-
question_answer1)
The function \[x+\frac{1}{x},(x\ne 0)\]is a non-increasing function in the interval
A)
[? 1, 1] done
clear
B)
[0, 1] done
clear
C)
[?1, 0] done
clear
D)
[?1,2] done
clear
View Solution play_arrow
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question_answer2)
The function \[\frac{1}{1+{{x}^{2}}}\]is decreasing in the interval
A)
\[(-\infty ,\,-1]\] done
clear
B)
\[(-\infty ,\,0]\] done
clear
C)
\[[1,\infty )\] done
clear
D)
\[(0,\infty )\] done
clear
View Solution play_arrow
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question_answer3)
Which of the following is not a decreasing function on the interval \[\left( 0,\frac{\pi }{2} \right)\]
A)
\[\cos x\] done
clear
B)
\[\cos 2x\] done
clear
C)
\[\cos 3x\] done
clear
D)
\[\cot x\] done
clear
View Solution play_arrow
-
question_answer4)
The function \[\frac{x-2}{x+1},(x\ne -1)\]is increasing on the interval
A)
\[(-\infty ,\,\,\,0]\] done
clear
B)
[0, \[\infty \]) done
clear
C)
R done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer5)
In the interval [0, 1], the function \[{{x}^{2}}-x+1\]is
A)
Increasing done
clear
B)
Decreasing done
clear
C)
Neither increasing nor decreasing done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer6)
The interval in which the function \[{{x}^{2}}{{e}^{-x}}\]is non decreasing, is
A)
\[(-\infty ,\,\,2]\] done
clear
B)
[0, 2] done
clear
C)
\[[2,\,\,\infty )\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer7)
On the interval \[\left( 0,\frac{\pi }{2} \right)\], the function log sin x is
A)
Increasing done
clear
B)
Decreasing done
clear
C)
Neither increasing nor decreasing done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer8)
The function \[\sin x-\cos x\]is increasing in the interval
A)
\[\left[ \frac{3\pi }{4},\frac{7\pi }{4} \right]\] done
clear
B)
\[\left[ 0,\frac{3\pi }{4} \right)\] done
clear
C)
\[\left[ \frac{\pi }{4},\frac{3\pi }{4} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer9)
The function \[\sin x-bx+c\]will be increasing in the interval \[(-\infty ,\,\,\infty )\], if
A)
\[b\le 1\] done
clear
B)
\[b\le 0\] done
clear
C)
\[b<-1\] done
clear
D)
\[b\ge 0\] done
clear
View Solution play_arrow
-
question_answer10)
The function \[{{x}^{4}}-4x\]is decreasing in the interval
A)
[?1, 1] done
clear
B)
\[(-\infty ,\,\,1)\] done
clear
C)
\[[1,\,\,+\infty )\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
For which interval the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\] is decreasing [MP PET 1993]
A)
\[(-2,\,\infty )\] done
clear
B)
\[(-2,\,-1)\] done
clear
C)
\[(-\infty ,\,-1)\] done
clear
D)
\[(-\infty ,\,\,-2)\]and \[(-1,\,\infty )\] done
clear
View Solution play_arrow
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question_answer12)
\[f(x)={{x}^{3}}-27x+5\]is an increasing function, when [MP PET 1995]
A)
\[x<-3\] done
clear
B)
\[|x|\,>3\] done
clear
C)
\[x\le -3\] done
clear
D)
\[|x|\,<3\] done
clear
View Solution play_arrow
-
question_answer13)
The function \[f(x)={{x}^{2}}\]is increasing in the interval
A)
\[(-1,\,1)\] done
clear
B)
\[(-\infty ,\,\infty )\] done
clear
C)
\[(0,\,\infty )\] done
clear
D)
\[(-\infty ,\,0)\] done
clear
View Solution play_arrow
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question_answer14)
Function \[f(x)={{x}^{4}}-\frac{{{x}^{3}}}{3}\]is
A)
Increasing for \[x>\,\frac{1}{4}\]and decreasing for \[x<\frac{1}{4}\] done
clear
B)
Increasing for every value of x done
clear
C)
Decreasing for every value of x done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer15)
For every value of x function \[f(x)={{e}^{x}}\]is
A)
Decreasing done
clear
B)
Increasing done
clear
C)
Neither increasing nor decreasing done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer16)
If \[f'(x)\]is zero in the interval (a, b) then in this interval it is
A)
Increasing function done
clear
B)
Decreasing function done
clear
C)
Only for a > 0 and b>0 is increasing function done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer17)
For the every value of x the function \[f(x)=\frac{1}{{{5}^{x}}}\]is
A)
Decreasing done
clear
B)
Increasing done
clear
C)
Neither increasing nor decreasing done
clear
D)
Increasing for x > 0 and decreasing for x < 0 done
clear
View Solution play_arrow
-
question_answer18)
The interval for which the given function \[f(x)=2{{x}^{3}}-3{{x}^{2}}-36x+7\] is decreasing, is
A)
(? 2, 3) done
clear
B)
(2, 3) done
clear
C)
(2,? 3) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer19)
If \[f(x)=\sin x-\frac{x}{2}\] is increasing function, then [MP PET 1987]
A)
\[0<x<\frac{\pi }{3}\] done
clear
B)
\[-\frac{\pi }{3}<x<0\] done
clear
C)
\[-\frac{\pi }{3}<x<\frac{\pi }{3}\] done
clear
D)
\[x=\frac{\pi }{2}\] done
clear
View Solution play_arrow
-
question_answer20)
If x tends 0 to \[\pi \], then the given function \[f(x)=x\sin x+\cos x+{{\cos }^{2}}x\] is
A)
Increasing done
clear
B)
Decreasing done
clear
C)
Neither increasing nor decreasing done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer21)
Let \[y={{x}^{2}}{{e}^{-x}}\], then the interval in which y increases with respect to x is [MNR 1994; Kurukshetra CEE 1998]
A)
\[(-\infty ,\infty )\] done
clear
B)
\[(-2,\,0)\] done
clear
C)
\[(2,\infty )\] done
clear
D)
\[(0,\,2)\] done
clear
View Solution play_arrow
-
question_answer22)
The function \[y=2{{x}^{3}}-9{{x}^{2}}+12x-6\] is monotonic decreasing, when [MP PET 1994]
A)
\[1<x<2\] done
clear
B)
\[x>2\] done
clear
C)
\[x<1\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer23)
For which value of x, the function \[f(x)={{x}^{2}}-2x\] is decreasing [BIT Ranchi 1990]
A)
\[x>1\] done
clear
B)
\[x>2\] done
clear
C)
\[x<1\] done
clear
D)
\[x<2\] done
clear
View Solution play_arrow
-
question_answer24)
The function \[f(x)=\cos x-2px\] is monotonically decreasing for [RPET 1987; MP PET 2002]
A)
\[p<\frac{1}{2}\] done
clear
B)
\[p>\frac{1}{2}\] done
clear
C)
\[p<2\] done
clear
D)
\[p>2\] done
clear
View Solution play_arrow
-
question_answer25)
If \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\]is monotonically increasing in each interval, then [RPET 1992; Kurukshetra CEE 2002]
A)
\[k<3\] done
clear
B)
\[k\le 3\] done
clear
C)
\[k>3\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer26)
In which interval is the given function \[f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+1\] is monotonically decreasing [RPET 1995]
A)
[2, 3] done
clear
B)
(2, 3) done
clear
C)
\[(-\infty ,\,2)\] done
clear
D)
\[(3,\,\infty )\] done
clear
View Solution play_arrow
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question_answer27)
The function \[f(x)=\tan x-x\] [MNR 1995; Pb. CET 2000; Karnataka CET 2002]
A)
Always increases done
clear
B)
Always decreases done
clear
C)
Never decreases done
clear
D)
Sometimes increases and sometimes decreases done
clear
View Solution play_arrow
-
question_answer28)
The function \[f(x)=\log (1+x)-\frac{2x}{2+x}\]is increasing on [EAMCET 2002]
A)
(0, \[\infty \]) done
clear
B)
(\[-\infty \], 0) done
clear
C)
\[(-\infty ,\infty )\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer29)
If the function \[f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}\]is increasing for all values of x, then
A)
\[K<1\] done
clear
B)
\[K>1\] done
clear
C)
\[K<2\] done
clear
D)
\[K>2\] done
clear
View Solution play_arrow
-
question_answer30)
The value of ?a? in order that \[f(x)=\sqrt{3}\] \[\sin x-\cos x-2ax+b\] decreases for all real values of x, is given by
A)
\[a<1\] done
clear
B)
\[a\ge 1\] done
clear
C)
\[a\ge \sqrt{2}\] done
clear
D)
\[a<\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer31)
The interval in which the function \[{{x}^{3}}\]increases less rapidly than\[6{{x}^{2}}+15x+5\], is
A)
\[(-\infty ,\,-1)\] done
clear
B)
(?5 , 1) done
clear
C)
(?1 ,5) done
clear
D)
(5 , \[\infty \]) done
clear
View Solution play_arrow
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question_answer32)
The values of ?a? for which the function \[(a+2){{x}^{3}}-3a{{x}^{2}}+9ax-1\] decreases monotonically throughout for all real x, are [Kurukshetra CEE 2002]
A)
\[a<-2\] done
clear
B)
\[a>-2\] done
clear
C)
\[-3<a<0\] done
clear
D)
\[-\infty <a\le -3\] done
clear
View Solution play_arrow
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question_answer33)
If \[f(x)=2x+{{\cot }^{-1}}x+\log (\sqrt{1+{{x}^{2}}}-x)\], then \[f(x)\]
A)
Increases in [0 ,\[\infty \]) done
clear
B)
Decreases in [0 ,\[\infty \]) done
clear
C)
Neither increases nor decreases in (0, \[\infty \]) done
clear
D)
Increases in (?\[\infty \],\[\infty \]) done
clear
View Solution play_arrow
-
question_answer34)
For all real values of x, increasing function f(x) is [MP PET 1996]
A)
\[{{x}^{-1}}\] done
clear
B)
\[{{x}^{2}}\] done
clear
C)
\[{{x}^{3}}\] done
clear
D)
\[{{x}^{4}}\] done
clear
View Solution play_arrow
-
question_answer35)
The least value of k for which the function \[{{x}^{2}}+kx+1\]is an increasing function in the interval \[1<x<2\]is
A)
? 4 done
clear
B)
? 3 done
clear
C)
? 1 done
clear
D)
? 2 done
clear
View Solution play_arrow
-
question_answer36)
The interval of the decreasing function \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\]is
A)
\[\left( \frac{1}{3},\,1 \right)\] done
clear
B)
\[\left( -\frac{1}{3},1 \right)\] done
clear
C)
\[\left( -\frac{1}{3},\,\frac{1}{3} \right)\] done
clear
D)
\[\left( -1,-\frac{1}{3} \right)\] done
clear
View Solution play_arrow
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question_answer37)
The function \[f(x)={{x}^{3}}-3{{x}^{2}}-24x+5\] is an increasing function in the interval given below [MP PET 1998]
A)
\[(-\infty ,\,-2)\cup (4,\infty )\] done
clear
B)
\[(-2,\infty )\] done
clear
C)
(?2, 4) done
clear
D)
\[(-\infty ,\,4)\] done
clear
View Solution play_arrow
-
question_answer38)
Which one is the correct statement about the function \[f(x)=\sin 2x\]
A)
\[f(x)\] is increasing in \[\left( 0,\frac{\pi }{2} \right)\] and decreasing in \[\left( \frac{\pi }{2},\pi \right)\] done
clear
B)
\[f(x)\] is decreasing in \[\left( 0,\frac{\pi }{2} \right)\] and increasing in \[\left( \frac{\pi }{2},\pi \right)\] done
clear
C)
\[f(x)\] is increasing in \[\left( 0,\frac{\pi }{4} \right)\] and decreasing in \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\] done
clear
D)
The statements , and are all correct done
clear
View Solution play_arrow
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question_answer39)
The function f defined by \[f(x)=(x+2){{e}^{-x}}\] is [IIT Screening 1994]
A)
Decreasing for all x done
clear
B)
Decreasing in \[(-\infty ,\,-1)\] and increasing in \[(-1,\infty )\] done
clear
C)
Increasing for all x done
clear
D)
Decreasing in \[(-1,\,\infty )\] and increasing in \[(-\infty ,\,-1)\] done
clear
View Solution play_arrow
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question_answer40)
If \[f(x)={{x}^{3}}-10{{x}^{2}}+200x-10\], then [Kurukshetra CEE 1998]
A)
\[f(x)\]is decreasing in \[]-\infty ,10]\] and increasing in \[[10,\,\infty [\] done
clear
B)
\[f(x)\]is increasing in \[]-\infty ,10]\] and decreasing in \[[10,\,\infty [\] done
clear
C)
\[f(x)\]is increasing throughout real line done
clear
D)
\[f(x)\]is decreasing throughout real line done
clear
View Solution play_arrow
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question_answer41)
If \[f(x)=\frac{x}{\sin x}\]and \[g(x)=\frac{x}{\tan x}\], where \[0<x\le 1\], then in this interval [IIT 1997 Re-Exam]
A)
Both \[f(x)\] and \[g(x)\] are increasing functions done
clear
B)
Both \[f(x)\] and \[g(x)\] are decreasing functions done
clear
C)
\[f(x)\]is an increasing function done
clear
D)
\[g(x)\] is an increasing function done
clear
View Solution play_arrow
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question_answer42)
Function \[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+29\] is monotonically decreasing, when [RPET 1996]
A)
\[x<2\] done
clear
B)
x > 2 done
clear
C)
x >1 done
clear
D)
1< x < 2 done
clear
View Solution play_arrow
-
question_answer43)
\[2{{x}^{3}}+18{{x}^{2}}-96x+45=0\]is an increasing function when [RPET 1997]
A)
\[x\le -8,\,x\ge 2\] done
clear
B)
\[x<-2,x\ge 8\] done
clear
C)
\[x\le -2,x\ge 8\] done
clear
D)
\[0\le x\le -2\] done
clear
View Solution play_arrow
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question_answer44)
The function \[\frac{a\sin x+b\cos x}{c\sin x+d\,\cos x}\] is decreasing, if [RPET 1999]
A)
\[ad-bc>0\] done
clear
B)
\[ad-bc<0\] done
clear
C)
\[ab-cd>0\] done
clear
D)
\[ab-cd<0\] done
clear
View Solution play_arrow
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question_answer45)
The function \[f(x)=1-{{e}^{-{{x}^{2}}/2}}\] is [AMU 1999]
A)
Decreasing for all x done
clear
B)
Increasing for all x done
clear
C)
Decreasing for \[x<0\] and increasing for \[x>0\] done
clear
D)
Increasing for \[x<0\] and decreasing for \[x>0\] done
clear
View Solution play_arrow
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question_answer46)
Consider the following statements S and R S : Both \[\sin x\] and cosx are decreasing functions in \[\left( \frac{\pi }{2},\pi \right)\] R : If a differentiable function decreases in (a, b) then its derivative also decreases in (a, b). Which of the following is true [IIT Screening 2000]
A)
Both S and R are wrong done
clear
B)
Both S and R are correct but R is not the correct explanation for S done
clear
C)
S is correct and R is the correct explanation for S done
clear
D)
S is correct and R is wrong done
clear
View Solution play_arrow
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question_answer47)
The function which is neither decreasing nor increasing in \[\left( \frac{\pi }{2},\frac{3\pi }{2} \right)\] is [MP PET 2000]
A)
cosec x done
clear
B)
\[\tan x\] done
clear
C)
\[{{x}^{2}}\] done
clear
D)
\[|x-1|\] done
clear
View Solution play_arrow
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question_answer48)
Function \[f(x)=\frac{\lambda \sin x+6\cos x}{2\sin x+3\cos x}\] is monotonic increasing, if [MP PET 2001]
A)
\[\lambda >1\] done
clear
B)
\[\lambda <1\] done
clear
C)
\[\lambda <4\] done
clear
D)
\[\lambda >4\] done
clear
View Solution play_arrow
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question_answer49)
On the interval (1,3), the function \[f(x)=3x+\frac{2}{x}\]is [AMU 1999]
A)
Strictly decreasing done
clear
B)
Strictly increasing done
clear
C)
Decreasing in (2, 3) only done
clear
D)
Neither increasing nor decreasing done
clear
View Solution play_arrow
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question_answer50)
If \[f(x)=\sin x-\cos x,\] the function decreasing in \[0\le x\le 2\pi \] is [UPSEAT 2001]
A)
\[[5\pi /6,\,3\pi /4]\] done
clear
B)
\[[\pi /4,\,\pi /2]\] done
clear
C)
\[[3\pi /2,\,5\pi /2]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer51)
The function \[f(x)=\frac{\log x}{x}\] is increasing in the interval [UPSEAT 2001]
A)
\[(1,\,2e)\] done
clear
B)
(0,e) done
clear
C)
(2, 2e) done
clear
D)
(1/e, 2e) done
clear
View Solution play_arrow
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question_answer52)
If \[f(x)=x{{e}^{x(1-x)}}\], then \[f(x)\] is [IIT Screening 2001]
A)
Increasing on \[\left[ -\frac{1}{2},\,1 \right]\] done
clear
B)
Decreasing on R done
clear
C)
Increasing on R done
clear
D)
Decreasing on \[\left[ -\frac{1}{2},1 \right]\] done
clear
View Solution play_arrow
-
question_answer53)
If \[f(x)={{x}^{3}}-6{{x}^{2}}+9x+3\] be a decreasing function, then x lies in [RPET 2002]
A)
\[(-\infty ,-1)\cap (3,\,\infty )\] done
clear
B)
\[(1,\,\,3)\] done
clear
C)
\[(3,\,\,\infty )\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer54)
If \[f(x)=\frac{1}{x+1}-\log \,(1+x),\,x>0,\]then \[f\]is [RPET 2002]
A)
An increasing function done
clear
B)
A decreasing function done
clear
C)
Both increasing and decreasing function done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer55)
The function \[f(x)=x\,+\,\cos x\] is [DCE 2002]
A)
Always increasing done
clear
B)
Always decreasing done
clear
C)
Increasing for certain range of x done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer56)
The function \[f(x)={{x}^{1/x}}\] is [AMU 2002]
A)
Increasing in \[(1,\,\,\infty )\] done
clear
B)
Decreasing in \[(1,\,\,\infty )\] done
clear
C)
Increasing in \[(1,\,e),\] decreasing in \[(e,\infty )\] done
clear
D)
Decreasing in \[(1,\,e),\] increasing in \[(e,\infty )\] done
clear
View Solution play_arrow
-
question_answer57)
The function \[f(x)=1-{{x}^{3}}-{{x}^{5}}\] is decreasing for [Kerala (Engg.) 2002]
A)
\[1\le x\le 5\] done
clear
B)
\[x\le 1\] done
clear
C)
\[x\ge 1\] done
clear
D)
All values of x done
clear
View Solution play_arrow
-
question_answer58)
The function \[{{x}^{x}}\] is increasing, when [MP PET 2003]
A)
\[x>\frac{1}{e}\] done
clear
B)
\[x<\frac{1}{e}\] done
clear
C)
\[x<0\] done
clear
D)
For all real x done
clear
View Solution play_arrow
-
question_answer59)
\[2{{x}^{3}}-6x+5\] is an increasing function if [UPSEAT 2003]
A)
\[0<x<1\] done
clear
B)
\[-1<x<1\] done
clear
C)
\[x<-1\] or \[x>1\] done
clear
D)
\[-1<x<-1/2\] done
clear
View Solution play_arrow
-
question_answer60)
The length of the longest interval, in which the function \[3\sin x-4\sin x\] is increasing, is [IIT Screening 2002]
A)
\[\frac{\pi }{3}\] done
clear
B)
\[\frac{\pi }{2}\] done
clear
C)
\[\frac{3\pi }{2}\] done
clear
D)
\[\pi \] done
clear
View Solution play_arrow
-
question_answer61)
Let \[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d,0<{{b}^{2}}<c\]. Then f [IIT Screening 2004]
A)
Is bounded done
clear
B)
Has a local maxima done
clear
C)
Has a local minima done
clear
D)
Is strictly increasing done
clear
View Solution play_arrow
-
question_answer62)
If \[f(x)=x,-1\le x\le 1\], then function \[f(x)\] is [SCRA 1996]
A)
Increasing done
clear
B)
Decreasing done
clear
C)
Stationary done
clear
D)
Discontinuous done
clear
View Solution play_arrow
-
question_answer63)
For all \[x\in (0,\,1)\] [IIT Screening 2000]
A)
\[{{e}^{x}}<1+x\] done
clear
B)
\[{{\log }_{e}}(1+x)<x\] done
clear
C)
\[\sin x>x\] done
clear
D)
\[{{\log }_{e}}x>x\] done
clear
View Solution play_arrow
-
question_answer64)
The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174\] is increasing in the interval [J & K 2005]
A)
\[\frac{1}{2}<x<1\] done
clear
B)
\[\frac{1}{2}<x<2\] done
clear
C)
\[3<x<\frac{59}{4}\] done
clear
D)
\[-\infty <x<\infty \] done
clear
View Solution play_arrow
-
question_answer65)
The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always an increasing function on the interval [Kerala (Engg.) 2005]
A)
\[(0,\,\pi )\] done
clear
B)
\[(0,\,\pi /2)\] done
clear
C)
\[(0,\pi /4)\] done
clear
D)
\[(0,\,3\pi /4)\] done
clear
E)
\[(0,\,5\pi /4)\] done
clear
View Solution play_arrow
-
question_answer66)
Given function \[f(x)=\left( \frac{{{e}^{2x}}-1}{{{e}^{2x}}+1} \right)\] is [Orissa JEE 2005]
A)
Increasing done
clear
B)
Decreasing done
clear
C)
Even done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer67)
Function \[f(x)=\frac{4{{x}^{2}}+1}{x}\] is decreasing for interval
A)
\[\left( \frac{-1}{2},\,\frac{1}{2} \right)\] done
clear
B)
\[\left[ \frac{1}{2},\,-\frac{1}{2} \right]\] done
clear
C)
(? 1, 1) done
clear
D)
[1, ?1] done
clear
View Solution play_arrow
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question_answer68)
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? [AIEEE 2005]
A)
Interval Function \[\left( -\infty ,\,\frac{1}{3} \right]\] \[3{{x}^{2}}-2x+1\] done
clear
B)
(? ¥, ? 4] \[{{x}^{3}}+6{{x}^{2}}+6\] done
clear
C)
(? ¥, ¥) \[{{x}^{3}}-3{{x}^{2}}+3x+3\] done
clear
D)
[2, ¥) \[2{{x}^{3}}-3{{x}^{2}}-12x+6\] done
clear
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