English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

Express the following in the form `p/q`, where p and q are integers and q ≠ 0.

`0.bar6`

Express 0.99999 .... in the form `p/q`. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of `1/17`? Perform the division to check your answer.

Look at several examples of rational numbers in the form `p/q` (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Write three numbers whose decimal expansions are non-terminating non-recurring.

Find the remainder when x³ + 3x² + 3x + 1 is divided by x+1.

Find the remainder when x³ + 3x² + 3x + 1 is divided by `x - 1/2`

Find the remainder when x³ + 3x² + 3x + 1 is divided by x.

Find the remainder when x³ + 3x² + 3x + 1 is divided by x + π.

Find the remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x.

Find the remainder when x³ – ax² + 6x – a is divided by x – a.

Check whether 7 + 3x is a factor of 3x³ + 7x.

In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.

Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

1. ΔABD ≅ ΔBAC
2. BD = AC
3. ∠ABD = ∠BAC.

AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.

l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.