Welcome to Ctanujit Institute of Statistics & Mathematics...An Initiative by 'ISI'ian



Urgent Notice:

Due to unavoidable reason, Ctanujit Classes will be closed from 1st November to 30th November 2018.
Postal Package will be available from 1st December 2018.

IIT JEE SOLVED PAPERS ON FUNCTIONS

Here is some solved problems from IIT-JEE previous year papers on functions


Q. [IIT-JEE 2002]Let function f : RR be defined by                     f(x)= 2x + sinx, then f is
(a) one-to-one& onto                    (b) one-to-one but not onto                   (c) onto but not one-to-one            (d) neither one-to-one nor onto
Solution :(a)  Given f(x)= 2x + sinx
On differentiation ,f ′(x)= 2 + cosx ;  as -1 ≤cosx ≤ 1
So, f ′(x) ≥ 0, so f(x) is strictly increasing. Thus f(x) is one-to-one & onto.
Q. [IIT-JEE 2001] Let E = {1,2,3,4} and F = {1,2}. Then the number of onto functions from E to F is
(a) 14   (b) 16    (c) 12    (d) 8
Solution : (a)  Each element of E should have image as 1 or 2.
Thus four elements of E can have images = 24.
Now, for all x E, f(x)=1 or f(x)=2, do not make it as an onto function.
Thus, the total number of onto functions from E to F is = 24 – 2=14.
Q. [IIT-JEE 2000] The domain of definition of the function y(x) given by the equation  2x + 2y = 2 is
(a) 0< x ≤1      (b) 0 x ≤1     (c) -∞< x ≤0     (d) -∞< x <1
Solution :(d)  Given 2y = 2 – 2x  ,
Taking log both sides, ylog2 = log(2 – 2x). Now, 2 – 2x> 0 -∞< x <1.