Tiêu đề 15.RELATIONS AND FUNCTIONS -II.pdf ✅

15. RELATIONS AND FUNCTIONS II-MCQS TYPE (1.) Let A 1,3,4,6,9 =   and B 2,4,5,8,10 =   . Let R be a relation defined on A B such that R a , b , a , b = (( 1 1 2 2 ) ( )): 1 2 a b  and b a 1 2   . Then the number of elements in the set R is [11 APRIL 2023 (AFTERNOON)] (a.) 52 (b.) 160 (c.) 26 (d.) 180 (2.) Let A 1, 2,3, 4,5,6,7 =   . Then the relation R x, y A A : x y 7 =   + = ( )  is [08 APRIL 2023 (EVENING)] (a.) Symmetric but neither reflexive nor transitive (b.) Transitive but neither symmetric nor reflexive (c.) An equivalence relation (d.) Reflexive but neither symmetric nor transitive (3.) Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A B each having at least 3 and at most 6 elements is: [08 APRIL 2023 (MORNING)] (a.) 752 (b.) 772 (c.) 782 (d.) 792 (4.) Let f : 2,6 R R − →   be real valued function defined as ( ) 2 2 2 1 8 12 x x f x x x + + = − + . Then range of f is [31 Jan 2023(Evening)] (a.)  ) 21 , 0, 4     − −    (b.) ( ) 21 , 0, 4       − −    (c.) 21 21 , , 4 4         − −       (d.)  ) 21 , 1, 4     − −    (5.) If the domain of the function ( )   2 x f x 1 x = + , where  x is greatest integer  x , is 2,6) , then its range is [31 Jan 2023(Morning)] (a.) 5 2 9 27 18 9 , , , , 26 5 29 109 89 53       −       (b.) 5 2 , 26 5       (c.) 5 2 9 27 18 9 , , , , 37 5 29 109 89 53       −       (d.) 5 2 , 37 5       (6.) The domain of ( ) ( ) ( ) ( ) 1 2log log 2 , 2 3 e x x x f x x R e x + − =  − + is [29 Jan 2023(Morning)] (a.) R − − 1 3 (b.) (2, 3  ) −  (c.) (− − 1, 3  )   (d.) R −3