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JEE Main and Advanced questions on relations and functions



In this page we have JEE Main and Advanced questions on relations and functions. Hope you like them and do not forget to like , social share and comment at the end of the page.

Multiple Choice Questions

Question 1
If the function f: R-> R defined as $f(x) =|x|(x -sin x)$, then which of the following statement is true
(a) f is bijective
(b) f is one-one but not Onto
(c) f is onto but not one-one
(d) f is neither one-one nor onto

Question 2
If the function f:$[1,\infty)$ -> [2,\infy)$ defined as $f(x) =x + \frac {1}{x}$, then $f^{-1}$ x is
(a) $\frac {x}{1+x^2}$
(b) $x + \frac {1}{x}$
(c) $\frac {x + \sqrt {x^2 -4}}{2}$
(d) $\frac {x - \sqrt {x^2 -4}}{2}$

Question 3
The function $f:[0,\infty)$ -> R given by $f(x)= \frac {x}{x+1}$ is
(a) one -one and onto
(b) one-one but not onto
(c) onto but not one-one
(d) Neither one-one nor onto

Question 4
if $g(f(x))=sin^2 x$ and $f(g(x)) =(sin \sqrt x)^2$ then
(a) $f(x) =x^2$ and $g(x) = sin \sqrt x$
(b) $f(x) =sinx $ and $g(x) = |x|$
(c) $f(x) =sin^2 x $ and $g(x) = \sqrt x$
(d) f and g cannot be determined

Question 5
The function $f(x)=[x] sin (\frac {\pi}{[x+1]})$ where [.] denotes the greatest integer function. The domain of the function f is
(a) $(-\infty ,\infty) - {-1}$
(b) $[0 ,\infty)$
(c) $(-\infty ,-1)$
(d) $(-\infty ,-1) \cup [0, \infty)$

Question 6
The domain of the function $f(x)=\frac {log_2 (x+3)}{x^2 + 3x +2}$?
(a) $R - {-1,-2,-3}$
(b) $R - {-1,-2}$
(c) $(-2,\infty)$
(d) $(-3, \infty) - {-1,-2}$

Question 7
Consider the below two relations A= {(x,y)|x,y are real numbers and x=wy for some rational number}
B= {(m/n,p/q)|m,n, p and q are integers such that n and q are not zero and qm=pn$ (a) A is a equivalence relation but B is not
(b) A and B both are equivalence relation
(c) A is not a equivalence relation but B is a equivalence relation

(d) A and B both are not equivalence relations

Question 8
let $f(x) = \frac {1}{\sqrt {|x| - x}}$, the domain of f(x) is
(a) $(-\infty ,\infty)$
(b) $(-\infty ,0)
(c) $(-\infty ,\infty) - {0}$
(d) $(0 ,\infty)

Question 9
Let f: R -> [-1/2,1/2] and $f(x) =\frac {x}{x^2 +1}$ then f(x) is
(a) one-one but not onto
(b) onto but not one -one
(c) one-one and onto
(d) neither one-one nor onto

Question 10
If $a \in R$ and the equation $-3(x-[x])^2+2(x−[x])+a^2=0$ (where [x] denotes the greatest integer ) has a no integral solution , then all possible values of a lie in the interval
(a)(1,2)
(b)(-2,-1)
(c)$(-1,0) \cup (0,1)$
(d) $(-2,0) \cup (0,2)$

Fill in the blanks

Question 11
(i) Let f :[0,1] -> R be defined by
$f(x) = \frac {4^x}{4^x +2}$
Then the value of
$f(\frac {1}{40}) + f(\frac {2}{40}) + f(\frac {3}{40}) + .............. + f(\frac {39}{40})$ is ______
(ii) if $f(x)= \frac {1}{2} (sin^2 x + sin^2(x + \pi/3) + cosx cos(x + \pi/3))$ and g(5/8) =1, then g(f(x)) is _____
(iii) The domain of the function $cos^{-1} (log_e (\frac {x}{x-1}))$ is _______

Match the column

Question 12
Let $f(x)=\frac {x^2 -6x +5}{x^2 -5x + 6}$
Then match the column A and B


Question 13
Let $f(x)=\frac {x^2 -3x -10}{x^2 -2x -3}$
Then match the column A and B


True and False

Question 14
(i) The function f(x)=sin(log(x + \sqrt {x^2 +1})) is odd function
(ii)If the function $f:[1, \infty) -> [1, \infty)$ is defined by $f(x)=2^{x(x−1)}, then $f^{−1}(x) is given as $\frac {1}{2}[1 + \sqrt {1+4log_2 x}]$
(iii) The relation R on the set A = {1, 2, 3} defined as R = {{1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

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