CBSE Important Questions

Maths Test - 2 SA (II)

TIME 1.30 Hrs. M.M.30

1. Using distance formula, prove that the points (0, 0), (2,3) & (6,9 lie on a straight line.
2. Find the ratio in which the line segment joining the points A (1, - 5 ) and B ( - 4, 5 ) is divided by the x-axis. Also find the coordinates of the point of division.
3. The line segment joining the points (-6,8) & (8,-6) is divided into 4 equal parts. Find the coordinates of the points of section.
4. From the top of a 7m high building, the angle of elevation of the top of a tower is 600 & the angle of depression of the foot of the tower is 300. Find the height of the tower.
5. The angle of elevation of jet fighter from a point on the ground is 600. After a flight of 15sec. the angle of elevation changes to 300.If the jet is flying at a speed of 720km/hr, find the constant height at which the jet is flying.
6. The angle of depression of the top & bottom of a tower, as seen from the top of a 100m high cliff, are 300 & 600 respectively. Find the height of the tower.
7. The circumference of a circular plot is 220m. A 14m wide track runs around outside the plot. Find the area of track.
8. The inner circumference of a circular track is 440m. The track is 14cm wide. Find the cost of leveling it at 20 paise/sq m. Also find the cost of putting up a fencing along outer circle at Rs2/m.
9. A playground has the shape of a rectangle with two semi-circles on its smaller sides as diameter added to it outside. If the sides of the rectangle are 36m & 24.5m, find the area of the playground.
10. If the 21st term of an A.P. is 25, find the sum of its first 41 terms.
11. The first term of an A.P. is 5, the last term is 45 & the sum is 400. Find the number of terms & the common difference.
12. A rectangular field is 20m long & 14m wide. There is a road of equal width all around it. It the area her boat at 5km/h in still water. If she takes 1 hr more to row the of the road is 72sq m, find the width of the road.
13. Meeta can row her boat at 5km/hr in still water. If she takes 1hr more to row the boat 5.25km upstream than to return downstream, find the speed of the stream.
14. For what value of k does (k- 12) x² +2(k-12) x + 2 = 0 have equal roots?
15. Solve for x each :
    (a) x² – 8x + 16 = 0
    (b) 2x² + (p² – q²)x q² = 0