12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. Find the diameter of each sphere.

If x = 2sin²Ɵ and y = 2cos²Ɵ + 1, then find x + y.

In a circle of diameter 42cm, if an arc subtends an angle of 60° at the centre where π=22/7, then what will be the length of arc.

Find the probability of getting a doublet in a throw of a pair of dice.

OR

Find the probability of getting a black queen when a card is drawn at random from a well-shuffled pack of 52 cards.

Case Study based-1

SUN ROOM

The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

• Four clear glass panels, trapezium in shape, all the same size

• One tinted glass panel, half a regular octagon in shape

(a) Refer to Top View

Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).

(i) (33/2,15/2)

(ii) (3/2,1/2)

(iii)(15/2,33/2)

(iv) (1/2,3/2)

(b) Refer to Top View

The distance of the point P from the y-axis is

(i) 4 (ii) 15 (iii) 19 (iv) 25

(c) Refer to Front View

The distance between the points A and S is

(i) 4 (ii) 8 (iii)16 (iv)20

(d) Refer to Front View

Find the co-ordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally.

(i) (8.5,2.0) (ii) (2.0,9.5) (iii) (3.0,7.5) (iv) (2.0,8.5)

(e) Refer to Front View

If a point (x,y) is equidistant from the Q(9,8) and S(17,8),then

(i) x+y=13 (ii) x-13=0 (iii) y-13=0 (iv)x-y=13