New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 9

EASY

10th CBSE

IMPORTANT

Earn 100

Prove that one and only one out of $n, n + 2, n + 4$ is divisible by $3$ where $n$ is any positive integer.

Important Questions on Number System

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 10

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

4 q

or

4 q + 1

for some integer

q

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 11

Show that the square of any positive integer can not be of the form

6 q + 2

or

6 q + 5

for any integer

q

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 12

Show that the square of any positive integer can be of the form

6 q, 6 q + 1, 6 q + 3, 6 q + 4

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 13

Show that cube of any positive integer is either of the form

4 q, 4 q + 1, 4 q + 3

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 14

Show that square of any odd integer is of the form

4 q + 1

for some integer

q

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 15

HCF of $126 and 35$ is $H$ . If $H$ is expressed as $H = 126 \times A + 35 \times B$ , then prove that $\frac{A \times B}{H} = - 2$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 16

If the HCF of

210 and 55

is expressible in the form of

210 \times 5 + 55 \times A

, then find the value of

[2 - A]

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 1 - Number System>EXERCISE>Q 17

Find HCF of

81 and 237

. Express the HCF in the form of

237 \times p + 81 \times q

. Find the value of

(3 p + q)

.