In a potato race, a bucket is placed at the starting point, which is
5 m from the first potato and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (as shown in figure)

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are dropped in the bucket.

(i) What is distance run to pick up the 1^st potato?

(a) 8 m

(b) 10 m

(c) 12 m

(d) 9 m

(ii) What is the distance run to pick up the 2^nd potato?

(a) 12 m

(b) 15 m

(c) 16 m

(d) 14 m

(iii) What is the distance run to pick up the 3^rd potato?

(a) 22 m

(b) 18 m

(c) 21 m

(d) 15 m

(iv) What is the distance run to pick up the 4^th potato?

(a) 26 m

(b) 30 m

(c) 25 m

(d) 28 m

(v) What is the total distance run by the competitor?

(a) 370 m

(b) 350 m

(c) 355 m

(d) 375 m

Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in given figure.

(i) Find the radius of each circular tile having diameters 50 cm .

(a) 1 m

(b) 0.75 m

(c) 0.50 m

(d) 0.25 m

(ii) Find the area of rectangle having dimensions 5 m × 4 m.

(a) 17.5 m²

(b) 15 m²

(c) 21 m²

(d) 20 m²

(iii) Find the area of each circular tiles.

(a) 0.15 m²

(b) 0.251 m²

(c) 0.196 m²

(d) 1.80 m²

(iv) Find the area of floor that remains uncovered with tiles

(a) 4.32 m²

(b) 1.85 m²

(c) 3.73 m²

(d) 2.87 m²

(v) A line segment joining the centre and a point on the circle is called its …..

(a) diameter

(b) radius

(c) chord

(d) arc

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which approaching the foot of the tower with a uniform speed. Six seconds later; the angle of depression of the car is found to be 60°.

(i) Find the time taken by the car to reach the foot of the tower from point D to B.

(a) 2 sec

(b) 3 sec

(c) 6 sec

(d) 4 sec

(ii) Write the value of 30^o.

(a) 2/3

(b) 3/2

(c) 1/3

(d) 3

(iii) Write the value of cosec 60^°.

(a) 3

(b) 2/3

(c) 3/2

(d) 1/3

(iv) The line drawn from the eye of an observer to the point in the object viewed by the observer.

(a) Horizontal time

(b) Vertical line

(c) Line of sight

(d) Parallel lines

(v) If the two lines are parallel; then the alternate opposite angles are …..

(a) different

(b) equal

(c) opposite

(d) None of these

An aeroplane leaves an airport and flies to north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and files to west at a speed of 1200 km/hr.

(i) Find the distance covered by first plane in the north direction after 1¹/₂ hours?

(a) 1500 km

(b) 1600 km

(c) 1400 km

(d) 1300 km

(ii) Find the distance covered by second plane in the west direction after 1¹/₂ hours

(a) 1700 km

(b) 1800 km

(c) 1900 km

(d) 2000 km

(iii) How far apart will be the two planes after 1¹/₂ hours?

(a) 300 59 km

(b) 300 63 km

(c) 300 61 km

(d) 300 65 km

(iv) The triangle having an angle of measure 90° is called .............. angle triangle.

(a) Right

(b) obtuse

(c) acute

(d) None of these

(v) If a line is drawn parallel to one side of a triangle to intersect the other two sides indistinct points; the other two sides are divided in the same ratio. This theorem is known as:

(a) Basic Proportionality

(b) Converse of Thales theorem

(c) Pythagoras theorem

(d) Similarity of triangles

Calculate the perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

OR

The point which divides the line segment joining the points (7, - 6) and (3, 4) in ratio 1:2 internally lies in which quadrant?