32. Let ab.c, e R. If f) =ae + br+e is such that 39. Ir :RR...

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32. Let ab.c, e R. If f) =ae + br+e is such that 39. Ir :RR is given by f)= a+b+c=3 and fx+y) f(x)+f0)+ xy.Vx.ye R. 1995 19961996 1) 997.5 2) 998 then 1996 10 then s equal to: 3) 997 4) 998.5 40. Let f(a)-2"+l and g(a)-3"-1. If (fog)(x)-x, then x is equal tor 1) 255 2) 330 3) 165 4) 190 33, Let f: R R and g: RR be two one-one and onto functions such that they are the mirror 1-20 1) 3-2-10 1-3 2) images of each other about the line y=a If h(x)= 2-1 4) 2-3 3) fix) + g(x), then h(x) is 30-20 1) one-one onto 2) one-one into JEB MAINS-2017) 3) many one-onto 4) many one into 41. The function :R defined as 34. Let flr) = (Ik]2 - Sk] +4)x3 -(6|k)2 -5 (k) + 1)x- (tan x) (sgn (x)), be an even function for all, xeR where [. denotes G.LF and -) denotes fractional part function. Then the sum of all possible values of "k is 1) neither injective nor surjective 2) invertible. 17 1) 31 2) 35 53 4) 6. 3) injective but not surjective. 4) surjective but not injective. 35. Let A= |1, 2, 3.41.The number of functions 42, The domain of the function f:AA satisfying f))=rfor all ISRS4IN 2) 6 3) 9 1) 1 4) 10 1) 10,1.2,3. 3) (0,) 2){1,2,3.) 36. Let f(x)= ax 2013 +esin 3x+20 where 4) (0,1) a. b, e are non- zero constants. If f-2014)= 36, then the value of f(2014) is equal to 1) 1 ANSWERS 2) 2 3) 3 4) 4 1)1 2) 3 3) 1 4) 1 5) 1 6) 2 7) 1 8) 1 9) 4 10) 2 37. f:RR where f(x) = ax + cos x, itf is bijective then 1) aER 3) aeR 11) 4 12) 4 13) 2 14) 4 15) 2 2) ae R 4) ae R(-1,1) 16) 1 17) 1 18) 2 19) 3 20) 3 21) 1 22) 4 23) 1 24) 3 25) 3 38. If a+b+c 1, Range of ab + be + ca in 26) 2 27) 1 28) 2 29) 3 30) 2 31) 3 32) 2 33) 4 34) 3 35) 4 2) 36) 4 37) 4 38) 1 39) 1 40) 4 4) a 41) 4 42) 4 32. Let ab.c, e R. If f) =ae + br+e is such that 39. Ir :RR is given by f)= a+b+c=3 and fx+y) f(x)+f0)+ xy.Vx.ye R. 1995 19961996 1) 997.5 2) 998 then 1996 10 then s equal to: 3) 997 4) 998.5 40. Let f(a)-2"+l and g(a)-3"-1. If (fog)(x)-x, then x is equal tor 1) 255 2) 330 3) 165 4) 190 33, Let f: R R and g: RR be two one-one and onto functions such that they are the mirror 1-20 1) 3-2-10 1-3 2) images of each other about the line y=a If h(x)= 2-1 4) 2-3 3) fix) + g(x), then h(x) is 30-20 1) one-one onto 2) one-one into JEB MAINS-2017) 3) many one-onto 4) many one into 41. The function :R defined as 34. Let flr) = (Ik]2 - Sk] +4)x3 -(6|k)2 -5 (k) + 1)x- (tan x) (sgn (x)), be an even function for all, xeR where [. denotes G.LF and -) denotes fractional part function. Then the sum of all possible values of "k is 1) neither injective nor surjective 2) invertible. 17 1) 31 2) 35 53 4) 6. 3) injective but not surjective. 4) surjective but not injective. 35. Let A= |1, 2, 3.41.The number of functions 42, The domain of the function f:AA satisfying f))=rfor all ISRS4IN 2) 6 3) 9 1) 1 4) 10 1) 10,1.2,3. 3) (0,) 2){1,2,3.) 36. Let f(x)= ax 2013 +esin 3x+20 where 4) (0,1) a. b, e are non- zero constants. If f-2014)= 36, then the value of f(2014) is equal to 1) 1 ANSWERS 2) 2 3) 3 4) 4 1)1 2) 3 3) 1 4) 1 5) 1 6) 2 7) 1 8) 1 9) 4 10) 2 37. f:RR where f(x) = ax + cos x, itf is bijective then 1) aER 3) aeR 11) 4 12) 4 13) 2 14) 4 15) 2 2) ae R 4) ae R(-1,1) 16) 1 17) 1 18) 2 19) 3 20) 3 21) 1 22) 4 23) 1 24) 3 25) 3 38. If a+b+c 1, Range of ab + be + ca in 26) 2 27) 1 28) 2 29) 3 30) 2 31) 3 32) 2 33) 4 34) 3 35) 4 2) 36) 4 37) 4 38) 1 39) 1 40) 4 4) a 41) 4 42) 4