JEE Main & Advanced Mathematics Linear Programming Question Bank

done Mock Test - Linear Inequalities Total Questions - 25

• question_answer1)
  Which of the following set does not satisfy \[\left| x-3 \right|>4\]?
  A)
  \[(-\infty ,-1)\]    done clear
  B)
  \[(7,-\infty )\] done clear
  C)
  \[(-1,7)\]            done clear
  D)
  none of these done clear
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• question_answer2)
  Which values of x satisfy the following inequalities simultaneously? (i) \[-3<2x-1<19\]          (ii) \[-1\le \frac{2x+3}{5}\le 3\]
  A)
  \[\left[ -4,10 \right)\]        done clear
  B)
  \[\left( -1,\,6 \right]\] done clear
  C)
   \[\left[ -1,\,6 \right)\]       done clear
  D)
  \[\left( -1,\,6 \right)\] done clear
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• question_answer3)
  If \[-9<x\le 6\] then \[\left| x \right|\in \]
  A)
  \[\left[ 6,\,9 \right)\]        done clear
  B)
  \[\left[ 0,\,6 \right]\] done clear
  C)
  \[\left[ 0,\,9 \right)\] done clear
  D)
  none of these done clear
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• question_answer4)
  The inequality \[\frac{2}{x}<3\]is true, when x belongs to
  A)
   \[\left[ 2/3,\,\infty  \right)\]           done clear
  B)
  \[(-\infty ,\,2/3]\] done clear
  C)
  \[(2/3,\,\infty )\cup (-\infty ,\,0)\] done clear
  D)
  None of these done clear
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• question_answer5)
  Complete solution set of \[\left| x-2 \right|<3\]is
  A)
  \[x<5\] done clear
  B)
  \[x>0\] done clear
  C)
  \[-1<x<5\]       done clear
  D)
  \[1<x<5\] done clear
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• question_answer6)
  Which of the following is not true?
  A)
  if \[-2<x\,\,then\,\,\left| x \right|\ge 0\] done clear
  B)
   if \[x\le 3\] then \[\left| x \right|\ge 0\] done clear
  C)
   if \[-3<x\le 4\] then \[\left| x \right|\in [0,4]\] done clear
  D)
   none of these done clear
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• question_answer7)
  If \[\left| x-2 \right|\le 1\], then
  A)
  \[x\in \,\left[ 1,3 \right]\]  done clear
  B)
  \[x\in \,(1,3)\] done clear
  C)
  \[x\in \,\left[ -1,3 \right)\] done clear
  D)
  \[x\in \,(-1,3)\] done clear
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• question_answer8)
  If \[x+y\le 2,x\ge 0,y\ge 0\]then the point at which maximum value of \[3x+2y\]is attained will be
  A)
  (0, 0) done clear
  B)
  \[\left( \frac{1}{2},\frac{1}{2} \right)\] done clear
  C)
  (0, 2)    done clear
  D)
  (2, 0) done clear
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• question_answer9)
  Solution of \[\frac{x-7}{x+3}>2\]is
  A)
  \[(-3,\,\infty )\]   done clear
  B)
  \[(-\infty ,\,-13)\] done clear
  C)
  (-13, -3)            done clear
  D)
  None of these done clear
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• question_answer10)
  The values of x which satisfy the inequalities simultaneously (i) \[-3<2x-1<19\] (ii) \[-1\le \frac{2x+3}{5}\le 3\]
  A)
  \[\left[ -4,\,10 \right)\]      done clear
  B)
  \[\left( -1,\,6 \right]\] done clear
  C)
  \[\left[ -1,\,6 \right)\]       done clear
  D)
  \[(-1,\,6)\] done clear
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• question_answer11)
  Which interval does the following number line represent?
  A)
  (1, 1)     done clear
  B)
  (-2, 3) done clear
  C)
  \[\left( -1,\,4 \right]\]       done clear
  D)
  \[\left( -\infty ,\,-1 \right)\] done clear
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• question_answer12)
  The set of values of x which satisfy the inequations\[5x+2<3x+8\]and \[\frac{x+2}{x-1}<4\]is
  A)
  \[(-\infty ,\,1)\]   done clear
  B)
  (2, 3) done clear
  C)
  \[(-\infty ,\,3)\]   done clear
  D)
  \[(-\infty ,\,1)\cup (2,3)\] done clear
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• question_answer13)
  Which of the following is not the solution of \[\left| x \right|-3|>1\]?
  A)
  \[-2<x<2\]       done clear
  B)
  \[x<-4\] done clear
  C)
  \[x>4\] done clear
  D)
  None of these done clear
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• question_answer14)
  For the inequality \[\frac{x}{3}+\frac{x}{2}<5\], the interval is
  A)
  \[(-\infty ,\,6)\]   done clear
  B)
  \[(-\infty ,\,6]\] done clear
  C)
  \[[-\infty ,\,6)\]   done clear
  D)
  \[[-\infty ,\,6]\] done clear
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• question_answer15)
  The solution set of \[\frac{5x+8}{4-x}\le 2\]is
  A)
  \[(4,\,\infty )\cup \left( -\infty ,\,0 \right]\] done clear
  B)
  \[[4,\,\infty ]\cup \left( -\infty ,\,4 \right]\] done clear
  C)
  \[\left( -\infty ,\,0 \right]\cup (4,\,\infty )\] done clear
  D)
  \[[4,\,\infty ]\cup \left( -\infty ,\,0 \right]\] done clear
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• question_answer16)
  The system \[2(2x+3)-10<6(x-2)\] and \[\frac{2x-3}{4}+\ge \frac{2+4x}{3}\] has
  A)
  infinite done clear
  B)
  two solutions done clear
  C)
  three sollutionns done clear
  D)
  no solutions done clear
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• question_answer17)
  Solution set of the inequality \[4x-3\ge 3x-4\]is
  A)
  (-1, 0)    done clear
  B)
  (1, \[\infty \]) done clear
  C)
  \[\left( -\infty ,\,0 \right]\] done clear
  D)
  \[\left[ -1,\,\infty  \right)\] done clear
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• question_answer18)
  Solution set of the inequality \[6\le -3(2x-5)<12\]is
  A)
  \[(0,\,3/2)\]        done clear
  B)
  \[\left( 1/2,\,3/2 \right]\] done clear
  C)
  \[\left[ 1/2,\,3/2 \right)\]   done clear
  D)
  \[\left[ 0,\,1/2 \right)\] done clear
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• question_answer19)
  Solution set of the following inequalities is \[2(x-1)<x+5,3(x+2)>2-x\]
  A)
  \[(-1,\,7)\]          done clear
  B)
  \[(1,\,7)\] done clear
  C)
  \[(-1,\,\infty )\]   done clear
  D)
  \[(-\infty ,\,7)\] done clear
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• question_answer20)
  Inequality \[y-x\le 0\]represents
  A)
  the half plane that contains the positive x-axis done clear
  B)
   closed half plane above the line y=x which contains positive y-axis done clear
  C)
   half plane that contains negative x-axis done clear
  D)
   none of these done clear
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• question_answer21)
  If the solution set of \[\left| x-k \right|<2\]is a subset of the solution set of the inequality\[\frac{2x-1}{x+2}<1\], then the number of possible integral value (s) of k is/are___.
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• question_answer22)
  The number \[N=6{{\log }_{10}}2+{{\log }_{10}}31\], lies between two successive integers whose sum is equal to ________.
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• question_answer23)
  Number of integers satisfying \[{{\log }_{x}}\frac{4x=5}{6-5x}<-1\]is____.
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• question_answer24)
  Bimal wants to invest Rs. 15,000 in saving certificates and national saving bonds. Minimum amount to be invested in saving certificate and national savaging bonds are respectively Rs. 2000 and Rs. 2500. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. If the invests RS. X in saving certificate and Rs. Y in national saving bonds, then the equation for the interest earned is \[kx+Ly\]. Then value of \[K+L\] is _________.
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• question_answer25)
  Let a, b, c, d be real numbers such that \[\left| a-b \right|=2,\left| b-c \right|=3,\left| c-d \right|=4\]. Then the sum of all possible values of \[\left| a-d \right|\] is _______.
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