MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 2

EASY

10th CBSE

IMPORTANT

Earn 100

Prove that the product of two consecutive positive integers is divisible by $2$ .

Important Questions on Real Numbers

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 3

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

6

.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 4

For any positive integer

n

, prove that

n^{3} - n

divisible by

6

.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 5

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.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 6

Prove that the square of any positive integer of the form

5 q + 1

is of the same form.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 7

Prove that the square of any positive integer is of the form

3 m

or,

3 m + 1

but not of the form

3 m + 2

.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 8

Prove that the square of any positive integer is of the form

4 q

or

4 q + 1

for some integer

q

.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 9

Prove that the square of any positive integer is of the form

5 q, 5 q + 1, 5 q + 4

for some integer

q

.

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 1 - Real Numbers>EXERCISE 1.1>Q 10

Show that the square of an odd positive integer is of the form

8 q + 1

, for some integer

q

.