JEE Main & Advanced Mathematics Relations Question Bank

done Numerical Value Type Questions - Relations and Functions-II Total Questions - 15

• question_answer1)
  Let \[E=\{1,2,3,4\}\] and \[F=\{1,2\}\]. Then the number of onto functions from E to F is
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• question_answer2)
  Given the relation \[R=\{(1,2),(2,3)\}\] on the set \[A=\{1,2,3\},\] the minimum number of ordered pairs which when added to R make it an equivalence relation is
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• question_answer3)
  Set A has 3 elements and set B has 4 elements. The number of injection that can be defined from A to B is
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• question_answer4)
  If \[f(x)=|x|\] and \[g(x)=[x],\] then value of \[fog\,\left( -\frac{1}{4} \right)+gof\left( -\frac{1}{4} \right)\]is
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• question_answer5)
  If \[f(x)={{\sin }^{2}}x+{{\sin }^{2}}\left( x+\frac{\pi }{3} \right)+\cos x\cos \left( x+\frac{\pi }{3} \right)\] and  \[g\left( \frac{5}{4} \right)=1,\] then \[(gof)\,(x)=\]
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• question_answer6)
  For \[x\in \left( 0,\frac{3}{2} \right),\] let \[f(x)=,\,g(x)=tan\,\,x\] and \[h(x)=\frac{1-{{x}^{2}}}{1+{{x}^{2}}}.\] If \[\phi \] \[(x)\,\left( \frac{\pi }{3} \right)=((hof)og)\,\,\,\,(x).\] If \[\phi \] is equal to \[\tan \frac{p\pi }{q},\] then \[p+q\] is
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• question_answer7)
  Let \[f(x)=\frac{ax}{x+1},\] \[x\ne -1\]. Then, the value of \[\alpha >0\] for which \[f[f(x)]=x\] is
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• question_answer8)
  If \[f(x)={{x}^{2}}+1,\] then \[|{{f}^{-1}}(17)|+|{{f}^{-1}}(-3)|\] will be
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• question_answer9)
   If \[f:R\to R,\] \[g:R\to R\]  and \[h:R\to R\] is such that \[f(x)={{x}^{2}},\] \[g(x)=\tan x\] and \[h(x)=\log x,\] then the value of \[[ho\,(gof)],\] if \[x=\frac{\sqrt{\pi }}{2}\]will be
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• question_answer10)
  Let R be the set of real numbers and the functions \[f:R\to R\] and \[g:R\to R\] be defined by \[f\left( x \right)={{x}^{2}}+2x-3\]and \[g\left( x \right)=x+1.\] If \[f\left( g\left( x \right) \right)=g\left( f\left( x \right) \right)\] for some value of x, then \[|x|\] is
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• question_answer11)
  Let \[g\left( x \right)=1+x-\left[ x \right]\] and \[f\left( x \right)=\left\{ \begin{matrix} -1, & x<0  \\ 0, & x=0,  \\ 1, & x>0  \\ \end{matrix} \right.\] then for all x, \[f[g(x)]\] is equal to
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• question_answer12)
  Let \[f\left( x \right)={{\left( x+1 \right)}^{2}}-1,\] \[\left( x\ge -1 \right)\]. Then the number of elements in the set \[S=\{x:f(x)={{f}^{-1}}(x)\}\] is
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• question_answer13)
  Let R be the set of real numbers and the mapping \[f:R\to R\] and \[g:R\to R\] be defined by \[f(x)=5-{{x}^{2}}\] and \[g(x)=3x-4,\] then the absolute value of \[(fog)\,(-1)\] is
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• question_answer14)
  Let \[f:R-\left\{ \frac{5}{4} \right\}\to R\] be a function defined as \[f\left( x \right)=\frac{5x}{4x+5}.\]The inverse of f is the map g: Range \[f\to R-\left\{ \frac{5}{4} \right\}\] given by \[{{f}^{-1}}(x)=\frac{ax}{a+by},\]then the value of \[a+b\] is
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• question_answer15)
  If \[f:R\to R\] and \[g:R\to R\] defined by \[f(x)=2x+3\] and \[g(x)={{x}^{2}}+7,\]then the value of \[\left| x \right|\]for which \[f(g(x))=25\] is
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