NIMCET 2024 Paper

Section: Mathematics

© examsiri.com

Question : 29 of 120

Marks: +1, -0

Let

Z

be the set of all integers and consider the sets

X= \{(x, y): x^2+2 y^2=3, x, y ∈ Z\}

and

Y=\{(x, y): x>y, x, y ∈ Z\}

. Then the number of elements in

X ∩ Y

is:

1
2
3
4

Solution:

The integers solutions of the equation

x^2+2 y^2=3

are

x^2=1

and

y^2=1

, the possible values of

(x, y)

are

(1,1),(1,-1),(-1,1)

, and

(-1,-1)

. Only in one case

x>y

, hence number of elements in

X ∩ Y

will be only one.

© examsiri.com

Go to Question:

Prev Question

Next Question