Home
Class 12
MATHS
Let x,y,z be positive integers such that...

Let x,y,z be positive integers such that HCF(x,y,z)=1 and `x^(2)+y^(2)=2z^(2)`. Which of the following statements are true ?
I. 4 divides x or 4 divides y.
II. 3 divides x+y or 3 divides x-y
III. 5 divides `z(x^(2-y^(2)))`

A

I and II only

B

II and III only

C

II only

D

III only

Text Solution

Verified by Experts

The correct Answer is:
B
Take combination such as x=1,y=7,z=5
Now, check option
(ii) & (iii) statement are correct.
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-1 MATHEMATICS|20 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2 MATHMATICS|10 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part A - Mathematics|20 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

The HCF of x^(3)y^(2)z^(5) and x^(2)y^(4)z^(3) is

Let x and y be natural numbers. If x divides y, then x^3 divides y^3 . True or false.

x, y and z are distinct positive integers in which x and y are odd and z is even. Which of thefollowing can not be true ? (1) (x-z)^2 y is even (2) (x-z)^2y^2 is odd (3) (x-z)y is odd(4) (x-y)^2z is even

Let x, y and z be unit vectors such that abs(x-y)^(2)+abs(y-z)^(2)+abs(z-x)^(2)=9 Then abs(x+y-z)^(2)-4x.y=

Let x,y,z be real numbers satisfying x+y+z=3,x^(2)+y^(2)+z^(2)=5 and x^(3)+y^(3)+z^(3)=7 then the value of x^(4)+y^(4)+z^(4) is

XY - plane divides the line joining A(x_(1),y_(1),z_(1)) and B(x_(2),y_(2),z_(2)) in the ratio