A motor boat whose speed is 24km/h in still water takes 1 hour more to go 32 km upstream than no return downstream to the same spot. Find the speed of the steam.

4

(a)

If the pth terms of an AP is \(\frac{1}{q}\) and the qth term is \(\frac{1}{p}\), show that the sum of pq terms is \(\frac{1}{2}\) (pq + 1).

4

(a)

Check graphically, whether the following pair of linear equations is consistent. If yes, solve it graphically.
2x-y=0, x+y=0

4

(a)

Solve the following pair of linear equations graphically:
2x + 3y = 12 and x - y = 1.
Find the area of the region bounded by the two lines representing the above equations and Y-axis.

4

(a)

A ladder 17 m long, reaches at a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.

4

(a)

In the right triangle, B is a point on AC such that AB + AD = BC + CD. If AB = x, BC = h and CD = d, then find x (in term of h and d).

4

(a)

Show that \(2(\sin ^{ 6 }{ \theta } +\cos ^{ 6 }{ \theta } )-3(\sin ^{ 4 }{ \theta } +\cos ^{ 4 }{ \theta } )+1=0.\)

4

(a)

The angle of elevation of a cloud from a point 120 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

4

(a)

The following table gives the daily income of 50 workers f a factory

Daily income (in Rs)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Find the mean, mode and median of the above data .

4

(a)