Question

The lines xy = 0 and x + y = 17 from a triangle in the x-y plane. The total
number of points having co-ordinates which are prime numbers and life inside the triangle is
(a) 23
(b) 24
(c) 25
(d) 26​

Answer 1

26  co-ordinates are prime numbers and lie inside the triangle is

Step-by-step explanation:

x + y = 17

xy = 0

=> x axis & y - axis

point lies inside triangle

0 < x & y < 17

prime numbers

2   ,  3  ,  5   ,  7    , 11   , 13

also x + y < 17  ( to lie inside triangle)

(2, 2) , (2 , 3) , (2 , 5) , (2 , 7)  , (2 , 11) , (2 , 13)

(3, 2) , ( 3, 3)    ,(3 , 5) , ( 3 , 7) , ( 3 , 11) . ( 3 , 13)

(5 , 2) , ( 5 , 3)  , ( 5 , 5) , (5 , 7)  , (5 , 11)

(7 , 2 ) , (7 , 3)    ( 7 , 5) , ( 7 , 7)  

(11 , 2) , (11 , 3)  ,  (11 , 5)

(13 , 2) , (13 , 3)

26  co-ordinates are prime numbers and lie inside the triangle is