1. Find X and Y if
2. Show that A[sup]2[/sup] - 5A + 7I[sub]2[/sub] = 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.
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