Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 8 - Real Numbers>Exercise>Q 25

MEDIUM

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IMPORTANT

Earn 100

If the H.C.F of $65$ and $117$ is expressible in the form of $65 m - 117$ , then the value of $m$ is

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Important Questions on Real Numbers

EASY

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 8 - Real Numbers>Exercise>Q 26

On dividing a positive integer

n

by

9

, we get

7

as remainder. What will be the remainder if

(3 n - 1)

is divided by

9

?

HARD

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 8 - Real Numbers>Exercise>Q 27

Use Euclid's division lemma to show that the cube of any positive integer is either of the form

9 m, 9 m + 1

or

9 m + 8

for some integer

m

.

HARD

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 8 - Real Numbers>Exercise>Q 28

Find the $HCF$ of the following using Euclid Division lemma.

$1860$ and $2015$

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 8 - Real Numbers>Exercise>Q 29

Show that any positive odd integer is of the form

6 q + 1

,

6 q + 3

, and

6 q + 5

, where

q

is some positive integer.