Q1. The angle of elevation of a bird at a particular instant from a point 200 m above a lake is found to be 30 degree and at the same instant the angle of depression of the bird’s reflection in the lake is found to be 60 degree. Find the height at which the bird is flying above the lake at the given instant. Q2. The internal angle of a polygon are in AP. The smallest angle measures 65 degree and the common difference is 18.75 degree. The number of sides of the polygon is Q3. A circular disc of diameter 2 √5 m is fixed horizontally at a height of 200 cm from the ground. The edge of the plate just touches a vertical wall. A point source of light is placed 400 cm vertically above the center of the plate. Find the length of the shadow of the plate along the edge where the wall meets the ground. Q4. A communication tower of height 10m is erected on the top of a building of height 30m. Find he distance of the point on the ground from the base of the building, at which the tower subtends the greatest angle. Q5. A window is in the shape of a rectangular with a semicircle above it. The diameter of the semicircle coincides with the upper side of rectangle. If the perimeter of the window is to be 357 cm, then find the radius of the semi-circular portion that maximizes the area of the window |
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Q5. A window is in the shape of a rectangular with a semicircle above it. The diameter of the semicircle coincides with the upper side of rectangle. If the perimeter of the window is to be 357 cm, then find the radius of the semi-circular portion that maximizes the area of the window
a. 45cm b.40cm
c. 50cm d. 54cm
Soln.
Perimeter 2(a+b) = 357
=>(a+b) = 178.5
Area wud be max when the diff between a & b will be min.
For option (a) a = 90cm. b = 88.5cm.
(a-b)=1.5 cm. This is minimum one.
So, i think (a)45cm. is correct one...
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n/a
Q5. A window is in the shape of a rectangular with a semicircle above it. The diameter of the semicircle coincides with the upper side of rectangle. If the perimeter of the window is to be 357 cm, then find the radius of the semi-circular portion that maximizes the area of the window
a. 45cm b.40cm
c. 50cm d. 54cm
i find the ans 54 but i cant upload image
perimeter =b+pi*b+2a=357 means b max so area max,
area at 45 5428.928571
40 5082.857143
50 5710.714286
54 5889.857143
Little Star
n/a
Q2. The internal angle of a polygon are in AP. The smallest angle measures 65 degree and the common difference is 18.75 degree. The number of sides of the polygon is
a. 8 b. 9
c. 10 d. 7
sum of interior angel of polygon=(n-2)*180=180n-360
means summation of angle divided by 180
sum=(n/2)(2*65+(n-1)18.75) if n=9 then (n-1)*18.75 became integer so if n=9 then
(9-2)*180=(9/2)(130+150) so ans is n=9
Little Star
Confusion is the part of Solution but remember Solution is also the part of Confusion
n/a
tan30 = 200/a
=> a = 200 √3
again a / (200+x) = tan 30
=> 200 √ 3 / (200 + x ) = 1/ radic 3
=>600 = 200 + x
=> x = 400
n/a
ans is (c)
20 radic 3
cot A =x/10+120/x
where A is the angle subtended at a point x from foot of tower
A to be maximum cotA will be min that happens at x = 20 radic 3
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