English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

If x⁵¹ + 51 is divided by x + 1, the remainder is ______.

By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x⁴ + 1; x – 1

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ – 2x² – 4x – 1, g(x) = x + 1

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ – 3x² + 4x + 50, g(x) = x – 3

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x³ – 12x² + 14x – 3, g(x) = 2x – 1

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ – 6x² + 2x – 4, g(x) = `1 - 3/2 x`

Check whether p(x) is a multiple of g(x) or not:

p(x) = x³ – 5x² + 4x – 3, g(x) = x – 2

Check whether p(x) is a multiple of g(x) or not:

p(x) = 2x³ – 11x² – 4x + 5, g(x) = 2x + 1

Determine which of the following polynomials has x – 2 a factor:

4x² + x – 2

Determine which of the following polynomials has x – 2 a factor:

4x² + x – 2

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)