English Medium Class 9 - CBSE Question Bank Solutions

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm².

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

The expression 2x³ + ax² + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.

The polynomials ax³ + 3x² – 3 and 2x³ – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.

When divided by x – 3 the polynomials x³ – px² + x + 6 and 2x³ – x² – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

How many pairs of adjacent angles are formed when two lines intersect in a point?

In the below fig, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ − 5 : 7,
find all the angles.

In the below fig, lines �1 and �2 intersect at O, forming angles as shown in the figure. If x = 45, Find the values of x, y, z and u.

In the below fig, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.

Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.

If one of the four angles formed by two intersecting lines is a right angle, then show that
each of the four angles is a right angle.

In the below fig, rays AB and CD intersect at O.
 Determine y when x = 60°

In the below fig, rays AB and CD intersect at O

Determine x when y =40

In the below fig, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF,
∠DOE and ∠BOF.

Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.

If l, m, n are three lines such that l || m and n ⊥ l, prove that n ⊥ m.

Plot the following point on the graph paper:

 (0, 0)

Write the coordinates of each of the following points marked in the graph paper: