English Medium Class 9 - CBSE Question Bank Solutions

For what value of m is x³ – 2mx² + 16 divisible by x + 2?

If the polynomials az³ + 4z² + 3z – 4 and z³ – 4z + a leave the same remainder when divided by z – 3, find the value of a.

The polynomial p(x) = x⁴ – 2x³ + 3x² – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.

Without actual division, prove that 2x⁴ – 5x³ + 2x² – x + 2 is divisible by x² – 3x + 2. [Hint: Factorise x² – 3x + 2]

If P(–1, 1), Q(3, –4), R(1, –1), S(–2, –3) and T(–4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are ______.

If P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the point(s) on the x-axis are ______.

In the following figure, coordinates of P are ______.

In the following figure, the point identified by the coordinates (–5, 3) is ______.

Write the coordinates of each of the points P, Q, R, S, T and O from the figure.

Plot the following points and write the name of the figure obtained by joining them in order:

P(– 3, 2), Q(– 7, – 3), R(6, – 3), S(2, 2)

Plot the points (x, y) given by the following table:

Plot the following points and check whether they are collinear or not:

(1, 3), (– 1, – 1), (– 2, – 3)

Plot the following points and check whether they are collinear or not:

(1, 1), (2, – 3), (– 1, – 2)

Plot the following points and check whether they are collinear or not:

(0, 0), (2, 2), (5, 5)

Which of the following points lie on y-axis?

A(1, 1), B(1, 0), C(0, 1), D(0, 0), E(0, – 1), F(– 1, 0), G(0, 5), H(– 7, 0), I(3, 3).

Plot the points (x, y) given by the following table. Use scale 1 cm = 0.25 units

Taking 0.5 cm as 1 unit, plot the following points on the graph paper:

A(1, 3), B(– 3, – 1), C(1, – 4), D(– 2, 3), E(0, – 8), F(1, 0)

Points A(5, 3), B(– 2, 3) and D(5, – 4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square.

From the figure, answer the following:

1. Write the points whose abscissa is 0.
2. Write the points whose ordinate is 0.
3. Write the points whose abscissa is –5.