Short Answer TypeA line passing through the point A with position vector 
is parallel to the vector 
Find the length of the perpendicular drawn on this line from a point p with vector 
Three schools X, Y, and Z organized a fete (mela) for collecting funds for flood victims in which they sold hand-held fans, mats and toys made from recycled material, the sale price of each being Rs. 25, Rs. 100 andRs. 50 respectively. The following table shows the number of articles of each type sold:
School/Article School X School Y School Z
Hand-held fans 30 40 35
Mats 12 15 20
Toys 70 55 75
Using matrices, find the funds collected by each school by selling the above articles and the total funds collected. Also write any one value generated by the above situation.
Long Answer TypeSketch the region bounded by the curves 
and find its area using integration.
Consider the given equation. 
This equation represents a semicircle with centre at the origin and radius = 
Given that the region is bounded by the above semicircle and the line 
Let us find the point of intersection of the given curve meets the line 
Squaring both the sides, we have,
Consider the following figure
Thus the intersection points are 1,2 and 2,1 ( ) ( ) Consider the following sketch of the bounded region.
Required Area, 
Find the particulars solution of the differential equation 
given that y =1 when x = 1.
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