English Medium इयत्ता १० - CBSE Question Bank Solutions

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm²

Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm³. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of  Rs 1.4  per cm²?

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?

Prove that the points (−2, 5), (0, 1) and (2, −3)  are collinear.

The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Which point on the y-axis is equidistant from (2, 3)  and (−4, 1)?

The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).

If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.

Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

If G be the centroid of a triangle ABC, prove that:

AB² + BC² + CA² = 3 (GA² + GB² + GC²)

If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A  and B. 

We have a right angled triangle,`triangle BOA`  right angled at O. Co-ordinates are B (0,2b); A (2a, 0) and C (0, 0).

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.