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JEEMAIN and NEET
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Mathematics
>>
Class12
>>
Relations and Functions
The inverse of $f(x)=x-[x],$ where $[x]$ is greatest integer function is
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
difficult
answered
Sep 29, 2019
by
pranav.awasarmol123
2
answers
If $f_k(x) = \large\frac{1}{k}$$(\sin^k x + \cos^k x)$, where $x\in R$ and $k \geq 1$. The $f_4(x) - f_6(x)$ equals
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
jeemain-2014
q44
medium
answered
Nov 15, 2017
by
ityagi002
1
answer
f(xy)=f(x)+f(y) . Then Prove that f(x) =Klog(x) where k is constant
answered
Dec 17, 2014
by
pady_1
1
answer
If $a\in R$ and the equation $-3 (x-[x])^2 + 2(x-[x])+a^2 = 0$, (where $[x]$ denotes the greatest integer $\leq x$) has no integral solution, then all possible values lie in the interval:
jeemain
math
class12
ch1
relations-and-functions
jeemain-2014
types
of
functions
q33
medium
asked
Apr 6, 2014
by
balaji.thirumalai
0
answers
The identity element of the binary operation $\large *$ defined on $Q-\{0\}$ as $a\large *$ $b=\large\frac{ab}{2},$ $ \forall \:a,b\:\in\:Q-\{0\}$
jeemain
math
class12
ch1
relations-and-functions
binary
operations
easy
answered
May 31, 2013
by
rvidyagovindarajan_1
1
answer
If a relation $R$ on the set $\{1,2,3\}$ is defined as $R=\{(1,2)\}$, then $R$ is
jeemain
math
class12
ch1
relations-and-functions
types
of
relations
easy
mock
answered
May 31, 2013
by
rvidyagovindarajan_1
1
answer
If $f:[0,1]\rightarrow\:[0,1]$ is defined as $f(x)=\left \{\begin {array}{c,c}x &if\:x\:is\:rational\\1-x & if\:x\:is\:irrational\end {array}\right.$ then $fof(x)=?$
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
easy
answered
May 31, 2013
by
rvidyagovindarajan_1
1
answer
The number of bijection mappings that are possible from $Set \:A$ containing 5 elements to $Set\:B$ containing 6 elements is ?
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
easy
answered
May 31, 2013
by
rvidyagovindarajan_1
1
answer
The maximum number of equivalence relations on the set $A=\{1,2,3\}$ is?
jeemain
math
class12
ch1
relations-and-functions
types
of
relations
easy
answered
May 31, 2013
by
rvidyagovindarajan_1
1
answer
Find the domain of $f(x)=\sqrt{cos(sinx)}+sin^{-1}\bigg(\large\frac{1+x^2}{2x}\bigg)$
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
medium
answered
May 30, 2013
by
rvidyagovindarajan_1
1
answer
Find the domain of $sin(log(\large\frac{\sqrt{4-x^2}}{1-x}))$
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
easy
answered
May 30, 2013
by
rvidyagovindarajan_1
1
answer
Which of the following pairs of functions are equal ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 30, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R$ is such that $f(x+y)=f(x).f(y)$, then $f(0)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 30, 2013
by
rvidyagovindarajan_1
1
answer
If function $f(x)$ is given by
$\small\left|\begin {array} {c,c,c} -cos(x+x^2) & -sin(x+x^2) & cos(x+x^2)\\sin(x^2-x) & -cos(x^2-x) & sin(x^2-x)\\sin2x &0 &sin2x^2 \end {array}\right|$, then find $f(0)$
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 30, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{1,2\},$ then how many binary operations having 1 as identity and 2 as inverse of 2 are possible?
jeemain
math
class12
ch1
relations-and-functions
binary operation
medium
answered
May 29, 2013
by
rvidyagovindarajan_1
1
answer
If a set $A$ has 2 elements, then how many binary operations are possible in $A$ ?
jeemain
math
class12
ch1
relations-and-functions
binary operation
medium
answered
May 29, 2013
by
rvidyagovindarajan_1
1
answer
If $g(x)=x^2+x-2\:\:and\:\:\large\frac{1}{2}$$gof(x)=2x^2-5x+2$ then $ f(x)= ?$
jeemain
math
class12
ch1
relations-and-functions
composition of functions
medium
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R$ is defined as $f(x)=[x]^2+[x+1]-3$ where $[x]$ is greatest integer of $x$, then what type of function is $f$?
jeemain
math
class12
ch1
relations-and-functions
types of functions
difficult
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=\left\{\begin{array}{c,c} |x| &x \leq 1 \\2-x &x>1\end{array}\right.$, then $fof(x)=?$
jeemain
math
class12
ch1
relations-and-functions
composition of functions
medium
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
If $f:A\rightarrow B$ is defined as $f(x)=\sqrt 3 sinx+cosx+4$ and $f$ is invertible then find A.
jeemain
math
class12
ch1
relations-and-functions
types of functions
medium
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
The value of $a\:\:and\:\:b$ for which $f:R\rightarrow R$ is defined as $f(x)=ax+b$ where $a,b\in R $ is bijection with $fof$ as its identity is ?
jeemain
math
class12
ch1
relations-and-functions
types of relations
difficult
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
Find the linear functions that maps $[-1,1]$ onto $[0,2]$.
jeemain
math
class12
ch1
relations-and-functions
types of functions
difficult
answered
May 28, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{1,2,3,4\}\:and\:B=\{3,4,7\}$ then the no. of onto functions from $A\rightarrow B$=?
jeemain
math
class12
ch1
relations-and-functions
types of functions
medium
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R\:\:and\:\:f(x)=|x|$ and $A=(0,1)$, then find $f^{-1}(A)$
jeemain
math
class12
ch1
relations-and-functions
composition of functions
medium
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=x^n$, $n\in N$ and $gof(x)=ng(x)$, then $g(x)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
easy
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
$If A\{x,y,z\},\:\:B=\{1,2,3\}$ and $f:A\rightarrow B\:\:is\:1-1\:$function. Also one out of the following statements, $f(z)\neq 2,\:\:f(x)=1\:\:and\:\:f(y)\neq 1$ is true. then $f^{-1}(1)=?$
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
medium
answered
May 25, 2013
by
rvidyagovindarajan_1
1
answer
If $ A=\{x:x\in R\:and\:x\geq 1\}$ and $ f:A\rightarrow A$ is defined as $f(x)=2^{x(x-1)},$ then find $ f^{-1}(x).$
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
medium
answered
May 25, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R$ is defined as $f(x)=6^x+6^{|x|}$ then what type of function is $f$ ?
jeemain
math
class12
ch1
relations-and-functions
types-of-functions
easy
answered
May 25, 2013
by
rvidyagovindarajan_1
1
answer
If $f(X)=\large\frac{kx}{1+x}$, $x\neq1$ and $fof(x)=x$, then find $k$.
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
easy
answered
May 25, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{-1,0,1\}$ and $f:A\rightarrow A$ is defined as $f(x)=x^2$, then what type of function is $f$ ?
jeemain
math
class12
ch1
relations-and-functions
types-of-functions
easy
answered
May 25, 2013
by
rvidyagovindarajan_1
1
answer
If $log_2(log_3(log_4(log_5x)))=0$ then x= ?
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
easy
answered
May 18, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=\cos \log x$ then $f(x).f(y)-\large\frac{1}{2}$$\bigg(f(\large\frac{x}{y}$)$+f(xy)\bigg)= ?$
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
medium
answered
May 18, 2013
by
rvidyagovindarajan_1
1
answer
$f:N\rightarrow Z$ is a function defined as $f(n)=\left\{ \begin {array} {1 1} \large\frac{n-1}{2}, \:\:when\:\: n\:\: is\:\: odd \\ -\large \frac{n}{2},\:\:when\:\: n\:\: is\:\: even \\ \end{array} \right.$, then $f$ is
jeemain
math
class12
ch1
relations-and-functions
easy
answered
May 13, 2013
by
rvidyagovindarajan_1
1
answer
If $M$ is the set of all $2\times 2$ matrices with real entries and $f :M\rightarrow R$ is defined as $ f(A)=|A| \:\forall\:A\in M$, then $f$ is
jeemain
math
class12
ch1
sets-relations-and-functions
medium
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If $g(x)=1+x-[x]$ where $[x]$ is greatest integer $x$ and $f(x)=\left\{\begin{array}{111}-1,\:\:\:\:x<0\\0,\:\:\:\:\:x=0\\1,\:\:\:\:\:x>0\end{array}\right.$ then $fog(x)=?$
jeemain
math
class12
ch1
relations-and-functions
difficult
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=x^2\:\:and\:\:g(x)=2^x$ and $fog(x)=gof(x)$ then $x$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
easy
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=\large\frac{1}{1-x}$ is a function defined in $R-\{1\}$ then $\;fofof(x)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
medium
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If $*$ is a binary operation defined as $a*b=3a-b$, then $(2*3)*4=$ ?
jeemain
math
class12
ch1
relations-and-functions
binary-operation
easy
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If * is a binary operation defined by a*b=$\frac{ab}{100}$ in $Q^+$ then the inverse element of 0.1 is:
jeemain
math
class12
ch1
relations-and-functions
binary-operations
easy
answered
May 12, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)=x^2$ $g(x)=sinx$, $\forall x\in R$, then the set of all $x$ satisfying $fogogof(x)=gogof(x)$ is
jeemain
math
class12
ch1
relations-and-functions
composition-of-functions
medium
answered
May 7, 2013
by
rvidyagovindarajan_1
1
answer
If $f(x)$ is a real valued function satisfying $f(x+1)+f(x-1)=2f(x)$ $\forall x\in R$ and $f(0)=0$, then for any $n\in N,\:f(n)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
difficult
answered
May 7, 2013
by
rvidyagovindarajan_1
1
answer
The domain of $y=sin^{-1}(1+3x+2x^2)$ is
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
medium
answered
May 7, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow S$ defined by $\:f(x)=\sin x-\sqrt3\; \cos x+1\;$ is onto function then $S$ = ?
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
difficult
answered
May 4, 2013
by
rvidyagovindarajan_1
1
answer
The value of $\alpha$ for which the function $f(x)=1+\alpha x,\:\:\alpha\neq 0$ is the inverse of itself is:
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
medium
answered
May 4, 2013
by
rvidyagovindarajan_1
1
answer
What is the inverse of the function $f(x)=\large\frac{e^x-e^{-x}}{e^x+e^{-x}}$
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
medium
answered
May 2, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{1,2,3\}$ then the no. of relations in $A$ containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is
jeemain
math
class12
ch1
relations-and-functions
types
of
relations
easy
answered
May 1, 2013
by
rvidyagovindarajan_1
1
answer
If * is binary operation defined in N as a*b=$a^3+b^3$ then * is
jeemain
math
class12
ch1
relations-and-functions
binary-operations
easy
answered
May 1, 2013
by
rvidyagovindarajan_1
1
answer
If n(A) = 4, n(B) = 6, then the number of 1-1 functions from A to B is
jeemain
math
class12
ch1
relations-and-functions
types-of-functions
medium
answered
May 1, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{1,2,3,4\}$ and $B=\{1,2\}$, then the number of onto functions from $A$ to $B$ is
jeemain
math
class12
ch1
relations-and-functions
functions
medium
answered
Apr 28, 2013
by
rvidyagovindarajan_1
1
answer
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