If the sum of the first n terms of an A.P. is given by 3n²+5n, find the common difference of the A.P.

3

(a)

Show that A (6,4), B (4,- 3)and C (8,- 3) are the vertices of an isosceles triangle. Also, find the length of the median through A.

3

(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.

3

(a)

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig). Find the sides AB and AC.

3

(a)

In given figure, find the perimeter of \(\angle ABC\), if AP = 10 cm.

3

(a)

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

3

(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.

 

3

(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.

3

(a)

How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm X 11 cm X 12 cm?

3

(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.

3

(a)