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question_answer1)
Which of the following is a linear equation?
A)
\[x-2y=7\] done
clear
B)
\[{{x}^{3}}-1=0\] done
clear
C)
\[x+\frac{6}{x}=12\] done
clear
D)
\[\frac{x}{2}+\frac{3}{x}=14\] done
clear
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question_answer2)
Which of the following is a solution of\[\text{2p}+\text{3q}=\text{5}\]?
A)
\[\text{p}=-\text{1},\text{q}=\text{1}\] done
clear
B)
\[\text{p }=\text{ 1},\text{ q }=\text{ }-\text{1}\] done
clear
C)
\[\text{p}=\text{1},\text{q}=\text{1}\] done
clear
D)
\[~\text{p}=-\text{1},\text{q}=-\text{1}\] done
clear
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question_answer3)
Which of the following is the other name for a pair of linear equations in two variables?
A)
Consistent equations done
clear
B)
Simultaneous equations done
clear
C)
Inconsistent equations done
clear
D)
Dependent equations done
clear
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question_answer4)
What is the condition that a system of simultaneous equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]must satisfy to have exactly one solution?
A)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\] done
clear
B)
\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] done
clear
C)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] done
clear
D)
\[\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] done
clear
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question_answer5)
How many solutions do the equations satisfying \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]have?
A)
One done
clear
B)
Two done
clear
C)
Three done
clear
D)
Infinitely many done
clear
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question_answer6)
What is a system of simultaneous equations called if it has no solution?
A)
Consistent system done
clear
B)
independent system done
clear
C)
Inconsistent system done
clear
D)
Dependent system done
clear
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question_answer7)
How many solutions does the system of equations \[\text{p}+\text{2q}=\text{4}\]and\[\text{2p}+\text{4q}-\text{12}=0\] have?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer8)
What is a system of simultaneous equations called if its graph has intersecting lines?
A)
Inconsistent system done
clear
B)
Consistent system done
clear
C)
Dependent system done
clear
D)
Independent system done
clear
View Solution play_arrow
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question_answer9)
HI What is the nature of the graphs of a dependent system?
A)
Parallel lines done
clear
B)
Perpendicular lines done
clear
C)
Intersecting lines done
clear
D)
Coincident lines done
clear
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question_answer10)
What is the nature of the graphs of a system of linear equations with exactly one solution?
A)
Parallel lines done
clear
B)
Perpendicular lines done
clear
C)
Coincident lines done
clear
D)
Intersecting lines done
clear
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question_answer11)
What is the number of solutions of the pair of linear equations\[\text{4p}-\text{6q}+\text{18}=0\]and\[\text{2p}-\text{3q}+\text{9}=0\]?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
Infinitely many done
clear
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question_answer12)
Which of the following is a consistent system of simultaneous equations?
A)
\[\text{m}+\text{3n}=\text{6}\] \[\text{2m}+\text{6n}=\text{12}\] done
clear
B)
\[\text{a }+\text{ 3b }=\text{ 6}\]\[\text{2a}-\text{3b}=\text{12}\] done
clear
C)
\[\text{x}-\text{4y}=\text{6}\]\[\text{2x}-\text{8y}=\text{12}\] done
clear
D)
\[l-\text{2m}=\text{6}\]\[3l-6m=12\] done
clear
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question_answer13)
Find the unique solution of the system of simultaneous equations\[\text{2x}-\text{y}=\text{2}\] and\[\text{4x}-\text{y}=\text{4}\].
A)
\[\text{x}=0,\text{y}=\text{1}\] done
clear
B)
\[\text{x}=0,\text{y}=0\] done
clear
C)
\[\text{x}=\text{1},\text{y}=0\] done
clear
D)
\[~\text{x}=\text{1},\text{y}=\text{1}\] done
clear
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question_answer14)
The sum of a two-digit number and the number obtained by reversing its digits is 154. If the digits differ by 4, find the number.
A)
95 done
clear
B)
73 done
clear
C)
84 done
clear
D)
62 done
clear
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question_answer15)
Choose the dependent system from the following.
A)
\[\text{m}+\text{n}=\text{7}\]\[\text{3m}+\text{3n}=\text{21}\] done
clear
B)
\[\text{3x}-\text{2y}=\text{5}\]\[\text{2x}-\text{3y}=\text{7}\] done
clear
C)
\[\text{3x}-\text{3y}=\text{18}\]\[\text{x}-\text{y}=\text{1}0\] done
clear
D)
\[\text{2x}+\text{y}=\text{6}\]\[\text{4x}-\text{2y}=\text{4}\] done
clear
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question_answer16)
Five years ago, a father's age was seven times his son's age. Five years from now, the father's age will be thrice the son's age. What are the respective present ages of father and son?
A)
40 years, 10 years done
clear
B)
10 years, 40 years done
clear
C)
25 years, 5 years done
clear
D)
30 years, 8 years done
clear
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question_answer17)
Rajesh buys 7 books and 6 pens for Rs.3800 and Amar buys 3 books and 5 pens of the same kind for Rs.1750. What are the respective costs of a book and a pen?
A)
Rs.350, Rs.50 done
clear
B)
Rs.500, Rs.75 done
clear
C)
Rs.250, Rs.100 done
clear
D)
Rs.500, Rs.50 done
clear
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question_answer18)
The system of simultaneous equations \[\text{3m}+\text{n}=\text{1and(2k}-\text{1)m}+(\text{k}-\text{1})\text{n}=\text{2k}+\text{1}\], is inconsistent. What is the value of 'k'?
A)
3 done
clear
B)
1 done
clear
C)
2 done
clear
D)
0 done
clear
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question_answer19)
What type of a system of equations is the pair of linear equations 2x - 3y = 8 and 4x - 6y = 9?
A)
Consistent system done
clear
B)
Inconsistent system done
clear
C)
Dependent system done
clear
D)
Independent system done
clear
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question_answer20)
If the pair of linear equations\[\text{2x}+\text{ky}-\text{3}=0\]and\[\text{6x}+\frac{2}{3}\text{y}+\text{7}=0\]has a unique solution, which of the following is true?
A)
\[k=\frac{2}{3}\] done
clear
B)
\[k\ne \frac{2}{3}\] done
clear
C)
\[k=\frac{2}{9}\] done
clear
D)
\[k\ne \frac{2}{9}\] done
clear
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question_answer21)
If the length of a rectangle is increased by 2 m and breadth is reduced by 2 m, its area decreases by 28 sq. m. If the length is reduced by 1 m and the breadth is increased by 2 m, the area increases by 33 sq m. Find the actual measurements of the rectangle.
A)
\[l=\text{13m},\text{b}=\text{11 m}\] done
clear
B)
\[l=\text{ 23 m},\text{ b }=\text{ 11 m}\] done
clear
C)
\[l=\text{23m},\text{b}=\text{2}0\text{m}\] done
clear
D)
\[l=\text{12 m},\text{ b }=\text{ 1}0\text{ m}\] done
clear
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question_answer22)
The side of a square is 4m more than the side of another square. The sum of their areas is 208 sq. m. What is the side of the larger square?
A)
12m done
clear
B)
8m done
clear
C)
9m done
clear
D)
5m done
clear
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question_answer23)
Two numbers are in the ratio 2:7. If 6 is added to each of the numbers, the ratio becomes 1:3. Find the numbers.
A)
14, 49 done
clear
B)
16, 56 done
clear
C)
18, 63 done
clear
D)
24, 84 done
clear
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question_answer24)
If the pair of equations \[3x+5y=k\] and\[9x+12y=6\]has infinitely many solutions, which of the following is true?
A)
k = 2 done
clear
B)
k = 6 done
clear
C)
\[k\ne 6\] done
clear
D)
k = 3 done
clear
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question_answer25)
If the pair of linear equations\[3x+5y=3\] and \[6x+ky=6\] do not have any solution, which of the following is true?
A)
k = 5 done
clear
B)
k = 10 done
clear
C)
\[k\ne 10\] done
clear
D)
\[k\ne 5\] done
clear
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question_answer26)
When is the pair of linear equations \[7x-3y=4;3x\frac{k}{7}y=4\] consistent?
A)
k = 9 done
clear
B)
\[~\text{k}=-\text{9}\] done
clear
C)
\[~\text{k}\ne -\text{9}\] done
clear
D)
\[~\text{k}\ne 7\] done
clear
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question_answer27)
When does the pair of linear equations \[7x+ky=k;14x+2y=k+1\]have infinitely many solutions?
A)
k = 1 done
clear
B)
\[k\ne 1\] done
clear
C)
k = 2 done
clear
D)
k = 4 done
clear
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question_answer28)
The pair of linear equations \[x+y=3\]; \[2x+5y=12\]has a unique solution \[x={{x}_{1}},\] \[y={{y}_{1}}\]Find the value of\[{{x}_{1}}\].
A)
1 done
clear
B)
2 done
clear
C)
-1 done
clear
D)
-2 done
clear
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question_answer29)
Which of the following solutions does the pair of linear equations\[x+2y=5\]; \[3x+12y=10\]have?
A)
A unique solution done
clear
B)
No solution done
clear
C)
More than two solutions done
clear
D)
Infinitely many solutions done
clear
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question_answer30)
If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father?
A)
45 years done
clear
B)
40 years done
clear
C)
50 years done
clear
D)
55 years done
clear
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question_answer31)
Three chairs and two tables cost Rs.1850.Five chairs and three tables cost Rs.2850. Find the total cost of one chair and one table.
A)
Rs.800 done
clear
B)
Rs.850 done
clear
C)
Rs.900 done
clear
D)
Rs.950 done
clear
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question_answer32)
If \[\text{a}+\text{b}=\text{5}\]and\[\text{3a}+\text{2b}=\text{2}0\], find\[\text{3a}+\text{b}\].
A)
25 done
clear
B)
20 done
clear
C)
15 done
clear
D)
10 done
clear
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question_answer33)
Which of the respective values of 'x' and 'y' satisfy the following equations I and II?
(I) \[3x+y=19\] |
(II) \[x-y=9\] |
A)
7, 2 done
clear
B)
7, -2 done
clear
C)
-7, 2 done
clear
D)
-7, -2 done
clear
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question_answer34)
If\[3x-5y=5\]and\[\frac{x}{x+y}=\frac{5}{7}\], what is the value of\[x-y\]?
A)
9 done
clear
B)
6 done
clear
C)
4 done
clear
D)
3 done
clear
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question_answer35)
If \[\text{12a}+\text{3b}=\text{1}\]and\[\text{7b}-\text{2a}=\text{9}\], find the average (arithmetic mean) of 'a' and 'b'.
A)
2.5 done
clear
B)
1 done
clear
C)
0.1 done
clear
D)
0.5 done
clear
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question_answer36)
If\[4x+6y=32\]and\[4x-2y=4\], find the value of 8y.
A)
24 done
clear
B)
28 done
clear
C)
36 done
clear
D)
42 done
clear
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question_answer37)
For the equations\[(p+2)\left( q-\frac{1}{2} \right)=pq-5\] and\[(p-2)\left( q-\frac{1}{2} \right)=pq-5\], find the solution set (p, q).
A)
\[\left( -10,-\frac{1}{2} \right)\] done
clear
B)
\[\left( -10,\frac{1}{2} \right)\] done
clear
C)
\[\left( 10,-\frac{1}{2} \right)\] done
clear
D)
\[\left( 10,\frac{1}{2} \right)\] done
clear
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question_answer38)
Identify the solution of\[\frac{2}{3}x-\frac{3}{4}y=1\]and\[8x-9y=16\].
A)
\[\text{x}=\text{6},\text{y}=\text{4}\] done
clear
B)
Infinitely many solutions done
clear
C)
\[\text{x}=\text{4},\text{y}=\text{6}\] done
clear
D)
No solution done
clear
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question_answer39)
Find the values of 'x' and y for \[x-y=0.9\];\[\frac{11}{x+y}=2\]
A)
3.2, 5.6 done
clear
B)
3.2, 2.3 done
clear
C)
5.6, 2.3 done
clear
D)
4.5, 6.4 done
clear
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question_answer40)
What is the solution of the equations,\[\frac{3x-y+1}{3}=\frac{2x+y+2}{5}=\frac{3x+2y+1}{6}?\]
A)
\[\text{x}=-\text{1},\text{y}=-\text{1}\] done
clear
B)
\[~\text{x}=\text{1},\text{ y}=\text{1}\] done
clear
C)
\[\text{x}=\text{1},\text{ y}=\text{2}\] done
clear
D)
\[\text{x}=\text{2},\text{y}=\text{1}\] done
clear
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question_answer41)
The course of an enemy submarine as plotted on a set of rectangular axes gives the equation \[2x+3y=5\]. On the same axes. the course of a destroyer is indicated by the equation \[x-y=10\]. Find the point \[(x,y)\]at which the submarine can be destroyed.
A)
(-7, 3) done
clear
B)
(7, -3) done
clear
C)
(-3, 7) done
clear
D)
(3, -7) done
clear
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question_answer42)
Find the solution of the equations\[8x-9y=6xy\]\[10x+6y=19xy\].
A)
\[x=\frac{3}{2},y=\frac{3}{2}\] done
clear
B)
\[x=\frac{2}{3},y=\frac{3}{2}\] done
clear
C)
\[x=\frac{3}{2},y=\frac{2}{3}\] done
clear
D)
\[x=3,y=2\] done
clear
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question_answer43)
Find the values of 'x' and y, for the equations \[\frac{{{a}^{2}}}{x}-\frac{{{b}^{2}}}{y}=0;\frac{{{a}^{2}}b}{x}+\frac{{{b}^{2}}a}{y}=a+b\] where \[x,y\ne 0\].
A)
\[x={{a}^{2}},y={{b}^{2}}\] done
clear
B)
\[x={{b}^{2}},y={{a}^{2}}\] done
clear
C)
\[x=\frac{b}{a},y=\frac{a}{b}\] done
clear
D)
\[x=\frac{1}{b},y=\frac{1}{a}\] done
clear
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question_answer44)
If \[x+\frac{1}{y}=5\]and \[2x+\frac{3}{y}=13\], what is the value of \[(2x-3y)\]?
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
5 done
clear
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question_answer45)
Which of the following is the solution of the system of equations \[\frac{4}{x}+5y=7\]and \[\frac{3}{x}+4y=5\]?
A)
\[x=-\frac{1}{3},y=-1\] done
clear
B)
\[x=\frac{1}{3},y=-1\] done
clear
C)
\[x=-\frac{1}{3},y=1\] done
clear
D)
\[x=\frac{1}{3},y=1\] done
clear
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question_answer46)
The solution of\[2x+3y=2\]and\[3x+2y=2\]can be represented by a point. In which of the following parts of the coordinate plane does the point lie?
A)
First quadrant done
clear
B)
Second quadrant done
clear
C)
Third quadrant done
clear
D)
Fourth quadrant done
clear
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question_answer47)
cm Find 'x' and 'y' for the equations\[\frac{x}{3}+\frac{y}{4}=4\]and\[\frac{5x}{3}+\frac{y}{4}=8\].
A)
\[\text{x}=\text{8},\text{y}=\text{6}\] done
clear
B)
\[\text{x}=\text{3},\text{y}=\text{4}\] done
clear
C)
\[\text{x}=\text{6},\text{y}=\text{8}\] done
clear
D)
\[~\text{x}=\text{4},\text{y}-\text{6}\] done
clear
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question_answer48)
How many solutions does the system of equations,\[3x-4y=5\]and\[12x-16y=20\]have?
A)
More than two solutions done
clear
B)
Exactly two solutions done
clear
C)
Exactly one solution done
clear
D)
No solution done
clear
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question_answer49)
Find the number of solutions of the equations \[x+\frac{1}{y}=2\]and\[2xy-3y=-2\].
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
Infinitely many done
clear
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question_answer50)
Which of the following solutions do the system of equations\[2x+y=5\]and\[x+2y=4\]have?
A)
Consistent and a unique solution done
clear
B)
Consistent and infinitely many solutions done
clear
C)
Inconsistent done
clear
D)
No solution done
clear
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question_answer51)
If the equations\[4x+7y=10\]and \[10x+ky=25\]represent coincident lines, what is the value of 'k'?
A)
5 done
clear
B)
\[\frac{17}{2}\] done
clear
C)
\[\frac{27}{2}\] done
clear
D)
\[\frac{35}{2}\] done
clear
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question_answer52)
For what value of 'k', will the equations\[4x+6y=11\]and\[2x+ky=7\]be inconsistent?
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
8 done
clear
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question_answer53)
For what value of 'k' will the system of equations\[3x+5y=2\]and\[kx+10y=0\] have a non zero solution?
A)
0 done
clear
B)
2 done
clear
C)
6 done
clear
D)
8 done
clear
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question_answer54)
If the cost of 3 audio cassettes and 2 VCDs is Rs. 350 and that of 2 audio cassettes and 3 VCDs is Rs.425, what is the cost of a VCD?
A)
Rs. 140 done
clear
B)
Rs. 125 done
clear
C)
Rs. 115 done
clear
D)
Rs. 110 done
clear
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question_answer55)
The difference between two numbers is 5 and the difference between their squares is 65. Find the larger number.
A)
9 done
clear
B)
10 done
clear
C)
11 done
clear
D)
12 done
clear
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question_answer56)
Rs.49 was divided among 150 children. Each girl got 50 paise and a boy 25 paise. How many boys were there?
A)
100 done
clear
B)
102 done
clear
C)
104 done
clear
D)
105 done
clear
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question_answer57)
The area of a rectangle increases by 76 square units, if the length and breadth are each increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Find the sum of the length and breadth of the rectangle.
A)
40 units done
clear
B)
42 units done
clear
C)
4 units done
clear
D)
36 units done
clear
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question_answer58)
What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate?
A)
2 done
clear
B)
1 done
clear
C)
3 done
clear
D)
5 done
clear
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question_answer59)
Two numbers differ by 3 and their product is 54. Find the numbers.
A)
9 and 6 done
clear
B)
-9 and -6 done
clear
C)
Both [a] and [b] done
clear
D)
9 and -4 done
clear
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question_answer60)
A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. 250 per quintal, the monthly expenses of the family is Rs. 1000 and when it is Rs. 240 per quintal, the monthly expenses is Rs. 980. Find the monthly expenses of the family on wheat when the cost of wheat is Rs. 350 a quintal.
A)
Rs. 900 done
clear
B)
Rs. 350 done
clear
C)
Rs. 650 done
clear
D)
Rs. 700 done
clear
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question_answer61)
The angles A, B, C and D in order in a cyclic quadrilateral are\[{{(2x+y)}^{o}},{{(2(x+y))}^{o}}\],\[{{(3x+2y)}^{o}}\], and\[{{(4x-2y)}^{o}}\]. Find their measures in the same order.
A)
\[\text{7}0{}^\circ ,\text{ 11}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 1}00{}^\circ \] done
clear
B)
\[\text{7}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 11}0{}^\circ ,\text{ 1}00{}^\circ \] done
clear
C)
\[\text{7}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 1}00{}^\circ ,\text{ 11}0{}^\circ \] done
clear
D)
80°, 100°, 110°, 70° done
clear
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question_answer62)
The smallest angle of a triangle is one-fifth the sum of the other two and the largest angle exceeds the sum of the other two by\[\text{2}0{}^\circ \]. Find the largest angle of the triangle.
A)
\[\text{1}00{}^\circ \] done
clear
B)
\[\text{9}0{}^\circ \] done
clear
C)
\[\text{12}0{}^\circ \] done
clear
D)
\[\text{11}0{}^\circ \] done
clear
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question_answer63)
The sum of Raju's age and half of Sameer's age is 4. One-third Raju's age added to twice Sameer's age is 5. Find the sum of their ages.
A)
7 years done
clear
B)
3 years done
clear
C)
5 years done
clear
D)
2 years done
clear
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