-
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
View Solution play_arrow
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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
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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
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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
View Solution play_arrow
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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
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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
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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
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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
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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
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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
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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
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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
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
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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
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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
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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
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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
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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
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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
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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
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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
View Solution play_arrow
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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
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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
View Solution play_arrow
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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
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
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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
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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
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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
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow
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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
View Solution play_arrow