1. Find X and Y if

and

.

2. Show that A² - 5A + 7I₂ = 0 if

.

3. Find the variance of the following data:-

Variable          10       6         18        14        22        2
Frequency       10       7          7         15        6         5

4. The probability that a student passes English test is

, the probability that he passes both English and French tests is

; the probability that he passes atleast one test is

.  What is the probability that he passes the French test?

5. Determine 'a' so that the points (a,a), (2,3), and (4,-1) are collinear.

6. The vertices of a triangle ABC are A(1,2), B(-4,5), and C(0,1). Find the slope of the altitudes.

7. Find the length of the segment joining the point (3,4) and the point of intersectionof the lines 5x+y-6 = 0 and 2xy-3 = 0.

8. In triangle ABC, the equation of AB is x-2y+8 = 0, that of BC is x-3y+10 = 0 and the equation of AC is x-y+2 = 0. Find the centroid.

9. Show that

.

10. Find the length of a side of a regualr polygon in centimeters inscribed in a circle of radius 1 meter if it has 24 sides.