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question_answer1)
The number of real values of x for which the equality \[\left| \,3{{x}^{2}}+12x+6\, \right|=5x+16\] holds good is [AMU 1999]
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
1 done
clear
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question_answer2)
If x is real and satisfies \[x+2>\sqrt{x+4},\] then [AMU 1999]
A)
\[x<-2\] done
clear
B)
\[x>0\] done
clear
C)
\[-3<x<0\] done
clear
D)
\[-3<x<4\] done
clear
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question_answer3)
The complete solution of the inequation \[{{x}^{2}}-4x<12\,\text{ is}\] [AMU 1999]
A)
\[x<-\,2\] or \[x>6\] done
clear
B)
\[-\,6<x<2\] done
clear
C)
\[2<x<6\] done
clear
D)
\[-\,2<x<6\] done
clear
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question_answer4)
The number of roots of the equation \[\log (-2x)\] \[=2\log (x+1)\] are [AMU 2001]
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
None of these done
clear
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question_answer5)
The set of all real numbers x for which \[{{x}^{2}}-|x+2|+x>0,\] is [IIT Screening 2002]
A)
\[(-\infty ,\,\,-2)\,\cup (2,\,\infty )\] done
clear
B)
\[(-\infty ,\,\,-\sqrt{2})\,\cup (\sqrt{2},\,\infty )\] done
clear
C)
\[(-\infty ,\,\,-1)\,\cup (1,\,\infty )\] done
clear
D)
\[(\sqrt{2},\,\infty )\] done
clear
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question_answer6)
If \[{{x}^{2}}+2ax+10-3a>0\] for all \[x\in R\], then [IIT Screening 2004]
A)
\[-5<a<2\] done
clear
B)
\[a<-5\] done
clear
C)
\[a>5\] done
clear
D)
\[2<a<5\] done
clear
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question_answer7)
The roots of the equation \[{{x}^{4}}-4{{x}^{3}}+6{{x}^{2}}-4x+1=0\] are [MP PET 1986]
A)
1, 1, 1, 1 done
clear
B)
2, 2, 2, 2 done
clear
C)
3, 1, 3, 1 done
clear
D)
1, 2, 1, 2 done
clear
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question_answer8)
If the roots of the equation \[8{{x}^{3}}-14{{x}^{2}}+7x-1=0\] are in G.P., then the roots are [MP PET 1986]
A)
\[1,\frac{1}{2},\frac{1}{4}\] done
clear
B)
2, 4, 8 done
clear
C)
3, 6, 12 done
clear
D)
None of these done
clear
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question_answer9)
If the sum of the two roots of the equation \[4{{x}^{3}}+16{{x}^{2}}-9x-36=0\] is zero, then the roots are [MP PET 1986]
A)
1, 2 -2 done
clear
B)
\[-2,\frac{2}{3},-\frac{2}{3}\] done
clear
C)
\[-3,\frac{3}{2},-\frac{3}{2}\] done
clear
D)
\[-4,\frac{3}{2},-\frac{3}{2}\] done
clear
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question_answer10)
One root of the following given equation \[2{{x}^{5}}-14{{x}^{4}}+31{{x}^{3}}-64{{x}^{2}}+19x+130=0\] is [MP PET 1985]
A)
1 done
clear
B)
3 done
clear
C)
5 done
clear
D)
7 done
clear
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question_answer11)
If two roots of the equation \[{{x}^{3}}-3x+2=0\] are same, then the roots will be [MP PET 1985]
A)
2, 2, 3 done
clear
B)
1, 1, -2 done
clear
C)
- 2, 3, 3 done
clear
D)
-2, -2, 1 done
clear
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question_answer12)
If \[a,b,c\] are real and \[{{x}^{3}}-3{{b}^{2}}x+2{{c}^{3}}\] is divisible by \[x-a\] and\[x-b\], then
A)
\[a=-b=-c\] done
clear
B)
\[a=2b=2c\] done
clear
C)
\[a=b=c\],\[a=-2b=-2c\] done
clear
D)
None of these done
clear
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question_answer13)
If a, b and g are the roots of \[{{x}^{3}}+8=0\], then the equation whose roots are \[{{\alpha }^{2}},{{\beta }^{2}}\]and \[{{\gamma }^{2}}\]is
A)
\[{{x}^{3}}-8=0\] done
clear
B)
\[{{x}^{3}}-16=0\] done
clear
C)
\[{{x}^{3}}+64=0\] done
clear
D)
\[{{x}^{3}}-64=0\] done
clear
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question_answer14)
If \[\alpha ,\,\beta ,\,\gamma \] are the roots of the equation \[{{x}^{3}}+4x+1=0,\] then \[{{(\alpha +\beta )}^{-1}}+{{(\beta +\gamma )}^{-1}}+{{(\gamma +\alpha )}^{-1}}=\] [EAMCET 2003]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer15)
If the sum of two of the roots of \[{{x}^{3}}+p{{x}^{2}}+qx+r=0\] is zero, then pq = [EAMCET 2003]
A)
- r done
clear
B)
r done
clear
C)
2 r done
clear
D)
- 2 r done
clear
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question_answer16)
If \[\alpha ,\beta ,\gamma \]are the roots of the equation \[{{x}^{3}}+x+1=0\], then the value of \[{{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}\] [MP PET 2004]
A)
0 done
clear
B)
- 3 done
clear
C)
3 done
clear
D)
- 1 done
clear
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question_answer17)
The roots of the equation \[{{x}^{4}}-2{{x}^{3}}+x=380\] are [UPSEAT 2004]
A)
\[5,-4,\frac{1\pm 5\sqrt{-3}}{2}\] done
clear
B)
\[-5,4,-\frac{1\pm 5\sqrt{-}3}{2}\] done
clear
C)
\[5,4,\frac{-1\pm 5\sqrt{-}3}{2}\] done
clear
D)
\[-5,-4,\frac{1\pm 5\sqrt{-}3}{2}\] done
clear
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question_answer18)
If a, b and g are the roots of equation \[{{x}^{3}}-3{{x}^{2}}+x+5=0\] then \[y=\sum {{\alpha }^{2}}+\alpha \beta \gamma \] satisfies the equation [J & K 2005]
A)
\[{{y}^{3}}+y+2=0\] done
clear
B)
\[{{y}^{3}}-{{y}^{2}}-y-2=0\] done
clear
C)
\[{{y}^{3}}+3{{y}^{2}}-y-3=0\] done
clear
D)
\[{{y}^{3}}+4{{y}^{2}}+5y+20=0\] done
clear
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question_answer19)
If a, b, g are the roots of the equation \[2{{x}^{3}}-3{{x}^{2}}+6x+1=0\], then \[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}\] is equal to [Karnataka CET 2005]
A)
-\[\frac{15}{4}\] done
clear
B)
\[\frac{15}{4}\] done
clear
C)
\[\frac{9}{4}\] done
clear
D)
4 done
clear
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question_answer20)
The solution set of the equation \[pq{{x}^{2}}-{{(p+q)}^{2}}x+{{(p+q)}^{2}}=0\] is [Kerala (Engg.) 2005]
A)
\[\left\{ \frac{p}{q},\,\frac{q}{p} \right\}\] done
clear
B)
\[\left\{ pq,\,\frac{p}{q} \right\}\] done
clear
C)
\[\left\{ \frac{q}{p},\,pq \right\}\] done
clear
D)
\[\left\{ \frac{p+q}{p},\,\frac{p+q}{q} \right\}\] done
clear
E)
\[\left\{ \frac{p-q}{p},\,\frac{p-q}{q} \right\}\] done
clear
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