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.

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.

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.

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

Case Study Based- 3

Applications of Parabolas-Highway Overpasses/Underpasses

A highway underpass is parabolic in shape.

Parabola

A parabola is the graph that results from p(x)=ax²+bx+c

Parabolas are symmetric about a vertical line known as the Axis of Symmetry.

The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the Vertex

(a) If the highway overpass is represented by x² – 2x – 8. Then its zeroes are

(i) (2,-4) (ii) (4,-2) (iii) (-2,-2) (iv) (-4,-4)

(b) The highway overpass is represented graphically.

Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial

(i) Intersects x-axis

(ii) Intersects y-axis

(iii) Intersects y-axis or x-axis

(iv)None of the above

(c) Graph of a quadratic polynomial is a

(i) straight line

(ii) circle

(iii)parabola

(iv)ellipse

(d) The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is

(i) x² – 6x + 2

(ii) x² – 36

(iii)x² – 6

(iv)x² – 3

(e) The number of real zeroes that polynomial f(x) = (x – 2)² + 4 can have is:

(i)1

(ii) 2

(iii) 0

(iv) 3