10th Class Mathematics Related to Competitive Exam Question Bank

done Quadratic Inequation Total Questions - 40

• question_answer1)
  The roots of the equation \[{{x}^{2}}-2px+4q=0\] are consecutive integers. The discriminant of the equation will be:
  A)
   1    done clear
  B)
   0             done clear
  C)
   6                                 done clear
  D)
   16 done clear
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• question_answer2)
  The product of two consecutive even numbers is more than twice their sum by more than 34. Which of the following is the range of values that the larger of the can take?
  A)
   \[n>14\]or \[n<-2\]        done clear
  B)
   \[-12<n<+12\] done clear
  C)
   \[n\ge 10,n\le -\,4\] done clear
  D)
   \[-15<n<+15\] done clear
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• question_answer3)
  If \[|y{{|}^{2}}-3|y|+2\le 0\], then which of the following is the range of y?
  A)
   \[[-6,6]\cup [1,3]\]          done clear
  B)
   \[[1,2]\] done clear
  C)
   \[[-2,-1]\]                       done clear
  D)
   \[[-2,-1]\cup [1,2]\] done clear
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• question_answer4)
    Solve \[{{x}^{2}}+6x+13>0\].
  A)
   \[(-\infty ,6)\]                 done clear
  B)
   \[(-\infty ,\infty )\] done clear
  C)
   \[(6,\infty )\]                  done clear
  D)
   \[(-100,100)\] done clear
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• question_answer5)
  Solve \[\frac{{{x}^{2}}+5x+3}{x+2}<x\].
  A)
   \[(-2,-1)\] done clear
  B)
   \[\left( \frac{-5-\sqrt{13}}{2},\frac{-5+\sqrt{13}}{2} \right)\] done clear
  C)
   \[\left( -\,2,\infty  \right)\] done clear
  D)
   \[(-1,\ \infty )\] done clear
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• question_answer6)
  If \[\alpha \]and \[\beta \]are the zeros of the quadratic polynomial \[a{{x}^{2}}+bx+c=0\]and x lies between \[\alpha \] and \[\beta \], then which of the following is true?
  A)
   \[If\,\,a<0\,\,than\,\,a{{x}^{2}}+bx+c>0\] done clear
  B)
   \[If\,\,a>0\,\,than\,\,a{{x}^{2}}+bx+c<0\] done clear
  C)
   \[If\,\,a>0\,\,than\,\,a{{x}^{2}}+bx+c>0\] done clear
  D)
   Both (a) and (b) done clear
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• question_answer7)
  The solution of the in equation\[{{2}^{-2x+1}}-\frac{7}{{{2}^{x}}}-4<0\,\,x\in R,\]is.
  A)
   \[\left( -2,\infty  \right)\]   done clear
  B)
   \[\left( 2,6 \right)\] done clear
  C)
   \[\left( 2,\frac{7}{2} \right)\]                   done clear
  D)
   \[\left( 2,14 \right)\] done clear
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• question_answer8)
  The real values of x for which \[{{3}^{72}}{{\left( \frac{1}{3} \right)}^{x}}{{\left( \frac{1}{3} \right)}^{\sqrt{x}}}>1\]
  A)
   \[x\in [0,81]\]                 done clear
  B)
   \[x\in \left( 0,{{3}^{72}} \right)\] done clear
  C)
   \[x\in [0,64)\]     done clear
  D)
   \[-\,64\le x\le +\,64\] done clear
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• question_answer9)
  The value of a which make the expression \[{{x}^{2}}-ax+1-2{{a}^{2}}\] always positive for real values of x, are
  A)
   \[-\frac{4}{3}<a<\frac{4}{3}\]             done clear
  B)
   \[-\frac{2}{3}<a<\frac{2}{3}\] done clear
  C)
   \[a\in \]null set               done clear
  D)
   \[0<a<\frac{7}{3}\] done clear
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• question_answer10)
  Find the range of values of x which satisfy the in equation,\[{{\left( x+1 \right)}^{2}}+{{\left( x+1 \right)}^{2}}<6\]
  A)
   \[\left( -\sqrt{2},\sqrt{2} \right)\]  done clear
  B)
   \[\left( -1,1 \right)\] done clear
  C)
   \[\left( -\infty ,-2 \right)\cup \left( 2,\infty  \right)\]    done clear
  D)
   \[\left( -\infty ,-1 \right)\cup \left( 1,\infty  \right)\] done clear
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• question_answer11)
  If a<b, then the solution of \[{{x}^{2}}+(a+b)x+ab<0\], is given by
  A)
   \[x\in (-\infty ,-a)\]                      done clear
  B)
   \[x\in (a,b)\] done clear
  C)
   \[x\in (-\infty ,a)\cup (b,\infty )\]   done clear
  D)
   \[-b<x<-a\] done clear
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• question_answer12)
  If \[2\le x\le 5\] and \[4\le y\le 6\], what is the maximum value of \[\left( \frac{x}{y} \right)\]?
  A)
   \[\frac{4}{5}\]                          done clear
  B)
   \[1\] done clear
  C)
   \[\frac{5}{4}\]  done clear
  D)
   \[6\] done clear
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• question_answer13)
  Which one of the following is correct for\[x\in R\]?
  A)
   \[x+\frac{1}{x}\le -2\] for all \[x<0\] done clear
  B)
   \[x+\frac{1}{x}=0\] done clear
  C)
   \[x+\frac{1}{x}\ge 2\] for all \[x>0\] done clear
  D)
   Both (a) and (c) done clear
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• question_answer14)
  Find the range of values that x can take in the in equation \[(x-1)(x-6)>0\]
  A)
   \[(-\infty ,1)\cup (6,\infty )\]         done clear
  B)
   \[[6,1]\] done clear
  C)
   \[(1,6)\]                         done clear
  D)
   \[(-\infty ,1)\cup (7,\infty )\] done clear
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• question_answer15)
  Find the ranges of the values of x for which \[{{x}^{2}}-4x+2\] lies between \[+1\] and\[-1\].
  A)
   \[(2,3)\]             done clear
  B)
   \[(0.27,1)\cup (2,2.73)\] done clear
  C)
   \[(0.5,1.5)\cup (2,2.5)\]   done clear
  D)
   \[\left( 2-\sqrt{3},1 \right)\cup \left( 3,2+\sqrt{3} \right)\] done clear
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• question_answer16)
  If x is real, prove that the value of the expression \[\frac{(x-1)(x+3)}{(x-2)(x+4)}\]cannot lie between:
  A)
   \[\frac{4}{9}and\,\,1\]   done clear
  B)
   \[\frac{2}{9}and\,\,4\] done clear
  C)
   \[1\,\,and\,\,4\]              done clear
  D)
   \[4\,\,and\,\,\frac{40}{3}\] done clear
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• question_answer17)
  If x be real, find the maximum value of\[\frac{(x+2)}{\left( 2{{x}^{2}}+3x+6 \right)}\].
  A)
   \[\frac{-1}{13}\]                                    done clear
  B)
   \[\frac{1}{3}\] done clear
  C)
   \[6\]                             done clear
  D)
   \[-\,6\] done clear
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• question_answer18)
  Solve the in equality \[\frac{x-2}{x+2}>\frac{2x-3}{4x+1}.\]
  A)
   \[(2,3)\]             done clear
  B)
   \[\left( -\infty ,-2 \right)\cup \left( \frac{1}{4}-1 \right)\cup (4,\infty )\] done clear
  C)
   \[\left( \frac{-1}{4},\frac{3}{2} \right)\] done clear
  D)
   \[(-\infty ,-2)\cup (4,\infty )\] done clear
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• question_answer19)
  Determine the range of values of x for which \[\frac{{{x}^{2}}-2x+5}{3{{x}^{2}}-2x-5}>\frac{1}{2}\].
  A)
   \[\left( -5,-1 \right)\cup \left( 3,\infty  \right)\]          done clear
  B)
   \[\left( -5,-1 \right)\cup \left( \frac{5}{3},3 \right)\] done clear
  C)
   \[\left( -1,\frac{4}{3} \right)\cup \left( \frac{5}{3},3 \right)\]            done clear
  D)
   \[(-5,-1)\cup \left( \frac{1}{2},\frac{5}{3} \right)\] done clear
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• question_answer20)
  Find the range of real values of x for which \[\frac{x-1}{(4x+5)}<\frac{x-3}{4x-3}\]
  A)
   \[\left( \frac{3}{4},3 \right)\]                   done clear
  B)
   \[\left( -\infty ,-\frac{5}{4} \right)\cup \left( \frac{3}{4},\infty  \right)\] done clear
  C)
   \[\left( -\infty ,\frac{3}{4} \right)\cup \left( 3.\infty  \right)\]  done clear
  D)
   \[\left( -\frac{5}{4},\frac{3}{4} \right)\] done clear
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• question_answer21)
  The expression\[\frac{(x-a)(x-b)}{(x-c)}\]will assume all real values for every\[x\in R\], if
  A)
   \[a<b<c\]                     done clear
  B)
   \[a>b>c\] done clear
  C)
   c lies between a and b done clear
  D)
   \[a<c<b\]or \[a>b>c\] done clear
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• question_answer22)
  The value of 'a' for which \[2{{x}^{2}}-2\,(2a+1)x+a\,(a+1)=0\] may have one root less than a and other root greater than a are given by:
  A)
   \[-1<a<0\]                   done clear
  B)
   \[0<a<1\] done clear
  C)
   \[a\ge 0\]                       done clear
  D)
   \[a>0\]or \[a<-1\] done clear
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• question_answer23)
  If the roots of \[a{{x}^{2}}+bx+c=0,a>0,\] be each greater than unity, then:
  A)
   \[a+b+c=0\]    done clear
  B)
   \[a+b+c>0\] done clear
  C)
   \[a+b+c<0\]                done clear
  D)
   None of these done clear
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• question_answer24)
  The minimum value of the expression \[a+\frac{1}{a}>0\]is:
  A)
   0                                 done clear
  B)
   1 done clear
  C)
   2                     done clear
  D)
   4 done clear
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• question_answer25)
  The set of values for which \[{{x}^{3}}-1\ge x-{{x}^{2}}\] holds true is:
  A)
   \[x\ge 0\]                       done clear
  B)
   \[x\le 0\] done clear
  C)
   \[x\ge 1\] done clear
  D)
   \[-1\le x\le 1\] done clear
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• question_answer26)
  Find the values that x can take in \[{{x}^{2}}-2x+3\ge 0\]
  A)
   \[[2,3]\]             done clear
  B)
   \[[1,2]\] done clear
  C)
   \[x\ge -1\]and \[x\in \left( -\infty ,1 \right)\cup \left( 2,\infty  \right)\] done clear
  D)
   \[\left( -\infty ,1 \right)\cup \left( 2,\infty  \right)\] done clear
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• question_answer27)
  Find the values that x can take in \[{{x}^{2}}-6x+9\ge 0\]
  A)
   Only zero                         done clear
  B)
   All values except zero done clear
  C)
   All value (including zero)       done clear
  D)
   \[x\in (3,\infty )\] done clear
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• question_answer28)
  Find the value that x can take in \[6x-{{x}^{2}}+16<0\]
  A)
   \[x\in (-2,8)\]                 done clear
  B)
   \[x\in (6,16)\] done clear
  C)
   \[x\in (16,\infty )\]                      done clear
  D)
   \[x\in (-\infty ,-2)\cup (8,\infty )\] done clear
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• question_answer29)
  Find the values that x can take in \[\frac{1}{x-1}\ge \frac{2}{2x-1}\].
  A)
   \[x\in (2,\infty )\]                        done clear
  B)
   \[x\in (-\infty ,2)\] done clear
  C)
   \[x\in \left( -\infty ,\left. \frac{1}{2} \right]\cup [1,\infty ) \right.\]     done clear
  D)
   \[x\in \left[ \frac{1}{2},1 \right)\] done clear
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• question_answer30)
  If \[m{{x}^{2}}<nx\] such that m and n have opposite signs, then which of the following can be true?
  A)
   \[x\in \left( \frac{n}{m},\infty  \right)\]                  done clear
  B)
   \[x\in \left( -\infty ,\frac{n}{m} \right)\] done clear
  C)
   \[x\in \left( \frac{n}{m},0 \right)\]                        done clear
  D)
   None of these done clear
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• question_answer31)
  Solution of \[{{2}^{x}}+{{2}^{|x|}}\ge {{2}^{\frac{3}{2}}}\] is
  A)
   \[\left[ -\infty ,{{\log }_{e}}\left( {{2}^{\frac{1}{2}}}+{{2}^{\frac{3}{2}}} \right) \right]\]         done clear
  B)
   \[\left( -\infty ,{{\log }_{2}}\left( {{2}^{\frac{1}{2}}}-1 \right) \right]\cup \left[ \frac{1}{2},\infty  \right)\] done clear
  C)
   \[\left[ {{\log }_{10}}{{2}^{\frac{1}{2}}},{{\log }_{e}}{{2}^{\frac{1}{2}}} \right]\] done clear
  D)
   \[\left( {{2}^{{{\log }_{e}}2}},\infty  \right)\] done clear
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• question_answer32)
  If \[\frac{{{m}^{2}}+m-6}{{{m}^{2}}+m-2}<0\], then which of the following is true?
  A)
   \[1<m<3\]                   done clear
  B)
   \[-3<m<-2\] done clear
  C)
   \[m\in (-3,-2)\cup (1,2)\]  done clear
  D)
   None of these done clear
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• question_answer33)
  Find the values of x for which the expression \[{{x}^{2}}-\left( {{\log }_{5}}4+{{\log }_{2}}25 \right)x+4\]is always positive.
  A)
   \[x>2{{\log }_{2}}5\]or \[x<2{{\log }_{5}}2\] done clear
  B)
   \[{{\log }_{5}}2<x<{{\log }_{2}}25\] done clear
  C)
   \[-{{\log }_{5}}2<x<{{\log }_{2}}25\] done clear
  D)
   \[x<-{{\log }_{5}}4\] or \[x>{{\log }_{2}}5\] done clear
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• question_answer34)
  Find the values that x can take in \[{{x}^{2}}-10x+25\le 0\]
  A)
   Only zero                        done clear
  B)
   Only 5 done clear
  C)
   All values less than 5               done clear
  D)
   None of at the above done clear
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• question_answer35)
  Solve\[\frac{-3}{1-3m}>\frac{1}{m-1}\].
  A)
   \[m\in \left( \frac{1}{3},\infty  \right)\]                  done clear
  B)
   \[m\in (1,\infty )\] done clear
  C)
   \[m\in \left( -\infty ,\frac{1}{3} \right)\cup (1,\infty )\]         done clear
  D)
   \[m\in \left( \frac{1}{3},1 \right)\] done clear
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• question_answer36)
  Find the value of x in\[\frac{x-1}{1-3m}<0\].
  A)
   \[x\in (1,2)\]                  done clear
  B)
   \[x\in \left( \frac{1}{3},1 \right)\] done clear
  C)
   \[x\in \left( -\infty \frac{1}{3}, \right]\cup \left[ 1,\infty  \right)\]       done clear
  D)
   \[x\in \left[ \frac{1}{3},1 \right]\] done clear
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• question_answer37)
  \[\left( x-1 \right)\left( 3-x \right){{\left( x-2 \right)}^{2}}>0\]
  A)
   \[1<x<3\]                    done clear
  B)
   \[1<x<3\]but \[x\ne 0\] done clear
  C)
   \[0<x,2\]                      done clear
  D)
   \[-1<x<3\] done clear
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• question_answer38)
  \[\frac{6x-5}{4x+1}<0\]
  A)
   \[-1/4<x<1\]     done clear
  B)
   \[-1/2<x<1\] done clear
  C)
   \[-1<x<1\]                   done clear
  D)
   \[-1/4<x<5/6\] done clear
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• question_answer39)
  \[\frac{2x-3}{3x-7}>0\]
  A)
   \[x<3/2\]or \[x>7/3\]     done clear
  B)
   \[3/2<x<7/3\] done clear
  C)
   \[x>7/3\]                      done clear
  D)
   None of these done clear
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• question_answer40)
  Find the smallest integral m satisfying the inequality\[\frac{m-5}{{{m}^{2}}+5m-14}>0\]
  A)
   \[m=-6\] done clear
  B)
   \[m=-3\] done clear
  C)
   \[m=-7\]                       done clear
  D)
   \[m=5\] done clear
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