minimum solution
(D) maximum solution

• The end points of minor axes of ellipse are:  

(A) foci    
(B) vertices        
(C) covertices    
(D) centre

• x² = y² + 1 represents       

(A) circle 
(B) ellipse           
(C) parabola      
(D) hyperbola

• Projection of  along  is equal to:       

(A) ,     
(B)      
(C)
(D) ,

• If vectors  and  have the same direction, then . is equal to:

(A) ab
(B) ab cos
(C) ab sin
(D) —ab

Gujranwala Board 2017
INTERMEDIATE PART-I (12th CLASS)
MATHEMATICS (NEW SCHEME)
(COMMERCE GROUP)
TIME ALLOWED: 2.10 Hours
MAXIMUM MARKS: 60
SUBJECTIVE
SECTION-I

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

• f (x) = x² —x then find f(x — 1)  
  
• f (x) = x³— x. Determine whether the f(x) is even or odd. 
  
• Evaluate
  
• Define the derivative, y = f(x) w.r.t ‘x’.
  
• Differentiate w.r.t. 'x’
  
• Find if xy+y²= 2
  
• Find f’(x) if f(x)=x³ e^1/x
  
• Find   If y = x²  
  
• Find y₂ If y=x².e^-x
  
• Differentiate w.r.t. ‘x’x⁴+ 2x³ + x²
  
• Differentiate w.r.t. ‘x’ cos-1      
  
• Find f' (x) If f (x) =n (ex + e-x )

3. Write short answers to any Eight questions.

• Find dy, when y = x2— 1 , and x changes from 3 to 3.02.  
  
• Evaluate   
  
• Evaluate
  
• Evaluate  
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Find the area between x-axis and the curve y = cos  from  = —  to  
  
• Solve the differential equation sin y cosec x =1
  
• Evaluate
  
• Define objective function.
  
• Graph the solution set of inequality 3x+7y 21.

4. Write short answers to any Nine questions.

• Find the coordinates of the point that divides join of A(-6 , 3) and B(5 , -2) in ratio 23 extend.         
  
• Using slopes, show that the triangle with vertices A (6, 1) , B(2, 7) and C(-6, C)-6,-7) is right train.   
  
• Find an equation of line through (-4, -6) and perpendicular to a fine having slope
  
• Convert the equation 15y -8x + 3 = 0 into two-intercept form.
  
• Check whether the lines are concurrent. x+3y-2=13 , 2x-y+4=0 , x-11y+14.0
  
• Find equation of circle with centre at (5, -2) and radius 4.
  
• Find focus and vertex of parabola x2 = 5y      
  
• Find the foci of equation of ellipse += 1  
  
• Find eccentricity of hyperbola with equation += 1
  
• Define parallel vectors.   
  
• Find the direction cosines of the vector 6-2
  
• What is scalar triple product of three vectors? Write down determinant formula of scalar triple product.          
  
• Find  such that the vectors -2-3&3 are coplanar.

SECTION-II

NOTE: - Attempt any three questions.

5. (a). Prove that
(b). Find  Ifx= +-, y= +1

6. (a). Evaluate
(b). Find the point three-fifth of the way along the line segment from A(-5, 8) to 6(5, 3).
7. (a). Evaluate
(b). Find the minimum and maximum value of f(x , y) = 4x+ 5y under the constraints 2x -3y 6      2x + y2       2x + 3y 12  x0, y0

8. (a).Find length of tangent from point P(x₁,y₁) to circle x₂ + y₂ + 2gx + 2fy + c = 0
(b) By vector method, prove that angle inscribed in a semi-circle is right angle.

9. (a). Find an equation of the hyperbola with foci (5 , -2), (5 , 4) and one vertex (5, 3).
(b). Prove by vector method: sin ()= sin  cos  + cos  sin