In the given figure, ∠QRU = 72°, ∠TRS = 15° and ∠PSR = 95°, then what is the value (in degrees) of ∠PQR ?
(A) 40
(B) 85
(C) 55
(D) 60
In a polygon, the sum of the interior angles is double the sum of the exterior angles. What is the number of sides of the polygon?
(A) 4
(B) 8
(C) 6
(D) 5
2x+3y=10 has?
(A) No solution
(B) A unique solution
(C) Only two solutions
(D) Infinitely many solutions
If $$ {a={1+x\over 2-x}}$$, then find the value $$ {1\over {a+1}}+{2a+1\over{a^{2}-1}}$$ ?
(A) $$ {(1+x)(2+x)\over {2x-1}}$$
(B) $$ {(1-x)(2-x)\over {x-1}}$$
(C) $$ {(1+x)(2-x)\over {2x-1}}$$
(D) $$ {(1+x)(2-x)\over {2x+1}}$$
If $$ {8x\over{2x^{2}+7x-2}}=1, x>0,$$ then what is the value of of $$ {x^{3}+{1\over x^{3}}}$$ ?
(A) $$ {3\over 8}{\sqrt{17}}$$
(B) $$ {3\over 4}{\sqrt{17}}$$
(C) $$ {5\over 8}{\sqrt{17}}$$
(D) $$ {5\over 4}{\sqrt{17}}$$
A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30° with the ground. How high on the wall does the ladder reach?
(A) 10 m
(B) 17.32 m
(C) 34.64 m
(D) 30 m
From the top of a lamp post of height x metres, two objects on the ground on the same side of it (and in line with the foot of the lamp post) are observed at angles of depression of 30° and 60°, respectively. The distance between the object is $$ {32{\sqrt{3}{\ meter}}}$$. The value of x is:
(A) 54
(B) 36
(C) 48
(D) 45
An observer who is 1.62-meter-tall is 45 meters away form a pole. The angle of elevation of the top of the pole from his eyes is 30°. The height ( in meter) of the pole is closet to:
(A) 26.8
(B) 27.6
(C) 26.2
(D) 25.8
From a point 12 meter above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill 30°. What is the height ( in meter) of the hill?
(A) $$ {48\sqrt{3}}$$
(B) 36
(C) $$ {36\sqrt{3}}$
(D) 48
There are two towers on a horizontal plane. The top of one tower makes an angle of 60 degrees from the horizontal on the original floor of the second tower. And the top of the second tower makes an angle of 30 degrees from the horizontal on the original floor of the first tower. Find the ratio of the height of the Towers.
(A) 3: 1
(B) 2 : 3
(C) 3 : 2
(D) 4 : 1
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