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question_answer1)
The shaded region shown in the figure is given by the in equations
A)
\[14x+5y\ge 70,\,\,\,y\le 14\] and \[x-y\ge 5\] done
clear
B)
\[14x+5y\le 70,\,\,\,y\le 14\] and \[x-y\ge 5\] done
clear
C)
\[14x+5y\ge 70,y\ge 14\] and \[x-y\ge 5\] done
clear
D)
\[14x+5y\ge 70,y\le 14\] and \[x-y\le 5\] done
clear
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question_answer2)
The number of real values of parameter k for which \[{{(lo{{g}_{16}}x)}^{2}}-{{\log }_{16}}x+{{\log }_{16}}k=0\] will have exactly one solution is
A)
0 done
clear
B)
2 done
clear
C)
1 done
clear
D)
4 done
clear
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question_answer3)
Solve for \[x,\,\,\,\frac{\left| x+3 \right|+x}{x+2}>1\]
A)
\[x\in (-5,-2)\cup (-1,\infty )\] done
clear
B)
\[x\in (5,2)\cup (-1,\infty )\] done
clear
C)
\[x\in (5,2)\] done
clear
D)
\[x\in (-1,\infty )\] done
clear
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question_answer4)
The solution set of the inequality \[37-(3x+5)\ge 9x-8(x-3)\] is
A)
\[(-\infty ,2)\] done
clear
B)
\[(-\infty ,-2)\] done
clear
C)
\[(-\infty ,2]\] done
clear
D)
\[(-\infty ,-2]\] done
clear
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question_answer5)
Solution of \[2x-1=\left| x+7 \right|\] is
A)
-2 done
clear
B)
8 done
clear
C)
-2, 8 done
clear
D)
None of these done
clear
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question_answer6)
The inequality representing the following graph is
A)
\[\left| x \right|<3\] done
clear
B)
\[\left| x \right|\le 3\] done
clear
C)
\[\left| x \right|>3\] done
clear
D)
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question_answer7)
If \[5\{x\}=x+[x]\] and \[[x]-\{x\}=\frac{1}{2}\] when \[\{x\}\] and \[[x]\] are fractional and integral part of x then x is
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[\frac{5}{2}\] done
clear
D)
\[\frac{7}{2}\] done
clear
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question_answer8)
Ravi obtained 70 and 75 marks in first two unit tests. Then the minimum marks he should get in the third test to have an average of at least 60 marks, are
A)
45 done
clear
B)
35 done
clear
C)
25 done
clear
D)
None of these done
clear
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question_answer9)
If \[R\ge r>0\] and \[d>0,\] then \[0<\frac{{{d}^{2}}+{{R}^{2}}-{{r}^{2}}}{2dR}\le 1\]
A)
Is satisfied if \[\left| d-R \right|\le r\] done
clear
B)
Is satisfied if \[\left| d-R \right|\le 2r\] done
clear
C)
Is satisfied if \[\left| d-R \right|\ge r\] done
clear
D)
Is not satisfied at all done
clear
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question_answer10)
The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then what can you say about breadth?
A)
\[\operatorname{breadth} = 20\] done
clear
B)
\[breadth\,\,\le 20\] done
clear
C)
\[breadth\,\,\ge 20\] done
clear
D)
\[breadth\,\,\ne 20\] done
clear
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question_answer11)
Which of the following linear inequalities satisfy the shaded region of the given figure?
A)
\[2x+3y\ge 3\] done
clear
B)
\[3x+4y\le 18\] done
clear
C)
\[x-6y\le 3\] done
clear
D)
All of these done
clear
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question_answer12)
The solution set of \[{{(x)}^{2}}+{{(x+1)}^{2}}=25,\] where (x) is the least integer greater than or equal to x, is
A)
\[(2,4)\] done
clear
B)
\[(-5,-4]\cup (2,3]\] done
clear
C)
\[[-4,-3)\cup [3,4)\] done
clear
D)
None of these done
clear
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question_answer13)
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. The possible length of the shortest board, if the third piece is to be at least 5 cm longer than the second, is
A)
Less than 8 cm done
clear
B)
Greater than or equal to 8 cm but less then or equal to 22 cm done
clear
C)
Less than 22 cm done
clear
D)
Greater than 22 cm done
clear
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question_answer14)
The solution set of \[\frac{2x-1}{3}\ge \left( \frac{3x-2}{4} \right)-\left( \frac{2-x}{5} \right)\] is\[(-\infty ,a]\]. The value of ?a? is
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer15)
For positive real numbers a, b, c such that \[a+b+c=p,\] which one does not hold?
A)
\[(p-a)(p-b)(p-c)\le \frac{8}{27}{{p}^{3}}\] done
clear
B)
\[(p-a)(p-b)(p-c)\ge 8abc\] done
clear
C)
\[\frac{bc}{a}+\frac{ca}{b}+\frac{ab}{c}\le p\] done
clear
D)
None of these done
clear
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question_answer16)
If x satisfies the inequalities \[x+7<2x+3\] and \[2x+4<5x+3,\] then x lies in the interval
A)
\[(-\infty ,3)\] done
clear
B)
\[(1,3)\] done
clear
C)
\[(4,\infty )\] done
clear
D)
\[(-\infty ,-1)\] done
clear
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question_answer17)
The solution set of the inequality \[{{5}^{x+2}}>{{\left( \frac{1}{25} \right)}^{1/x}}\]is
A)
\[(-2,0)\] done
clear
B)
\[(-2,2)\] done
clear
C)
\[(-5,5)\] done
clear
D)
\[(0,\infty )\] done
clear
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question_answer18)
The solution set of the inequality \[\left| x+2 \right|-\left| x-1 \right|<x-\frac{3}{2}\] is
A)
\[\left( \frac{9}{2},\infty \right)\] done
clear
B)
\[\left( -\infty ,\frac{3}{2} \right)\] done
clear
C)
\[\left( -2,-\frac{3}{2} \right)\] done
clear
D)
\[\left( -1,\frac{3}{2} \right)\] done
clear
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question_answer19)
If \[\frac{3x-4}{2}\ge \frac{x+1}{4}-1,\] then \[x\in \]
A)
\[[1,\infty )\] done
clear
B)
\[(1,\infty )\] done
clear
C)
\[(-5,5)\] done
clear
D)
\[[-5,5]\] done
clear
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question_answer20)
Solution set of the inequality \[{{\log }_{3}}(x+2)(x+4)+lo{{g}_{1/3}}(x+2)<\frac{1}{2}\log \sqrt{3}\,\,7\,(1)\] is
A)
\[(-2,-1)\] done
clear
B)
\[(-2,3)\] done
clear
C)
\[(-1,3)\] done
clear
D)
\[(3,\infty )\] done
clear
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question_answer21)
The area and perimeter of a rectangle are A and P respectively. Then P and A satisfy the inequality.
A)
\[P+A>PA\] done
clear
B)
\[{{P}^{2}}\le A\] done
clear
C)
\[A-P<2\] done
clear
D)
\[{{P}^{2}}\ge 16A\] done
clear
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question_answer22)
If \[\left| \frac{12x}{4{{x}^{2}}+9} \right|\ge 1\] for all real values of \[x,\] the inequality being satisfied only if \[\left| x \right|\] is equal to
A)
\[\frac{3}{2}\] done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer23)
A manufacturer has 600 liters of a 12% solution of acid. How many liters of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?
A)
More than 120 liters but less than 300 liters done
clear
B)
More than 140 liters but less than 600 liters done
clear
C)
More than 100 liters but less than 280 liters done
clear
D)
More than 160 liters but less than 500 liters done
clear
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question_answer24)
The number of integral roots of the equation\[\left| x-1 \right|+\left| x+2 \right|-\left| x-3 \right|=4\] is
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer25)
Solution of \[\left| x-1 \right|\ge \left| x-3 \right|\] is
A)
\[x\le 2\] done
clear
B)
\[x\ge 2\] done
clear
C)
\[[1,3]\] done
clear
D)
None of these done
clear
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question_answer26)
If, a, b, c, distinct positive real numbers then the expression \[\left( b+c-a \right)\text{ }\left( c+a-b \right)\text{ }\left( a+b-c \right)-abc\] is
A)
Positive done
clear
B)
Negative done
clear
C)
Non-positive done
clear
D)
Non-negative done
clear
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question_answer27)
The set of real values of x satisfying \[\left| x-1 \right|\le 3\] and \[\left| x-1 \right|\ge 1\] is
A)
\[[2,4]\] done
clear
B)
\[(-\infty ,2]\cup [4,+\infty )\] done
clear
C)
\[[-2,0]\cup [2,4]\] done
clear
D)
None of these done
clear
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question_answer28)
The set of real values of x satisfying \[\left| x-1 \right|\le 3\] And \[\left| x-1 \right|\ge 1\] is
A)
\[[2,4]\] done
clear
B)
\[(-\infty ,2]\cup [4,+\infty )\] done
clear
C)
\[[-2,0]\cup [2,4]\] done
clear
D)
None of these done
clear
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question_answer29)
Set of values of x satisfying the inequality \[\frac{{{x}^{2}}+6x-7}{\left| x+4 \right|}<0\] is/are
A)
\[(-\infty ,-7)\] done
clear
B)
\[(-7,4)\] done
clear
C)
\[(-4,1)\] done
clear
D)
\[(1,\infty )\] done
clear
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question_answer30)
A vertex of a feasible region by the linear constraints \[3x+4y\le 18,\,\,\,2x+3y\ge 3\] and \[x,y\ge 0\], is
A)
\[(0,2)\] done
clear
B)
\[(4.8,0)\] done
clear
C)
\[(0,3)\] done
clear
D)
None of these done
clear
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question_answer31)
For \[x\in R,\,\,\,\,\left\langle x \right\rangle \] is defined as follows: \[\left\langle x \right\rangle =\left\{ \begin{matrix} x+1, \\ \left| x-4 \right|, \\ \end{matrix}\,\,\,\begin{matrix} 0\le x<2 \\ x\ge 2 \\ \end{matrix}\begin{matrix} {} \\ {} \\ \end{matrix} \right.\] Then the solution set of the equation \[{{\left\langle x \right\rangle }^{2}}+x=\left\langle x \right\rangle +{{x}^{2}}\] is
A)
\[\{-1,1\}\] done
clear
B)
\[[2,\infty )\] done
clear
C)
\[[0,2)\] done
clear
D)
\[\{0,2\}\] done
clear
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question_answer32)
If \[\frac{\left| x+3 \right|+x}{x+2}>1,\] then \[x\in \]
A)
\[(-5,-2)\] done
clear
B)
\[(-1,\infty )\] done
clear
C)
\[(-5,-2)\cup (-1,\infty )\] done
clear
D)
None of these done
clear
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question_answer33)
The equation \[\left| |x-1|+a \right|=4\] can have real solution for x if 'a' belongs to the interval
A)
\[(-\infty ,+\infty )\] done
clear
B)
\[(-\infty ,4]\] done
clear
C)
\[(4,+\infty )\] done
clear
D)
\[[-4,4]\] done
clear
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question_answer34)
Number of integral values of x satisfying the inequality \[{{\left( \frac{3}{4} \right)}^{6x+10-{{x}^{2}}}}<\frac{27}{64}\] is
A)
5 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
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question_answer35)
The graph of in equations \[x\le y\] and \[y\le x+3\] is located in
A)
II quadrant done
clear
B)
I, II quadrants done
clear
C)
I, II, III quadrants done
clear
D)
II, III, IV quadrants done
clear
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question_answer36)
Consider the following statements.
I. Solution set of the inequality \[-15<\frac{3(x-2)}{5}\le 0\]is \[(-23,2]\] |
II. Solution set of the inequality |
\[7\le \frac{3x+11}{2}\le 11\] is \[\left[ 1,\frac{11}{3} \right]\] |
III. Solution set of the inequality |
\[-5\le \frac{2-3x}{4}\le 9\] is \[[-1,\,\,\,1]\cup [3,\,\,\,5]\] |
Choose the correct option |
A)
Only I and II are true. done
clear
B)
Only II and III are true. done
clear
C)
Only I and III are true. done
clear
D)
All are true. done
clear
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question_answer37)
The marks obtained by a student of class \[XI\]in first and second terminal examinations are 62 and 48, respectively. The minimum marks he should get in the annual examination to have an average of at least 60 marks, are
A)
70 done
clear
B)
50 done
clear
C)
74 done
clear
D)
48 done
clear
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question_answer38)
Solution set of the inequality \[\frac{1}{{{2}^{x}}-1}>\frac{1}{1-{{2}^{x-1}}}\] is
A)
\[(1,\infty )\] done
clear
B)
\[(0,lo{{g}_{2}}(4/3))\] done
clear
C)
\[(-1,\infty )\] done
clear
D)
\[(0,lo{{g}_{2}}(4/3))\cup (1,\infty )\] done
clear
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question_answer39)
If the equation \[{{2}^{x}}+{{4}^{y}}={{2}^{y}}+{{4}^{x}}\] is solved for y in terms of x where\[x<0\], then the sum of the solutions is
A)
\[x{{\log }_{2}}(1-{{2}^{x}})\] done
clear
B)
\[x+{{\log }_{2}}(1-{{2}^{x}})\] done
clear
C)
\[{{\log }_{2}}(1-{{2}^{x}})\] done
clear
D)
\[x{{\log }_{2}}({{2}^{x}}+1)\] done
clear
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question_answer40)
The set of real value of x satisfying \[\left| |x-1|-1 \right|\le 1\]is
A)
\[[-1,3]\] done
clear
B)
\[[0,2]\] done
clear
C)
\[[-1,1]\] done
clear
D)
None of these done
clear
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question_answer41)
A company manufactures cassettes. Its cost and revenue functions are \[C(x)=26000+30x\] and \[R(x)=43x,\] respectively, where x is the number of cassettes produced and sold in a week. The number of cassettes must be sold by the company to realise some profit, is
A)
More than 2000 done
clear
B)
Less than 2000 done
clear
C)
More than 1000 done
clear
D)
Less than 1000 done
clear
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question_answer42)
If a, b and c are three positive real numbers such that \[a+b\ge c,\] then
A)
\[\frac{a}{1+a}+\frac{b}{1+b}\ge \frac{c}{1+c}\] done
clear
B)
\[\frac{a}{1+a}+\frac{b}{1+b}<\frac{c}{1+c}\] done
clear
C)
\[\frac{a}{1+a}+\frac{b}{1+b}>\frac{c}{1+c}\] done
clear
D)
None of these done
clear
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question_answer43)
The least integer a, for which \[1+{{\log }_{5}}({{x}^{2}}+1)\le lo{{g}_{5}}(a{{x}^{2}}+4x+a)\] is true for all \[x\in R\] is
A)
6 done
clear
B)
7 done
clear
C)
10 done
clear
D)
1 done
clear
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question_answer44)
Solution of \[\left| 2x-3 \right|<\left| x+2 \right|\] is
A)
\[\left( -\infty ,\frac{1}{3} \right)\] done
clear
B)
\[\left( \frac{1}{3},5 \right)\] done
clear
C)
\[(5,\infty )\] done
clear
D)
\[\left( -\infty ,\frac{1}{3} \right)\cup (5,\infty )\] done
clear
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question_answer45)
The solution set of the inequalities \[3x-7>2(x-6)\] and \[6-x>11-2x,\] is
A)
\[(-5,\infty )\] done
clear
B)
\[[5,\infty )\] done
clear
C)
\[(5,\infty )\] done
clear
D)
\[[-5,\infty )\] done
clear
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question_answer46)
If \[{{(\sqrt{2})}^{x}}+{{(\sqrt{3})}^{x}}={{(\sqrt{13})}^{x/2}},\] then the number of values of x is
A)
2 done
clear
B)
4 done
clear
C)
1 done
clear
D)
None of these done
clear
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question_answer47)
Number of real roots of the equation \[\sqrt{x}+\sqrt{x-\sqrt{1-x}}=1\] is
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
View Solution play_arrow
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question_answer48)
The number of real roots of the equation \[\left| 2-\left| 1-\left| x \right| \right| \right|=1\] is
A)
1 done
clear
B)
3 done
clear
C)
5 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer49)
The set of points (x, y) satisfying the inequalities \[x+y\le 1,-x-y\le 1\] lies in the region bounded by the two straight lines passing through the respective pair of points
A)
\[\{(1,0)(0,1)\}\] and \[\{(-1,0),(0,-1)\}\] done
clear
B)
\[\{(1,0),(1,1)\}\] and \[\{(-1,0),(0,-1)\}\] done
clear
C)
\[\{(-1,0),(0,-1)\}\] and \[\{(1,0),(-1,1)\}\] done
clear
D)
\[\{(1,0),(0,-1)\}\] and \[\{(-1,0),(0,1)\}\] done
clear
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question_answer50)
The equation \[{{\log }_{3}}({{3}^{x}}-8)=2-x\] has the solution
A)
\[x=1\] done
clear
B)
\[x=2\] done
clear
C)
\[x=3\] done
clear
D)
\[x=4\] done
clear
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