Multan Board 2017
Mathematics
PART-II
Time: 30 Minutes
Note: Write answers to the questions on the objective answer sheet provided. Four possible answers A, B, C and D to each question are given. Which answer you consider correct, fill the corresponding circle  A, B, C and D given in front of each question with Marker or pen ink on the answer sheet provided.

• =:

•  =:

•  =:

• The degree of the differential equation  is:

1. 1
2. 2
3. 0
4. 3

• A linear equation in two variables represents:

1. Circle
2. Ellipse
3. Parabola
4. Straight line

• The slope of the line through the points  and  is:

1. 
2. 0
3. 1
4. 2

• Slope of a line

• the perpendicular distance of the line  from (0, 0) is:

1. 0
2. 1
3. 2
4. 3

•  is satisfied by:

1. (1, 1)
2. (1, 2)
3. (2, 3)
4. (-1, 1)

• The length of the diameter of circle x2 + y2- 6x + 8y = 0 is:

1. 4
2. 10
3. 13
4. 12

• The mid point of the line segment joining the foci of an ellipse is called:

1. Vertex
2. Centre
3. Directrix
4. Minor axis

• The angle between the vectors  and  is:

• Projection of  along  is:

•  2at are parametric equations of a:

1. Circle
2. Ellipse
3. Parabola
4. Hyperbola

•  (where a is constant) is:

•    =:

• If then y2:

SUBJECTIVE PART
SECTION B

Q 2. Write short answers to any EIGHT parts.

1. Define the term Odd and Even function.
2. Find Domain and Range of function = 
3. Evaluate
4. Differentiate
5. Find  if.
6. Find  if =
7. What is a Stationary Point?
8. Differentiate
9. Find if y – 2xyr + x2y + 3x = O. dx
10. Differentiate  
11. Find  If
12. Find the first two derivatives of Cos (ax + b).

Q 3. Write short answer to any EIGHT parts.

1. Using differential find  if  = 4.
2. Evaluate dx.
3. Evaluate dx.
4. Evaluate
5. Find
6. Evaluate dx
7. Evaluate dx.
8. Solve the differential equation.
9. Find the area below the curve y=3 and above the x— axis between x= 1 and x =4
10. Evaluate
11. Define Objective Function.
12. Graph the solution region of

Q 4. Write short answer to any SIX parts.

1. Find the slope and Inclination of the line joining the points (4, 6), (4, 8).
2. Find equation of the line bisecting the first and third quadrants.
3. Convert 2x —4y + 11 = 0 in slope intercept form.
4. Check whether the lines are concurrent
5. Find measure of angle of the lines represented by the equation 2x2+ 7xy + 2y2=0.
6. Find equation of circle with center (5, -2) and radius 4.
7. Find the Directrix of the parabola y2= 80.
8. Find equation of ellipse having Foci  and minor axis of length 10.
9. Find an equation of hyperbola having Foci  and e = 2.
10. State Parallel Vectors.
11. Find the unit vector in the direction of Vector.
12. Define Vector product of two Vectors.
13. Find constant a such that the vectors are coplana
    

                                                                       SECTION - C
Attempt any THREE questions. Each question carries 08 Marks.

Q 5.

1. If = discuss continuity at x = 2.
2. If  show that

Q 6.

1. Evaluate
2. Find equation of line through the point (2, -9) and Intersection of lines  and

Q 7.

1. Evaluate
2. Minimize  subject to constraints

Q 8.

1. Find an equation of the parabola whose focus is  and directrix is
2. Prove that in any triangle ABC b² = c² + a² -2caCosB by Vector Method.

Q 9.

1. Find the points of intersection of the conics 3x² + 5y² = 60 and 9x² + y² = 124.
2. Find the area of the triangle with vertices and  by using Vectors.