JEE Main & Advanced Mathematics Functions Question Bank

done Self Evaluation Test - Relations and Functions-I Total Questions - 70

• question_answer1)
  If \[R=\{x,y\}:x,y\in I\] and \[{{x}^{2}}+{{y}^{2}}\le 4\}\] is a relation in I, the domain of R is
  A)
  \[\{0,1,2\}\] done clear
  B)
  \[\{-2,-1,0\}\] done clear
  C)
  \[\{-2,-1,\,\,0,\,1,\,\,2\}\] done clear
  D)
         I done clear
  View Solution play_arrow

• question_answer2)
  If \[A=\{8,9,10\}\] and \[B=\{1,2,3,4,5\},\] Then the number of elements in \[A\times A\times B\] are
  A)
  15 done clear
  B)
                                 30 done clear
  C)
  45 done clear
  D)
                                 75 done clear
  View Solution play_arrow

• question_answer3)
  The Cartesian product of two sets P and Q i.e., \[P\times Q=\phi ,\] if
  A)
  either P or Q is the null set done clear
  B)
  neither P nor Q is the null set done clear
  C)
  Both (a) and (b) done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  The relation R defined on the set \[A=\{1,2,3,4,5\}\]by \[R=\{(x,y):\left| {{x}^{2}}-{{y}^{2}} \right|<16\}\] is given by
  A)
  \[\{(1,1),(2,1),(3,1),(4,1),(2,3)\}\] done clear
  B)
  \[\{(2,2),(3,2),(4,2),(2,4)\}\] done clear
  C)
  \[\{(3,3),(3,4),(5,4),(4,3),(3,1)\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  A relation R is defined over the set of nonnegative integers as \[xRy\Rightarrow {{x}^{2}}+{{y}^{2}}=36\] what is R?
  A)
  \[\{(0,6)\}\] done clear
  B)
  \[\{(6,0)(\sqrt{11},5),(3,3,\sqrt{3})\] done clear
  C)
  \[\{(6,0)(0,6)\}\] done clear
  D)
  \[(\sqrt{11},5),(2,4\sqrt{2}),(5\sqrt{11}),(4\sqrt{2}2)\}\] done clear
  View Solution play_arrow

• question_answer6)
  The domain and range of the relation R given by \[R=\{(x,y):y=x+\frac{6}{x};\}\] where \[x,y\in N\] and \[x<6\}\] is
  A)
  \[\{1,2,3\},\{7,5\}\] done clear
  B)
         \[\{1,2\},\{7,5\}\] done clear
  C)
  \[\{2,3\},\{5\}\] done clear
  D)
                     None of these done clear
  View Solution play_arrow

• question_answer7)
  If \[A=\{1,2\},B=\{1,3\},\] then \[(A\times B)\cup (B\times A)\] is equal to
  A)
  \[\{(1,3),(2,3),(3,1),(3,2),(1,1),(2,1),(1,2)\}\] done clear
  B)
  \[\{(1,3),(3,1)(3,2),(2,3)\}\] done clear
  C)
  \[\{(1,3),(2,3),(3,2),(1,1)\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  If \[A=\{a,b,c,d\},B=\{1,2,3\},\] which of the following sets of ordered pairs are not relations from A to B?
  A)
  \[\{(a,1),(a,3)\}\] done clear
  B)
  \[\{(b,1),(c,2),(d,1)\}\] done clear
  C)
  \[\{(a,2),(b,3),(3,b)\}\] done clear
  D)
  \[\{(a,1),(b,2),(c,3)\}\] done clear
  View Solution play_arrow

• question_answer9)
  Let \[A=\{1,2\},B=\{3,4\}.\] Then, number of subsets of \[A\times B\] is
  A)
  4 done clear
  B)
         8 done clear
  C)
  18 done clear
  D)
         16 done clear
  View Solution play_arrow

• question_answer10)
  Let \[R=\{x|x\in N,x\] is a multiple of 3 and \[x\le 100\}\] \[S=\{x|x\in N,\,\,x\] is a multiple of 5 and \[x\le 100\}\] What is the number of elements in \[(R\times S)\cap (S\times R)\]
  A)
  36 done clear
  B)
         33 done clear
  C)
  20 done clear
  D)
         6 done clear
  View Solution play_arrow

• question_answer11)
  Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in \[A\times B\] is 7. Then \[{{p}^{2}}+{{q}^{2}}=\]
  A)
  42 done clear
  B)
         49 done clear
  C)
  50 done clear
  D)
         51 done clear
  View Solution play_arrow

• question_answer12)
  Let \[A=\{x\in W,\] the set of whole numbers and \[x<3\},\] \[B=\{x\in N,\] the set of natural number and \[2\le x<4\}\] and \[C=\{3,\,\,\,4\},\] then how many elements will \[(A\cup B)\times C\] contain?
  A)
  6 done clear
  B)
  8 done clear
  C)
  10 done clear
  D)
         12 done clear
  View Solution play_arrow

• question_answer13)
  A relation R is defined in the set Z of integers as follows \[(x,y)\in R\] iff \[{{x}^{2}}+{{y}^{2}}=9.\] Which of the following is false?
  A)
  \[R=\{(0,3),(0,-3),(3,0),(-3,0)\}\] done clear
  B)
  Domain of \[R=\{-3,0,3\}\] done clear
  C)
  Range of \[R=\{-3,0,3\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  The domain of the function \[\sqrt{{{x}^{2}}-5x+6}\]\[+\sqrt{2x+8-{{x}^{2}}}\] is
  A)
  \[[2,3]\] done clear
  B)
         \[[-2,4]\] done clear
  C)
  \[[-2,2]\cup [3,4]\] done clear
  D)
         \[[-2,1]\cup [2,4]\] done clear
  View Solution play_arrow

• question_answer15)
  Find the domain of \[f(x)=\sqrt{{{(0.625)}^{4-3x}}-{{(1.6)}^{x(x+8)}}}\]
  A)
  \[[-3,2]\] done clear
  B)
         \[[1,4]\] done clear
  C)
  \[[2,5]\] done clear
  D)
         \[[-4,-1]\] done clear
  View Solution play_arrow

• question_answer16)
  The range of the function \[f(x)={{x}^{2}}+2x+2\] is
  A)
  \[(1,\infty )\] done clear
  B)
         \[(2,\infty )\] done clear
  C)
  \[(0,\infty )\] done clear
  D)
         \[[1,\infty )\] done clear
  View Solution play_arrow

• question_answer17)
  Find the domain of the function \[f(x)=\sqrt{\left( \frac{2}{{{x}^{2}}-x+1}-\frac{1}{x+1}-\frac{2x-1}{{{x}^{3}}+1} \right)}\]
  A)
  \[(-\infty ,2]-\{-1\}\] done clear
  B)
         \[(-\infty ,2)\] done clear
  C)
  \[]-1,2]\] done clear
  D)
         None of these done clear
  View Solution play_arrow

• question_answer18)
  The domain of \[f(x)=\frac{1}{\sqrt{2x-1}}-\sqrt{1-{{x}^{2}}}\] is:
  A)
  \[\left] \frac{1}{2},1 \right[\] done clear
  B)
         \[\left[ -1,\infty  \right[\] done clear
  C)
  \[\left[ 1,\infty  \right[\] done clear
  D)
         None of these done clear
  View Solution play_arrow

• question_answer19)
  Which of the following relation is NOT a functions?
  A)
  \[f=\{(x,x)|x\in R\}\] done clear
  B)
  \[g=\{(x,3)|x\in R\}\] done clear
  C)
  \[h=\{(n,\frac{1}{n})|n\in I\}\] done clear
  D)
       \[t=\{(n,\,\,{{n}^{2}})|n\in N\}\] done clear
  View Solution play_arrow

• question_answer20)
  The domain of two definition of the function \[f(x)\]is given by the equation \[{{2}^{x}}+{{2}^{y}}=2\] is
  A)
  \[0<x\le 1\] done clear
  B)
  \[0\le x\le 1\] done clear
  C)
  \[-\infty <x\le 0\] done clear
  D)
         \[-\infty <x<1\] done clear
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• question_answer21)
  The domain of the function \[f(x)=\frac{1}{\sqrt{\left| x \right|-x}}\] is
  A)
  \[(0,\infty )\] done clear
  B)
         \[(-\infty ,0)\] done clear
  C)
  \[(-\infty ,\infty )-\{0\}\] done clear
  D)
         \[(-\infty ,\infty )\] done clear
  View Solution play_arrow

• question_answer22)
  If \[f(x)=4x-{{x}^{2}},x\in R,\] then \[f(a+1)-f(a-1)\] is equal to
  A)
  \[2(4-a)\] done clear
  B)
         \[4(2-a)\] done clear
  C)
  \[4(2+a)\] done clear
  D)
         \[2(4+a)\] done clear
  View Solution play_arrow

• question_answer23)
  The domain of the function\[f(x)=\sqrt{x-\sqrt{1-{{x}^{2}}}}\] is
  A)
  \[\left[ -1,-\frac{1}{\sqrt{2}} \right]\cup \left[ \frac{1}{\sqrt{2}},1 \right]\] done clear
  B)
  \[[-1,1]\] done clear
  C)
  \[\left( -\infty ,-\frac{1}{2} \right]\cup \left[ \frac{1}{\sqrt{2}},+\infty  \right)\] done clear
  D)
  \[\left[ \frac{1}{\sqrt{2}},1 \right]\] done clear
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• question_answer24)
  The domain of the function \[f(x)=lo{{g}_{2}}\left( -{{\log }_{1/2}}\left( 1+\frac{1}{{{x}^{1/4}}} \right)-1 \right)\] is
  A)
  \[\left( 0,\text{ }1 \right)\] done clear
  B)
         \[\left( 0,\text{ }1 \right]\] done clear
  C)
  \[[1,\infty )\] done clear
  D)
         \[(1,\infty )\] done clear
  View Solution play_arrow

• question_answer25)
  The range of the function \[f(x)=\frac{{{e}^{x}}-{{e}^{\left| x \right|}}}{{{e}^{x}}+{{e}^{\left| x \right|}}}\] is
  A)
  \[(-\infty ,\infty )\] done clear
  B)
         \[[0,1)\] done clear
  C)
  \[(-1,0]\] done clear
  D)
         \[(-1,1)\] done clear
  View Solution play_arrow

• question_answer26)
  Let f be a function on R given by \[f(x)={{x}^{2}}\] and let \[E=\{x\in R:-1\le x\le 0\}\] And \[F=\{x\in R:0\le x\le 1\}\] then which of the following is false?
  A)
  \[f(E)=f(F)\] done clear
  B)
  \[E\cap F\subset f(E)\cap f(F)\] done clear
  C)
  \[E\cup F\subset f(E)\cup f(F)\] done clear
  D)
  \[f(E\cap F)=\{0\}\] done clear
  View Solution play_arrow

• question_answer27)
  If \[3f(x)-f\left( \frac{1}{x} \right)=\log {{x}^{4}},\] then \[f({{e}^{-x}})\] is
  A)
  \[1+x\] done clear
  B)
         \[1/x\] done clear
  C)
  \[x\] done clear
  D)
         \[-x\] done clear
  View Solution play_arrow

• question_answer28)
  If \[f(x)=\frac{{{2}^{x}}+{{2}^{-x}}}{2}\], then \[f(x+y).f(x-y)\] is equal to
  A)
  \[\frac{1}{2}[f(x+y)+f(x-y)]\] done clear
  B)
  \[\frac{1}{2}[f(2x)+f(2y)]\] done clear
  C)
  \[\frac{1}{2}[f(x+y).f(x-y)]\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  If \[f(x+1)={{x}^{2}}-3x+2,\] then \[f(x)\]is equal to:
  A)
  \[{{x}^{2}}-5x-6\] done clear
  B)
         \[{{x}^{2}}+5x-6\] done clear
  C)
  \[{{x}^{2}}+5x+6\] done clear
  D)
         \[{{x}^{2}}-5x+6\] done clear
  View Solution play_arrow

• question_answer30)
  A function f is defined by \[f(x)=x+\frac{1}{x}.\] Consider the following.

  (1) \[{{(f(x))}^{2}}=f({{x}^{2}})+2\]

  (2) \[{{(f(x))}^{3}}=f({{x}^{3}})+3f(x)\]

  Which of the above is/are correct?

  A)
  (1) only done clear
  B)
         (2) only done clear
  C)
  Both (1) and (2) done clear
  D)
                     Neither (1) nor (2) done clear
  View Solution play_arrow

• question_answer31)
  If \[f:R\to R\] is defined by \[f(x)=3x+\left| x \right|,\] then\[f(2x)-f(-x)-6x=\]
  A)
  \[f(x)\] done clear
  B)
         \[2f(x)\] done clear
  C)
  \[-f(x)\] done clear
  D)
         \[f(-x)\] done clear
  View Solution play_arrow

• question_answer32)
  If \[f:R\to R\,\,\And \,\,g:R\to R\] be two given functions, then 2 min \[\{f(x)-g(x),0\}\] equals
  A)
  \[f(x)+g(x)-\left| g(x)-f(x) \right|\] done clear
  B)
  \[f(x)+g(x)+\left| g(x)-f(x) \right|\] done clear
  C)
  \[f(x)-g(x)+\left| g(x)-f(x) \right|\] done clear
  D)
  \[f(x)-g(x)-\left| g(x)-f(x) \right|\] done clear
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• question_answer33)
  A real valued function f(x) satisfies the functional equation \[f(x-y)=f(x)f(y)-f(a-x)f(a+y)\]where a is a given constant and \[f(0)=1,f(2a-x)\] is equal to
  A)
  \[-f(x)\] done clear
  B)
         \[f(x)\] done clear
  C)
  \[f(a)+f(a-x)\] done clear
  D)
         \[f(-x)\] done clear
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• question_answer34)
  Which of the following functions is even,
  A)
  \[f(x)=\sqrt{1+x+{{x}^{2}}}-\sqrt{1-x+{{x}^{2}}}\] done clear
  B)
  \[f(x)=log\left( \frac{1-x}{1+x} \right)\] done clear
  C)
  \[f(x)=log\left( x+\sqrt{1+{{x}^{2}}} \right)\] done clear
  D)
  \[f(x)=\frac{{{e}^{x}}+{{e}^{-x}}}{2}\] done clear
  View Solution play_arrow

• question_answer35)
  \[f(x)=\frac{x(x-p)}{q-p}+\frac{x(x-q)}{p-q},\] \[p\ne q\]. What is the value of\[f\left( q \right)+f\left( q \right)\]?
  A)
  \[f(p-q)\] done clear
  B)
         \[f(p+q)\] done clear
  C)
  \[f(p(p+q))\] done clear
  D)
         \[f(q(p-q))\] done clear
  View Solution play_arrow

• question_answer36)
  Let \[f(x)\] be define on \[[-2,2]\] and is given by \[f(x)=\left\{ \begin{matrix}    -1,\,-2\le x\le 0  \\    x-1,\,0\le x\le 2  \\ \end{matrix} \right.\], then \[f(\left| x \right|)\] is defined as
  A)
  \[f(\left| x \right|)=\left\{ \begin{matrix}    1-2\le x\le 0  \\    1-x,0<x\le 2  \\ \end{matrix} \right.\] done clear
  B)
  \[f(\left| x \right|)=x-1\forall x\in R\] done clear
  C)
  \[f(\left| x \right|)=\left\{ \begin{matrix}    -x-1,-2\le x\le 0  \\    x-1,0<x\le 2  \\ \end{matrix} \right.\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  Let \[{{f}_{1}}(x)=\left\{ \begin{matrix}    x,0\le x\le 1  \\    1,x>1  \\    0,otherwise  \\ \end{matrix} \right.\]

  \[{{f}_{2}}(x)={{f}_{1}}(-x)\] for all x

  \[{{f}_{3}}(x)=-{{f}_{2}}(x)\] for all x

  \[{{f}_{4}}(x)={{f}_{3}}(-x)\] for all x

  Which of the following is necessarily true?

  A)
  \[{{f}_{4}}(x)={{f}_{1}}(x)\] for all x done clear
  B)
  \[{{f}_{1}}(x)=-{{f}_{3}}(-x)\] for all x done clear
  C)
  \[{{f}_{2}}(-x)={{f}_{4}}(x)\] for all x done clear
  D)
  \[{{f}_{1}}(x)+{{f}_{3}}(x)=0\] for all x done clear
  View Solution play_arrow

• question_answer38)
  Consider the following statements. Let \[A=\{1,2,3,4\}\] and \[B=\{5,7,9\}\]

  I. \[A\times B=B\times A\]

  II. \[n(A\times B)=n(B\times A)\]

  Choose the correct option.

  A)
  Statement-I is true. done clear
  B)
  Statement-II is true. done clear
  C)
  Both are true. done clear
  D)
  Both are false. done clear
  View Solution play_arrow

• question_answer39)
  Let R be a relation on N defined by \[x+2y=8.\]The domain of R is
  A)
  \[\{2,4,8\}\] done clear
  B)
         \[\{2,4,6,8\}\] done clear
  C)
  \[\{2,4,6\}\] done clear
  D)
         \[\{1,2,3,4\}\] done clear
  View Solution play_arrow

• question_answer40)
  Consider the following statements.

  I. If (a, 1), (b, 2) and (c, 1) are in \[A\times B\] and \[n(A)=3,\,\,n(B)=2\] then \[A=\{a,b,c\}\] and \[B=\{1,2\}\]

  II. If \[A=\{1,2\}\] and \[B=\{3,4\},\] then \[A\times (B\cap \phi )\]is equal to \[A\times B.\]

  Choose the correct option.

  A)
  Only I is true done clear
  B)
  Only II is true done clear
  C)
  Both are true done clear
  D)
  Neither I nor II is true done clear
  View Solution play_arrow

• question_answer41)
  Let \[X=\{1,2,3,4,5\}\] and \[Y=\{1,3,5,7,9\},\]which of the following is not relation form X to Y?
  A)
  \[{{R}_{1}}=\{(x,y):y=x+2,x\in X,y\in Y\}\] done clear
  B)
  \[{{R}_{2}}=\{(1,1),(2,1),(3,3),(4,3),(5,5)\}\] done clear
  C)
  \[{{R}_{3}}=\{(1,1),(1,3),(3,5),(3,7),(5,7)\}\] done clear
  D)
  \[{{R}_{4}}=\{(1,3),(2,5),(2,4),(7,9)\}\] done clear
  View Solution play_arrow

• question_answer42)
  Domain of definition of the function \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x),\] is
  A)
  \[(-1,0)\cup (1,2)\cup (2,\infty )\]   done clear
  B)
  \[(a,2)\] done clear
  C)
  \[(-1,0)\cup (a,2)\] done clear
  D)
         \[(1,2)\cup (2,\infty )\] done clear
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• question_answer43)
  The domain for which the functions \[f(x)=2{{x}^{2}}-1\] and \[g(x)=1-3x\] is equal, i.e., \[f(x)=g(x).\], is
  A)
  \[\{0,\,\,2\}\] done clear
  B)
         \[\left\{ \frac{1}{2},-2 \right\}\] done clear
  C)
  \[\left\{ -\frac{1}{2},2 \right\}\] done clear
  D)
         \[\left\{ \frac{1}{2},2 \right\}\] done clear
  View Solution play_arrow

• question_answer44)
  The domain of the function \[f(x)=lo{{g}_{e}}\{sgn(9-{{x}^{2}})\}+\sqrt{{{[x]}^{3}}-4[x]}\] (where [.] represents the greatest integer function) is
  A)
  \[\left[ -2,1 \right)\cup \left[ 2,3 \right)\] done clear
  B)
         \[\left[ -4,1 \right)\cup \left[ 2,3 \right)\] done clear
  C)
  \[\left[ 4,1 \right)\cup \left[ 2,3 \right)\]        done clear
  D)
         \[\left[ 2,1 \right)\cup \left[ 2,3 \right)\] done clear
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• question_answer45)
  The domain of the function \[f(x)=\frac{\left| x+3 \right|}{x+3}\] is
  A)
  \[\{-3\}\] done clear
  B)
         \[R-\{-3\}\] done clear
  C)
  \[R-\{-3\}\] done clear
  D)
         \[R\] done clear
  View Solution play_arrow

• question_answer46)
  The domain of the real valued function \[f(x)=\sqrt{5-4x-{{x}^{2}}}+{{x}^{2}}\log (x+4)\] is
  A)
  \[(-5,1)\] done clear
  B)
         \[-5\le x\,\,and\,\,x\ge 1\] done clear
  C)
  \[\left( -4,1 \right]\] done clear
  D)
         \[\phi \] done clear
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• question_answer47)
  The domain and range of the function  f given by \[f(x)=2-\left| x-5 \right|\] is
  A)
  \[Domain=\,{{R}^{+}},\,\,Range=(-\infty ,\,\,1]\] done clear
  B)
  \[Domain=\,R,\,\,Range=(-\infty ,\,\,2]\] done clear
  C)
  \[Domain=R,\text{ }Range=(-\infty ,\,\,2)\] done clear
  D)
  \[\operatorname{Domain} ={{R}^{+}}, Range=(-\infty ,\,\,2)\] done clear
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• question_answer48)
  The domain of \[F(x)=\frac{{{\log }_{2}}(x+3)}{{{x}^{2}}+3x+2}\] is
  A)
  \[R-\{-1,-2\}\] done clear
  B)
         \[(-2,\infty )\] done clear
  C)
  \[R-\{-1,-2-3\}\] done clear
  D)
         \[(-3,\infty )-\{-1,-2\}\] done clear
  View Solution play_arrow

• question_answer49)
  The Domain of the function \[f(x)=\sqrt{\frac{1}{\left| x-2 \right|-(x-2)}}\] is:
  A)
  \[\left( -\infty ,2 \right]\] done clear
  B)
         \[(2,\infty )\] done clear
  C)
  \[(-\infty ,2)\] done clear
  D)
         \[[2,\infty )\] done clear
  View Solution play_arrow

• question_answer50)
  Find the range of \[f(x)=sgn({{x}^{2}}-2x+3).\]
  A)
  \[\{1,-1\}\] done clear
  B)
         \[\{1\}\] done clear
  C)
  \[\{-1\}\]            done clear
  D)
         None of these done clear
  View Solution play_arrow

• question_answer51)
  If \[{{\log }_{1/2}}\left( {{x}^{2}}-5x+7 \right)>0,\] then exhaustive range of values of x is
  A)
  \[(-\infty ,2)\cup (3,\infty )\] done clear
  B)
  \[(2,3)\] done clear
  C)
  \[(-\infty ,1)\cup (1,2)\cup (2,\infty )\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  The domain of the function \[f(x)=lo{{g}_{3+x}}({{x}^{2}}-1)\] is
  A)
  \[(-3,-1)\cup (1,\infty )\] done clear
  B)
  \[[-3,-1)\cup [1,\infty )\] done clear
  C)
  \[(-3,-2)\cup (-2,-1)\cup (1,\infty )\] done clear
  D)
  \[[-3,-2)\cup (-2,-1)\cup [1,\infty )\] done clear
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• question_answer53)
  If \[f(x)=\frac{1}{\sqrt{(x+1)({{e}^{x}}-1)(x-4)(x+5)(x-6)}}\]Then the domain of f(x) is
  A)
  \[(-\infty ,-5)\cup (-1,4)\cup (6,\infty )\] done clear
  B)
  \[(-\infty ,-5)\cup (-1,0)\cup (0,4)\cup (6,\infty )\] done clear
  C)
  \[(-5,-1)\cup (0,4)\cup (6,\infty )\] done clear
  D)
  None of these done clear
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• question_answer54)
  The domain of the function\[f(x)=\sqrt{{{x}^{14}}-{{x}^{11}}+{{x}^{6}}-{{x}^{3}}+{{x}^{2}}+1}\] is
  A)
  \[(-\infty ,\infty )\] done clear
  B)
         \[[0,\infty )\] done clear
  C)
  \[(-\infty ,0]\] done clear
  D)
         \[R\backslash [0,1]\] done clear
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• question_answer55)
  The domain of the function\[\sqrt{{{x}^{2}}-5x+6}+\sqrt{2x+8-{{x}^{2}}}\] is
  A)
  \[[2,3]\] done clear
  B)
         \[[-2,\,\,4]\] done clear
  C)
  \[[-2,2]\cup [3,4]\] done clear
  D)
         \[[-2,1]\cup [2,4]\] done clear
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• question_answer56)
  If f(x) = x and \[g(x)=\left| x \right|\], then \[(f+g)(x)\] is equal to
  A)
  0 for all \[x\in R\] done clear
  B)
         2x for all \[x\in R\] done clear
  C)
  \[\left\{ \begin{matrix}    2x,for\,\,x\ge 0  \\    0,for\,\,x<0  \\ \end{matrix} \right.\] done clear
  D)
         \[\left\{ \begin{matrix}    0,for\,\,x\ge 0  \\    2x,for\,\,x<0  \\ \end{matrix} \right.\] done clear
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• question_answer57)
  Let \[f(x)=x,g(x)=\frac{1}{x}\] and \[h(x)=f(x)g(x).\]Then, \[h(x)=1\] if and only if
  A)
  x is a real number done clear
  B)
  x is a rational number done clear
  C)
  x is an irrational number done clear
  D)
  x is a non-zero real number done clear
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• question_answer58)
  The function \[f(x)=log\left( x+\sqrt{{{x}^{2}}+1} \right)\], is
  A)
  neither an even nor an odd function done clear
  B)
  an even function done clear
  C)
  an odd function done clear
  D)
  a periodic function done clear
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• question_answer59)
  Let \[f(x)=\frac{\alpha {{x}^{2}}}{x+1},x\ne -1.\] The value of \[\alpha \] for which \[f(a)=a,(a\ne 0)\] is
  A)
  \[1-\frac{1}{a}\] done clear
  B)
         \[\frac{1}{a}\] done clear
  C)
  \[1+\frac{1}{a}\] done clear
  D)
         \[\frac{1}{a}-1\] done clear
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• question_answer60)
  If \[f(2x+3y,2x-7y)=20x,\] then \[f(x,y)\] equals
  A)
  \[7x-3y\] done clear
  B)
         \[7x+3y\] done clear
  C)
  \[3x-7y\] done clear
  D)
         \[3x+7y\] done clear
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• question_answer61)
  Which of the following function are periodic?
  A)
  \[f(x)=log\,\,x,x>0\] done clear
  B)
  \[f(x)={{e}^{x}},x\in R\] done clear
  C)
  \[f(x)=x-[x],x\in R\] done clear
  D)
  \[f(x)=x+[x],x\in R\] done clear
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• question_answer62)
  Let \[f(x)=[x],\] where \[[x]\] denotes the greatest integer less than or equal to x. if \[a=\sqrt{{{2011}^{2}}+2012}\], then the value of fis equal to
  A)
  2010 done clear
  B)
  2011 done clear
  C)
  2012 done clear
  D)
         2013 done clear
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• question_answer63)
  If f and g are two functions defined as \[f(x)=x+2,\]\[x\le 0;\,\,g(x)=3,\,\,x\ge 0,\] then the domain of \[f+g\] is
  A)
  \[\{0\}\] done clear
  B)
                     \[\left[ 0,\infty  \right)\] done clear
  C)
  \[(-\infty ,\infty )\] done clear
  D)
         \[(-\infty ,0)\] done clear
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• question_answer64)
  If \[f(x)={{e}^{-x}},\] then \[\frac{f(-a)}{f(b)}\] is equal to
  A)
  \[f(a+b)\] done clear
  B)
         \[f(a-b)\] done clear
  C)
  \[f(-a+b)\] done clear
  D)
         \[f(-a-b)\] done clear
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• question_answer65)
  If \[f(x)=\frac{x}{x-1},\] then \[\frac{f(a)}{f(a+1)}\]is equal to:
  A)
  \[f({{a}^{2}})\] done clear
  B)
         \[f\left( \frac{1}{a} \right)\] done clear
  C)
  \[f(-a)\] done clear
  D)
         \[f\left| \frac{-a}{a-1} \right|\] done clear
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• question_answer66)
  Let \[f(x)=\frac{x}{1-x}\] and ?a? be a real number. If \[{{x}_{0}}=a,{{x}_{1}}=f({{x}_{0}}),{{x}_{2}}=f({{x}_{1}}),{{x}_{3}}=f({{x}_{2}})...\] If \[{{x}_{2009}}=1,\] then the value of a is
  A)
  0 done clear
  B)
         \[\frac{2009}{2010}\] done clear
  C)
  \[\frac{1}{2009}\] done clear
  D)
         \[\frac{1}{2010}\] done clear
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• question_answer67)
  If a function F is such that \[F(0)=2,F(1)=3,\]\[F(x+2)=2F(x)-F(x+1)\] for \[x\ge 0,\] then \[F(5)\] is equal to
  A)
  -7 done clear
  B)
         -3 done clear
  C)
  17 done clear
  D)
         13 done clear
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• question_answer68)
  Which of the following statements is incorrect
  A)
  x sgn x = \[\left| x \right|\] done clear
  B)
  \[\left| x \right|\] sgn x = x done clear
  C)
  \[x(sgn\,x)(sgn\,x)=x\] done clear
  D)
  \[\left| x \right|\,{{(sgn\,x)}^{3}}=\left| x \right|\] done clear
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• question_answer69)
  If \[f(x)\] and \[g(x)\] are periodic functions with periods 7 and 11, respectively, then the period of \[F(x)=f(x)g\left( \frac{x}{5} \right)-g(x)f\left( \frac{x}{3} \right)\] is
  A)
  177 done clear
  B)
         222 done clear
  C)
  433 done clear
  D)
         1155 done clear
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• question_answer70)
  The graph of the function \[y=f(x)\] is symmetrical about the line \[x=2,\] then
  A)
  \[f(x)=-f(-x)\] done clear
  B)
  \[f(2+x)=f(2-x)\] done clear
  C)
  \[f(x)=f(-x)\] done clear
  D)
  \[f(x+2)=f(x-2)\] done clear
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