NIMCET 2025 Paper

Section: Mathematics

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Question : 23 of 120

Marks: +1, -0

Let

A=\{1,2,3, . . ., 20\} .

Let

R ⊆ A × A

be defined as

R=\{(x, y): y=2 x-7\} .

Then the number of elements in

R

is equal to:

7
13
10
17

Solution:

For

(x, y)

to be in

A \times A

, both

x

and

y

must be in

\{1,2, . . ., 20\}

.
Given:

y=2 x-7

We need:

1 ≤ 2 x-7 ≤ 20

Solve:

1 ≤ 2 x-7 ⇒ 2 x ≥ 8 ⇒ x ≥ 4

2 x-7 ≤ 20 ⇒ 2 x ≤ 27 ⇒ x ≤ 13.5

So

x

can be integers from 4 to 13, inclusive.
That is:

13-4+1=10

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