Q1. At a distance of 15 meters from the foot A of a tower AB of height 8 meters and a flagstaff BC mounted on top of the tower AB subtends the same angle. Then find the height of the flagstaff?
Q2. A tower subtends angle α, 2α, 3α respectively at points A, B & C all lying in a horizontal line through the foot of the tower. Then
Q3. Ratio in which the x-axis divides the line segment joining (3, 6) and (4, -3) is
(a) 2 : 1
(b) 1 : 2
(c) 3 : 4
(d) 4 : 3
Q4. If the centroid of the triangle formed by the points (a, b) (b, c) & (c, a) is at the origin, then a³ + b³ + c³ =?
Q5. Find the area of trapezium having the length of parallel sides as 16, 23 and length of other two sides as 24 & 25 find the area of the trapezium?
(a) 468 sq. units
(b) 543 sq. units
(c) 453 sq. units
(d) 472 sq. units
Q6. Let be the line y = 2x in the two dimensional plane. The points (0, 1) and lie on
(a) same side of line
(b) opposite side of line
(c) on the line
(d) can’t be determined
Q7. In what ratio the y-axis divides the line segment joining the points P(-4, 5) and Q(3, 7)?
Q8. In a right angle triangle ABC having length of sides AB= 3cm, BC=4cm and CA=5cm. angle bisector of angle A, B and C cuts the sides BC, CA and AB at R, Q and P respectively. Find the area of triangle PQR?
Q9. Amit rows potatos in his backyard which is the shape of square. Each tree takes 1 cm². To increase his production he planted 279 more trees. Find the total no. of trees planted by him if the shape of farm remains a square?
Q10. A sphere of radius R is being cut by plane into two pieces at a certain distance ‘x’, from its centre such that the total area is 130% of the original area of the sphere. Find x = ?