ANSWERS ARE IN RED.
Q1. P and Q are the mid points of two chords (not diameter) AB and AC of a
circle with center O. OP and OQ lines are extended to points S and R
respectively, to touch the circle. In major arc T is another point between R and
S. Then if ∠BAC = 32° then ∠RTS = ?
Q2. A triangle is formed with x-axis and two lines having equations 2x +y = 4 and x- y + 1 = 0. Then if we take x-axis side as base then what will be the height of triangle?
(a) 2 unit
(b) 3 unit
(c) √5 unit
(d) 1 unit
Q3. ABCD is a cyclic quadrilateral. After extension side AB and DC meet at P and extended AD and BC meet Q. If ∠ADC = 85° and ∠BPC = 40°, then ∠CQD is?
Q4. ABC is a triangle. Angle bisectors of ∠A, ∠B and ∠C intersect the circumcircle at X, Y and Z respectively. If ∠A = 50°, ∠CZY = 30°, then ∠BYZ will be?
Q5. If A and B are complementary angles then sin A cos B + cos A sin B – tan A tan B + sec² A – Cot² B is equals to?
Q6. A tower is situated on a horizontal plane. If angle of elevations of top of the tower from two points at 9 ft and 16 ft distant from foot of the tower are complementary. Then height of the tower is?
(a) 9 ft
(b) 12 ft
(c) 16 ft
(d) 144 ft
Q7. The angle bisector of ∠A of a triangle ABC cuts BC at D and D meets circumcircle of ∆ABC at E. Then it is always true that AB.AC + DE.AE =
Q8. From top of a 100 m high tower a man sees a car at 30° angle of depression, after some times angle changes to 60°. The distance travelled by car during this period is
Q9. At a distance of 50 m from the foot of a pole. A shower is seen at 30° angle of depression from 1/3 height of the pole. Then the height of the pole is
(a) 150 m
(b) 150/√3 m
(c) 50/√3 m
(d) 50√3 m
Q10. There are two concentric circles with center O. The chord AB of external circle intersects the internal circle at C and D. If chord is 3 cm distant from center ; external and internal radii are 13 cm and 7 cm respectively. Then AC =?