If a₁, a₂, a₃, ....., be an A.P. of non-zero terms, prove that: \(\frac { 1 }{ { a }_{ 1 }{ a }_{ 2 } } +\frac { 1 }{ { a }_{ 2 }{ a }_{ 3 } } +......+\frac { 1 }{ { a }_{ n-1 }{ a }_{ n } } =\frac { n-1 }{ { a }_{ 1 }{ a }_{ n } } .\)

2

(a)

The angles of depression of top and bottom of tower as seen from the top of a 100m high cliff are 30⁰ and 60⁰ respectively.Find the height of the tower.

2

(a)

Draw a triangle PQR, with PQ = 4 cm, angle \(\angle\) Q = 60^o and the median PL = 3.6 cm. Draw another triangle PQ'R' similar to given triangle \(\Delta\)PQR, such that PQ' = \(\frac { 4 }{ 3 } \) PQ.

2

(a)

Construct a triangle whose perimeter is 13.5 cm and the ratio of the three sides is 2 : 3 : 4.

2

(a)

In the given figure, from each corner of a square ABCD, of side 4 cm, quadrant of a circle of radius 1 cm each is cut and a circle of radius 1 cm is cut from the centre. Find the area of the shaded region.

 

2

(a)

In the adjoining figure, PQR is an equilateral triangle inscribed in a circle of radius 7 cm. Find the area of the shaded region.

2

(a)

Calculate the area of the shaded portion of the figure alongside.

2

(a)

In the figure alongside, crescent is formed by two circles which touch at the point A, O is the centre of the point A, O is the centre of the bigger circle.If CB=9cm and ED=5cm, find the area of the shaded region.[Take \(\pi\)=3.14]

2

(a)

A vessel is in form of an inverted cone.Its height is 8cm and the radius of its top, which is open, is 5cm.It is filled with water up to the brim.When lead shots, each of which is a sphere of radius 0.5cm are dropped into the vessel, one-fourth of the water flows out.Find the number of lead shots dropped in the vessel.

2

(a)

From a group of 3 Girls and 2 Boys, two children are selected at random.Find the probability such that at least one boy is selected.

2

(a)