1. Suppose that a circle C has equation x^{2} + y^{2} 4x  6y + 9 = 0. What is the equation of the image of C after it has been reflected about the line l: y=x + 3? 

( x  1) ^{2} + ( y  4)) ^{2} = 4 

x^{2} + y^{2}  10y + 21 =0 

x^{2} + y^{2}  4x  6y + 9 = 0 

(x  2) ^{2} + (y  3) ^{2}=9 
2. If a translation T takes the point (1,3)to the point , then what is the image of the origin under T? 

(0,0) 

(2,3) 

(3,1) 


3. , for x > 1, then which one of the following is the inverse of f? 










4. a rectangular field of length 1 and width w meters for w < 1 has perimeter 400 meters. If a circular region of area w^{2} is to be reserved for office purpose , what should be the length of the field so that the area of the remaining region is maximum? 

150 meters 

120 meters 

50 meters 

100 meters 
5. f(x)=xe^{3x}cos(2x), then f ^{'}(0) is equal to 

0 

2 

6 

10 
6. You are given a data on the age of students, in a primary school. Age  8  10  11  12  13  Number of students  5  15  8  10  2  Which of the following is NOT true about the data? 

The median is 10.5 

The mode is 10 

The mean is 10.5 

The range is 5 
7. Let A and B 3x3 matrices such that Which of the following is equal to AB^{T}? 

400 

100 

1 

4 
8. Consider an airplane that flies in straight line from Addis Ababa to city X in a planned time. If it flies at a speed of 1000 km/hr, it will reach at X 30 minutes before the planned time. On the other hand, if it flies at 900 km/hr, it will reach there 20 minutes after the planned time. Which of the following is the distance between Addis Ababa and city X? 

8000km 

7250km 

8500km 

7500km 
9. Let What is the value of a if f is continuous at x =1? 

4 

0 

8 

2 
10. Consider a gate whose shape is a parabolic arch of height 3m and base width 3m as shown in the figure below. If the origin of the coordinate system is at the vertex, the equation that represents the edge of the gate is 

3y^{2}4x=0 

y=3x^{2}+1 

3x^{2}+ 3y = 0 

4X^{2}+ 3y = 0 
