Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 65

EASY

10th Tamil Nadu Board

IMPORTANT

Earn 100

Find the average of first $100$ natural numbers.

Important Questions on Numbers and Sequences

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 1

A number when divided by

61

gives

27

as quotient and

32

as remainder. Find the number.

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 2

Prove that the product of three consecutive positive integer is divisible by

6

.

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 3

Prove that if a positive integer is of the form $6 q + 5,$ then it is of the form $3 q + 2$ for some integer $q,$ but not conversely.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 4

The sum of first $20$ odd natural numbers is equal to:

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 5

The value of

9^{\frac{1}{3}} \cdot 9^{\frac{1}{9}} \cdot 9^{\frac{1}{27}} . . . . .

upto infinity is

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 6

Show that any positive odd integer is of the form

6 q + 1

or

6 q + 3

or

6 q + 5,

where

q

is some integer.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 7

An army contingent of

616

members is to march behind an army band of

32

members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 8

Express $156$ as a product of its prime factors.