
Which of the following is a solution of the equation \[3x+5y=8\]?
A)
\[x=1,\,y=0\] done
clear
B)
\[x=0,\,y=1\] done
clear
C)
\[x=1,\,y=1\] done
clear
D)
\[x=0,\,y=0\] done
clear
View Solution play_arrow

Which of the following is not a solution of the equation \[3x+2y=5\]?
A)
\[x=1,\,y=1\] done
clear
B)
\[x=3,\,y=2\] done
clear
C)
\[x=1,\,y=4\] done
clear
D)
\[x=1,\,y=2\] done
clear
View Solution play_arrow

\[x=3,\] \[y=4\] is a solution of the linear equation:
A)
\[2x+3y17=0\] done
clear
B)
\[3x+2y17=0\] done
clear
C)
\[2x3y+17=0\] done
clear
D)
\[2x+3y+17=0\] done
clear
View Solution play_arrow

\[x=2,\] \[y=1\]is a solution of the linear equation:
A)
\[2x+7y=11\] done
clear
B)
\[4x2y=5\] done
clear
C)
\[x3y=5\] done
clear
D)
\[3x4y=8\] done
clear
View Solution play_arrow

The point of intersection of the lines represented by \[3x2y=6\] and the xaxis is:
A)
\[(2,0)\] done
clear
B)
\[(0,3)\] done
clear
C)
\[(2,0)\] done
clear
D)
\[(0,3)\] done
clear
View Solution play_arrow

5 chairs and 4 tables together cost Rs.2800 while 4 chairs and 3 tables together cost Rs.2170. Algebraic representation of the situation can be:
A)
\[5x4y=2800,\] \[4x3y=2170\] done
clear
B)
\[5x+4y=2800,\] \[4x+3y=2170\] done
clear
C)
\[5x+3y=2800,\] \[4x+3y=2170\] done
clear
D)
\[5x3y=2800,\] \[4x3y=2170\] done
clear
View Solution play_arrow

The sum of the numerator and denominator of a fraction is 8. If the denominator is increased by 1, the fraction becomes \[\frac{1}{2}\]. Algebraic representation of the situation can be:
A)
\[x+y=8,\,\,\frac{x+1}{y}=\frac{1}{2}\] done
clear
B)
\[x+y=8,\,\,\frac{x}{y}+1=\frac{1}{2}\] done
clear
C)
\[\frac{x}{y}=8,\,\frac{x}{y+1}=\frac{1}{2}\] done
clear
D)
\[x+y=8,\,\frac{x}{y+1}=\frac{1}{2}\] done
clear
View Solution play_arrow

The age of a daughter is onethird the age of her mother. If the present age of mother is x years, then the age (in years) of the daughter after 15 years is:
A)
\[\frac{x}{3}+15\] done
clear
B)
\[\frac{x+15}{3}\] done
clear
C)
\[x+5\] done
clear
D)
\[\frac{x}{3}15\] done
clear
View Solution play_arrow

The sum of two numbers is 137 and their difference is 43. Algebraic representation of the situation can be:
A)
\[xy=137,\,\,x+y=180\] done
clear
B)
\[2(x+y)=137,\,(xy)=43\] done
clear
C)
\[x+y=137,\,\,xy=43\] done
clear
D)
\[x+y=43,\,\,xy=137\] done
clear
View Solution play_arrow

The value of a so that the point \[(3,a)\] lies on the line represented by \[2x3y=5,\] is:
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow

If \[x=a\] and \[y=b\] is the solution of the equations \[\text{x}\text{y}=\text{2}\]and \[\text{x}+\text{y}=\text{4},\]then the values of a and b are, respectively: (NCERT EXEMPLAR)
A)
3 and 5 done
clear
B)
5 and 3 done
clear
C)
3 and 1 done
clear
D)
\[1\] and \[1\] done
clear
View Solution play_arrow

The solution of equations \[\text{2x}+\text{y}\text{6}=0\]and \[\text{4x}\text{2y}\text{4}=0\]is:
A)
\[(2,4)\] done
clear
B)
\[(4,2)\] done
clear
C)
\[(2,2)\] done
clear
D)
\[(2,2)\] done
clear
View Solution play_arrow

If \[x=a,\] \[y=b\] is the solution of the pair of equation \[\text{x}\text{y}=\text{l}\]and \[\text{x}+\text{y}=\text{4},\]then the respective values of a and b are: (CBSE 2012)
A)
3, 5 done
clear
B)
5, 3 done
clear
C)
3, 1 done
clear
D)
1, 3 done
clear
View Solution play_arrow

\[ax+by+c=0\] where a, b, c are real numbers is called a Linear equation in two variables x and y if:
A)
\[a\ne b\] done
clear
B)
\[{{a}^{2}}={{b}^{2}}\] done
clear
C)
\[{{a}^{2}}+{{b}^{2}}=0\] done
clear
D)
\[{{a}^{2}}+{{b}^{2}}\ne 0\] done
clear
View Solution play_arrow

Every solution of \[ax+by+c=0\]is a pair of values:
A)
one for a and other for b done
clear
B)
one for a and other for c done
clear
C)
one for b and other for c done
clear
D)
one for x and other for y done
clear
View Solution play_arrow

Graphically \[\text{ax}+\text{by}+\text{c}=0\]represents a line. Every solution of the equation is a point:
A)
on the line representing it done
clear
B)
not on the line representing it done
clear
C)
on the xaxis done
clear
D)
on the yaxis done
clear
View Solution play_arrow

Every point on the line representing the linear equation in two variables:
A)
may not be a solution of the equation done
clear
B)
is a solution of the equation done
clear
C)
is a solution if it is also a point on xaxis done
clear
D)
is a solution of the equation if it is also a point on yaxis done
clear
View Solution play_arrow

\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\]where \[{{a}_{1}},{{b}_{1}},{{c}_{1}},{{a}_{2}},{{b}_{2}},{{c}_{2}}\] are all real numbers and \[a_{1}^{2}+b_{1}^{2}\ne 0,\] \[a_{2}^{2}+b_{2}^{2}\ne 0,\] is called a:
A)
family of two different straight lines done
clear
B)
family of two coincident lines done
clear
C)
pair of linear equations in two variables done
clear
D)
None of the above done
clear
View Solution play_arrow

\[y=a+\frac{b}{x}\]where a, bare real numbers, if \[y=1\]when \[x=1\]and \[y=5\] when \[x=5,\] then \[a+b\] equals:
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[11\] done
clear
D)
\[10\] done
clear
View Solution play_arrow

If \[\text{47x}+\text{31y}=\text{18}\]and \[\text{31x}+\text{47y}=\text{6}0,\] then value of \[\text{x}+\text{y}\]is:
A)
1 done
clear
B)
0 done
clear
C)
23 done
clear
D)
47 done
clear
View Solution play_arrow

If \[ax+by={{a}^{2}}{{b}^{2}}\] and \[bx+ay=0,\] then value of \[\text{x+y}\] is:
A)
\[a+b\] done
clear
B)
\[ab\] done
clear
C)
0 done
clear
D)
1 done
clear
View Solution play_arrow

The point of the form \[(a,a)\] always Lies on the line is:
A)
\[y=x\] done
clear
B)
\[x=y\] done
clear
C)
\[x=y\] done
clear
D)
\[x=2y\] done
clear
View Solution play_arrow

If \[x=a,\] \[y=b\] is the solution of the pair of equations \[\text{x}\text{y}=\text{2}\]and \[\text{x}+\text{y}=\text{4},\]then the value of a and b are:
A)
3, 1 done
clear
B)
1, 3 done
clear
C)
1, 3 done
clear
D)
3, 1 done
clear
View Solution play_arrow

The points \[(7, 2)\] and \[(1,0)\] lie on a line:
A)
\[7y=3x7\] done
clear
B)
\[4y=x+1\] done
clear
C)
\[y=7x+7\] done
clear
D)
\[x=4y+1\] done
clear
View Solution play_arrow

If \[3x+4y:x+2y=9:4,\]then \[3x+5y:3xy\] is equal to:
A)
4:1 done
clear
B)
1:4 done
clear
C)
7:1 done
clear
D)
1:7 done
clear
View Solution play_arrow

If \[3x+5y=8\]and \[7x3y=48,\]then the value of \[x+y\] is:
A)
5 done
clear
B)
4 done
clear
C)
4 done
clear
D)
The value does not exist done
clear
View Solution play_arrow

If a pair of linear equations in two variables is inconsistent, then the lines represented by two equations are:
A)
intersecting done
clear
B)
parallel done
clear
C)
always coincident done
clear
D)
intersecting or coincident done
clear
View Solution play_arrow

The pair of equations \[x+3y+5=0\] and \[3x9y+2=0\]has:
A)
a unique solution done
clear
B)
exactly two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

The pair of equations \[\text{2x}\text{3y}+\text{4}=0\] and \[\text{2x}+\text{y}\text{6}=0\]has:
A)
a unique solution done
clear
B)
exactly two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

The pair of equations \[\text{x}+\text{y}=\text{1}\]and \[\text{x}+\text{y}=\text{5}\] has:
A)
one solution done
clear
B)
two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

The pair of equations \[\text{9x}+\text{3y}+\text{5}=0\] and \[\text{6x}+\text{2y}+\text{7}=0\]represents lines which are:
A)
parallel done
clear
B)
intersecting at one point done
clear
C)
coincident done
clear
D)
perpendicular to each other done
clear
View Solution play_arrow

The graphs of the equations \[\text{6x}\text{2y}+\text{9}=0\] and \[\text{3x}\text{y}+\text{12}=0\] are two lines which are:
A)
coincident done
clear
B)
parallel done
clear
C)
intersecting exactly at one point done
clear
D)
perpendicular to each other done
clear
View Solution play_arrow

The graphs of the equations \[\text{2x}+\text{3y}\text{2}=0\] and \[\text{x}\text{y}\text{5}=0\]represent two lines which are:
A)
coincident done
clear
B)
parallel done
clear
C)
intersecting exactly at one point done
clear
D)
perpendicular to each other done
clear
View Solution play_arrow

The pair of equations \[\text{y}=\text{3}\]and \[\text{y}=8\] has:
A)
one solution done
clear
B)
two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

The pair of equations \[\text{x}=\text{1}\]and \[y=\text{1}\] represents:
A)
parallel lines done
clear
B)
coincident lines done
clear
C)
intersecting lines which are perpendicular done
clear
D)
intersecting lines but not perpendicular done
clear
View Solution play_arrow

If \[am\ne bl,\] then the pair of equations \[\text{ax}+\text{by}=\text{c},\] \[lx+my=n:\]:
A)
has a unique solution done
clear
B)
has no solution done
clear
C)
has infinitely many solutions done
clear
D)
may or may not have a solution done
clear
View Solution play_arrow

If the system of equations \[\text{2x}+\text{3y}=\text{6}\] and \[2ax+(a+b)y=24\]has infinitely many solutions, then:
A)
\[a=2b\] done
clear
B)
\[b=2a\] done
clear
C)
\[a+2b=0\] done
clear
D)
\[2a+b=0\] done
clear
View Solution play_arrow

The value of k for which the system of equations \[\text{x}+\text{3y}\text{3}=0\]and \[\text{4x}+\text{ky}+\text{7}=0\] has no solution, is:
A)
10 done
clear
B)
7 done
clear
C)
3 done
clear
D)
12 done
clear
View Solution play_arrow

For what value of k does the system of equations \[x+2y=8\] and \[\text{4x}+\text{ky}+\text{7}=0\] have no solution?
A)
\[k=8\] done
clear
B)
\[k=\frac{7}{8}\] done
clear
C)
\[k=56\] done
clear
D)
\[k\ne 8\] done
clear
View Solution play_arrow

Find the value of k for which the system of equations \[\text{x}+\text{3y}=\text{4}\]and \[\text{3x}+\text{ky}+\text{12}=0\] are inconsistent.
A)
\[k=12\] done
clear
B)
\[k=12\] done
clear
C)
\[k=9\] done
clear
D)
\[k=9\] done
clear
View Solution play_arrow

For what value of c does the pair of equations or \[cxy=3\]and \[\text{6x}\text{2y}=\text{4}\] have infinitely many solutions?
A)
\[c=3\] done
clear
B)
\[c=3\] done
clear
C)
\[c=12\] done
clear
D)
not possible for any value of c done
clear
View Solution play_arrow

For what value of k does the pair of equations \[\text{x}\text{2y}=\text{3}\]and \[\text{2x}+\text{ky}=5\] have a unique solution?
A)
\[k=4\] done
clear
B)
\[k=0\]only done
clear
C)
\[k\ne 1\] done
clear
D)
\[k\ne 4\] done
clear
View Solution play_arrow

Find the value(s) of k for which the system of equations \[kxy=4\] has \[10x2y=3\]has no solution.
A)
6 done
clear
B)
4 done
clear
C)
5 done
clear
D)
2 done
clear
View Solution play_arrow

The point of the intersection of the lines \[x3=0\] and \[\text{y}\text{5}=0\]is:
A)
\[(3,5)\] done
clear
B)
\[(3,5)\] done
clear
C)
\[(0,5)\] done
clear
D)
\[(3,5)\] done
clear
View Solution play_arrow

Which of the following equations represents a line coincident with the equation \[7x+y6=0\]?
A)
\[x+7y6=0\] done
clear
B)
\[\text{21x}+\text{3y}\text{7=}0\] done
clear
C)
\[\text{7x}+\text{7y}\text{5}=0\] done
clear
D)
\[\text{14x}+\text{2y}\text{12}=0\] done
clear
View Solution play_arrow

Two Lines are to be parallel. The equation of one of the Lines is \[\text{3x}+\text{4y}=\text{11}\]The equation of the other line can be:
A)
\[4x+3y=12\] done
clear
B)
\[6x+8y=24\] done
clear
C)
\[9x+12y=36\] done
clear
D)
\[9x=12y+35\] done
clear
View Solution play_arrow

If one Linear equation is \[\text{x}\text{2y}+\text{5=0,}\] then another linear equation to have parallel Line as its geometrical construction will be:
A)
\[\text{2x}\text{4y}+\text{1}0=0\] done
clear
B)
\[\text{3x}\text{6y}+\text{15}=0\] done
clear
C)
\[\text{4x}\text{8y}+\text{2}0=0\] done
clear
D)
\[\text{3x}\text{6y}+\text{2}0=0\] done
clear
View Solution play_arrow

Find the conditions to be satisfied by coefficients for which the following pair of equations \[\text{ax}+\text{by}+\text{c}=0,\] \[dx+ey+f=0\]represent coincident lines.
A)
\[ab=ed;\,\,bf=ce\] done
clear
B)
\[ae=bd;\,\,bc=ef\] done
clear
C)
\[ad=bc,\,\,bf=ce\] done
clear
D)
\[ae=bd,\,\,bf=ce\] done
clear
View Solution play_arrow

Equation of Line which is parallel to \[\sqrt{3}x\sqrt{5}y=8\] is:
A)
\[\sqrt{3}x+\sqrt{5}y=1\] done
clear
B)
\[\sqrt{3}x\sqrt{5}y=8\] done
clear
C)
\[\sqrt{3}x\sqrt{5}y=1\] done
clear
D)
\[\sqrt{3}x+\sqrt{5}y=8\] done
clear
View Solution play_arrow

Graphically, the pair of equations \[\text{6x}\text{5y}+\text{1}0=0\] \[\text{2x}\text{y}+\text{9}=0\] represents two lines which are: (ncert exemplar)
A)
intersecting at exactly one point done
clear
B)
intersecting at exactly two points done
clear
C)
coincident done
clear
D)
parallel done
clear
View Solution play_arrow

The pair of equations \[\text{x}+\text{2y}+\text{5=0}\]and \[\text{3x}\text{6y}+\text{1}=0\]have: (NCERT EXEMPLAR)
A)
a unique solution done
clear
B)
exactly two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

If a pair of linear equations is consistent, then the lines will be: (NCERT EXEMPLAR)
A)
parallel done
clear
B)
always coincident done
clear
C)
intersecting or coincident done
clear
D)
always intersecting done
clear
View Solution play_arrow

The pair of equations \[\text{y}=0\]and \[\text{y}=\text{7}\]has: (NCERT EXEMPLAR)
A)
one solution done
clear
B)
two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

The pair of equations \[x=a\] and \[y=b\] graphically represents lines which are: (NCERT EXEMPLAR)
A)
parallel done
clear
B)
intersecting at \[(b,a)\] done
clear
C)
coincident done
clear
D)
intersecting at \[(a,b)\] done
clear
View Solution play_arrow

For what value of k, do the equations \[\text{3x}\text{y}+\text{8}=0\]and \[\text{6x}k\text{y}=\text{16}\] represent coincident lines? (NCERT EXEMPLAR)
A)
\[1/2\] done
clear
B)
\[1/2\] done
clear
C)
\[2\] done
clear
D)
\[2\] done
clear
View Solution play_arrow

If the lines given by \[\text{3x}+\text{2ky}=\text{2}\] and \[\text{2x}+\text{5y}+\text{1}=0\] are parallel, then the value of k is: (NCERT EXEMPLAR)
A)
\[\frac{5}{4}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[\frac{15}{4}\] done
clear
D)
\[\frac{3}{2}\] done
clear
View Solution play_arrow

The value of c for which the pair of equations \[cxy=2\]and \[\text{6x}\text{2y}=\text{3}\] will have infinitely many solutions is: (NCERT EXEMPLAR)
A)
\[3\] done
clear
B)
\[3\] done
clear
C)
\[12\] done
clear
D)
no value done
clear
View Solution play_arrow

One equation of a pair of dependent linear equations is \[5x+7y=2\] The second equation can be: (NCERT EXEMPLAR)
A)
\[10x+14y+4=0\] done
clear
B)
\[10x14y+4=0\] done
clear
C)
\[10x+14y+4=0\] done
clear
D)
\[10x14y=4\] done
clear
View Solution play_arrow

A pair of linear equations which has a unique solution \[x=2\]and \[y=3\] is: (NCERT EXEMPLAR)
A)
\[x+y=1\]and \[2x3y=5\] done
clear
B)
\[2x+5y=11\] and \[4x+10y=22\] done
clear
C)
\[2xy=1\] and \[3x+2y=0\] done
clear
D)
\[x4y14=0\]and \[5xy13=0\] done
clear
View Solution play_arrow

The equations \[\text{2x}\text{2y}\text{2}=0\] and \[\text{4x}\text{4y}\text{5}=0\] have: (NCERT EXERCISE)
A)
a unique solution done
clear
B)
no solution done
clear
C)
infinitely many solutions done
clear
D)
None of these done
clear
View Solution play_arrow

The pair of equations \[\text{5x15y}=\text{8}\] and \[3x9y=\frac{24}{5}\]has/have: (NCERT EXEMPLAR)
A)
solution done
clear
B)
two solutions done
clear
C)
infinitely many solutions done
clear
D)
no solution done
clear
View Solution play_arrow

For what value of p, do the equations \[\text{3x}+\text{5y}=\text{7}\]and \[\text{2px}\text{3y}=\text{1}\]represent intersecting lines? (NCERT EXEMPLAR)
A)
All real values of p except \[\frac{9}{10}\] done
clear
B)
All real values of p done
clear
C)
All real values of p except \[\frac{10}{9}\] done
clear
D)
None of the above done
clear
View Solution play_arrow

The value of k for which the system of linear equations \[\text{x}+\text{2y}=\text{3}\]and \[\text{5x}+\text{ky}+\text{7}=0\] is inconsistent is: (CBSE 2020)
A)
\[14/3\] done
clear
B)
\[2/5\] done
clear
C)
\[5\] done
clear
D)
\[10\] done
clear
View Solution play_arrow

One equation of a pair of dependent linear equations is \[\text{5x}+\text{7y}=\text{2},\] the second equation can be: (CBSE 2011)
A)
\[10x+14y+4=0\] done
clear
B)
\[10x14y+4=0\] done
clear
C)
\[10x+14y+4=0\] done
clear
D)
\[10x14y=4\] done
clear
View Solution play_arrow

The pair of linear equations \[\text{2x}\text{3y}=\text{1}\]and \[\text{3x}\text{2y}=\text{4}\]has: (CBSE 201I)
A)
one solution done
clear
B)
two solutions done
clear
C)
no solution done
clear
D)
many solutions done
clear
View Solution play_arrow

Two lines are given to be parallel The equation of one of the lines is \[\text{4x}+\text{3y}=\text{14}\]. The equation of the second Line can be: (CBSE 2012)
A)
\[3x+4y=14\] done
clear
B)
\[8x+6y=28\] done
clear
C)
\[12x+9y=42\] done
clear
D)
\[12x=9y\] done
clear
View Solution play_arrow

The pair of equations \[\text{x}=\text{4}\]and \[y=3\] graphically represents lines which are: (CBSE 2012)
A)
parallel done
clear
B)
intersecting at \[(3,4)\] done
clear
C)
coincident done
clear
D)
intersecting at \[(4,3)\] done
clear
View Solution play_arrow

For given two lines in a plane, which of the following is not possible?
A)
the two lines will intersect at a point done
clear
B)
the two lines will be parallel done
clear
C)
the two lines will be coincident done
clear
D)
the two lines will neither intersect nor parallel done
clear
View Solution play_arrow

Match the column:
1.  \[2x+3y=40\] \[6x+5y=10\]  A.  Coincident lines 
2.  \[2x+3y=40\] \[6x+9y=50\]  B.  Intersecting lines 
3.  \[2x+3y=10\] \[4x+6y=20\]  C.  Parallel lines 
A)
1A, 2B, 3C done
clear
B)
1B, 2A, 3C done
clear
C)
1B, 2C, 3A done
clear
D)
1C, 2A, 3B done
clear
View Solution play_arrow

Match the column:
1.  \[2x+5y=10\] \[3x+4y=7\]  A.  Unique solution 
2.  \[2x+5y=10\] \[6x+15y=20\]  B.  Infinitely many solutions 
3.  \[5x+2y=10\] \[10x+4y=20\]  C.  No common solution 
A)
1A, 2B, 3C done
clear
B)
1B, 2C, 3A done
clear
C)
1C, 2B, 3A done
clear
D)
1A, 2C, 3B done
clear
View Solution play_arrow

Match the column:
1.  \[2x+5y=7\] \[3x+4y=7\]  A.  Inconsistent pair of equations 
2.  \[2x+5y=7\] \[4x+10y=7\]  B.  Consistent pair of equations 
3.  \[2x+5y=7\] \[4x+10y=14\]  C.  Dependent consistent pair of equations 
A)
1A, 2C, 3B done
clear
B)
1B, 2C, 3A done
clear
C)
1B, 2A, 3C done
clear
D)
1C, 2A, 3B done
clear
View Solution play_arrow

The pair of linear equations \[x=y\] and \[\text{x}+\text{y}=0\]has:
A)
no common solution done
clear
B)
infinitely many solutions done
clear
C)
unique solution done
clear
D)
None of these done
clear
View Solution play_arrow

The pair of Linear equations \[x=2\] and \[x=5\] has:
A)
no common solution done
clear
B)
infinitely many solutions done
clear
C)
unique solution done
clear
D)
None of these done
clear
View Solution play_arrow

The pair of linear equations \[\text{3x}+\text{4y}=\text{12}\]and \[\text{y}=\text{4}\] has:
A)
no common solution done
clear
B)
infinitely many solutions done
clear
C)
unique solution done
clear
D)
None of these done
clear
View Solution play_arrow

The pair of linear equations \[\text{2x}+\text{3y}=\text{5}\] and \[\text{4x}+\text{6y}=\text{1}0\] is:
A)
inconsistent done
clear
B)
consistent done
clear
C)
dependent consistent done
clear
D)
None of these done
clear
View Solution play_arrow

For what value of k, the pair of equations \[\text{2x}+\text{5y}+\text{5}=0\]and \[kx+4y=10,\] has a unique solution?
A)
\[k=\frac{8}{3}\] done
clear
B)
\[k\ne \frac{8}{3}\] done
clear
C)
\[k=3\] done
clear
D)
\[k\ne 3\] done
clear
View Solution play_arrow

If the pair of equations \[x+y=\sqrt{2}\] and \[x\,\,\sin \theta +y\,\,\cos \theta =1\] has infinitely many solutions, then \[\theta =\]
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow

The value of k for which the lines \[3x+4y=5,\]\[5x+4y=4\] and \[\text{kx}+\text{4y}=\text{6}\] meet at a point is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow

The equations \[ax+by+c=0\]and \[dx+ey+c=0\]represent the same straight line if:
A)
\[ad=be\] done
clear
B)
\[ac=bd\] done
clear
C)
\[bc=ad\] done
clear
D)
\[ab=de\] done
clear
View Solution play_arrow

The pair of equations \[ax+2y=7\] and \[3x+by=16\] represent parallel lines if:
A)
\[a=b\] done
clear
B)
\[3a=2b\] done
clear
C)
\[2a=3b\] done
clear
D)
\[ab=6\] done
clear
View Solution play_arrow

The value of a for which the lines \[x=1,\] \[y=2\] and \[\text{ax}+\text{2y}\text{6}=0\]are concurrent is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow

Equation of line \[{{L}_{1}}:{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\] 
Equation of line \[{{L}_{2}}:{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\] 
Equation of line \[{{L}_{3}}:({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})+({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})=0\] 
if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then line \[{{L}_{3}}\]is: 
A)
parallel to line \[{{L}_{1}}\] done
clear
B)
parallel to line \[{{L}_{2}}\] done
clear
C)
is coincident with \[{{L}_{2}}\]or \[{{L}_{1}}\] done
clear
D)
None of these done
clear
View Solution play_arrow

Given the pair of equations \[ax+(a1)y=1\] and \[(a+1)xay=1,\] for which one of the following values of is there no common solution of the given pair of equations?
A)
\[\pm \sqrt{2}\] done
clear
B)
\[\pm \frac{1}{\sqrt{2}}\] done
clear
C)
\[\pm 2\] done
clear
D)
\[1\pm \frac{1}{2}\] done
clear
View Solution play_arrow

The condition for infinitely many solutions of system of linear equations is:
A)
\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] done
clear
B)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] done
clear
C)
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] done
clear
D)
None of these done
clear
View Solution play_arrow

The equations \[\text{3x}\text{5y}=\text{7}\] and \[\text{9x}\text{15y}=\text{21}\]have:
A)
a unique solution done
clear
B)
no solution done
clear
C)
infinitely many solutions done
clear
D)
None of these done
clear
View Solution play_arrow

The values of k for which the system of equations \[x+ky=0,\] \[2xy=0\] has unique solution, is/are:
A)
\[k=2\] done
clear
B)
\[k=3\] done
clear
C)
\[k\ne \frac{15}{2}\] done
clear
D)
\[k\ne \frac{1}{2}\] done
clear
View Solution play_arrow

If one equation of a pair of dependent linear equations is \[\text{5x}\text{7y}+\text{2}=0,\] then the second equation is given by:
A)
\[5kx7ky+2k=0\] done
clear
B)
\[5kx+7ky+2k=0\] done
clear
C)
\[5kx7ky2k=0\] done
clear
D)
\[2kx7ky+5k=0\] done
clear
View Solution play_arrow

If a pair of linear equations is consistent with a unique solution, then the lines representing them are:
A)
parallel done
clear
B)
coincident done
clear
C)
intersecting done
clear
D)
None of these done
clear
View Solution play_arrow

If the pair of equations \[\text{ax}+\text{2y}=\text{7}\]and \[3x+by=16\]represent parallel Lines, then ab is:
A)
2 done
clear
B)
6 done
clear
C)
\[3\] done
clear
D)
\[5\] done
clear
View Solution play_arrow

The Line \[\text{4x}+\text{3y}\text{12}=0\] cuts the coordinate axes at A and B. The area of \[\Delta OAB\] is:
A)
2 sq. units done
clear
B)
\[\frac{3}{2}\] sq. units done
clear
C)
6 sq. units done
clear
D)
12 sq. units done
clear
View Solution play_arrow

The system of equations \[ax+3y=1,\] \[12x+ay=2\] has.......... for all real values of
A)
no solution done
clear
B)
unique solution done
clear
C)
infinitely many solution done
clear
D)
None of these done
clear
View Solution play_arrow

The pair of linear equations \[\text{2kx}+\text{5y}=\text{7},\] \[\text{6x}\text{5y}=1\text{1}\] has a unique solution, if:
A)
\[k\ne 3\] done
clear
B)
\[k\ne \frac{2}{3}\] done
clear
C)
\[k\ne 5\] done
clear
D)
\[k\ne \frac{2}{9}\] done
clear
View Solution play_arrow

Which of the following pair of equations are inconsistent?
A)
\[3xy=9,\,\,x\frac{y}{3}=3\] done
clear
B)
\[4x+3y=24,\,2x+3y=6\] done
clear
C)
\[5xy=10,\,\,10x2y=20\] done
clear
D)
\[2x+y=3,\,\,4x+2y=10\] done
clear
View Solution play_arrow

The value of a for which the lines \[x=1,\] \[y=2\] and \[{{a}^{2}}x+2y20=0\]are concurrent, is:
A)
1 done
clear
B)
8 done
clear
C)
\[4\] done
clear
D)
\[2\] done
clear
View Solution play_arrow

The ratio of the areas of the two triangles formed by the lines representing the equations \[\text{2x}+\text{y}=\text{6}\]and \[2xy+2=0\] with the Xaxis and the Lines with the Yaxis is:
A)
\[1:2\] done
clear
B)
\[2:1\] done
clear
C)
\[4:1\] done
clear
D)
\[1:4\] done
clear
View Solution play_arrow

The difference between two numbers is 24 and one number is three times the other number find them.
A)
\[36,12\] done
clear
B)
\[30,10\] done
clear
C)
\[40,14\] done
clear
D)
\[33,11\] done
clear
View Solution play_arrow

Shruti has only Rs.2 and Rs.5 coins with her. If the total number of coins that she has is 25 and the amount of money with her is Rs.92, then the number of Rs.2 and Rs.5 coins are, respectively:
A)
13 and 12 done
clear
B)
11 and 14 done
clear
C)
5 and 20 done
clear
D)
15 and 10 done
clear
View Solution play_arrow

The larger of two complementary angles exceeds the smaller by 16 degrees. Find them.
A)
\[58{}^\circ ,\,\,32{}^\circ \] done
clear
B)
\[53{}^\circ ,\,\,37{}^\circ \] done
clear
C)
\[64{}^\circ ,\,26{}^\circ \] done
clear
D)
\[29{}^\circ ,\,63{}^\circ \] done
clear
View Solution play_arrow

In a \[\Delta ABC,\] if \[\angle C=50{}^\circ \] and \[\angle A\] exceeds \[\angle B\] by \[44{}^\circ ,\] then \[\angle A=\]
A)
\[43{}^\circ \] done
clear
B)
\[40{}^\circ \] done
clear
C)
\[67{}^\circ \] done
clear
D)
\[87{}^\circ \] done
clear
View Solution play_arrow

The sum of numerator and denominator of a proper fraction is 13 and their difference is 3. Find the fraction.
A)
\[5/8\] done
clear
B)
\[8/5\] done
clear
C)
\[3/5\] done
clear
D)
\[4/7\] done
clear
View Solution play_arrow

5 years hence, the age of a man shall be 4 times the age of his son while 3 years earlier the age of the man was 16 times the age of his son. The present age of the man is:
A)
35 years done
clear
B)
40 years done
clear
C)
37 years done
clear
D)
30 years done
clear
View Solution play_arrow

The solution of the pair of equations \[\text{x}\text{y}=0\]and \[\text{3x}\text{2y}=\text{3}\] is:
A)
\[x=1,\,\,y=1\] done
clear
B)
\[x=2,\,\,y=2\] done
clear
C)
\[x=3,\,\,y=3\] done
clear
D)
\[x=0,\,\,y=0\] done
clear
View Solution play_arrow

If \[5x3y=9\]and \[(ab)x(a+b3)y=a4b\]represent coincident Lines, then values of a and b are:
A)
\[\frac{11}{10},\frac{9}{10}\] done
clear
B)
\[\frac{9}{10},\frac{11}{10}\] done
clear
C)
\[\frac{33}{2},6\] done
clear
D)
\[6,\frac{33}{5}\] done
clear
View Solution play_arrow

The sum of the two digits of a two digit number is 9. The number obtained by interchanging the two digits exceeds the given number by 45. Find the number.
A)
72 done
clear
B)
27 done
clear
C)
54 done
clear
D)
45 done
clear
View Solution play_arrow

Solve: \[\text{2x}+\text{3y}=\text{16}\]and \[\text{3x}\text{4y}=\text{7}\].
A)
\[\text{x}=\text{3},\text{y}=\text{2}\] done
clear
B)
\[\text{x}=\text{6},\text{y}=\text{2}\] done
clear
C)
\[\text{x}=0,\text{y}=\text{5}\] done
clear
D)
\[\text{x}=\text{5},\text{y}=\text{2}\] done
clear
View Solution play_arrow

If \[{{3}^{xy}}=9\]and \[\text{x}\text{2y}=\text{6}\]represent a system of the equations, then the value of \[\text{x+y}\] is:
A)
\[2\] done
clear
B)
\[6\] done
clear
C)
\[4\] done
clear
D)
None of these done
clear
View Solution play_arrow

If \[\text{3x}\text{2y}=\text{4}\] and \[\text{2x}+\text{y}=\text{5},\] then the value of m such that \[\text{y}=\text{x}+\text{m},\] is:
A)
\[m=1\] done
clear
B)
\[m=1\] done
clear
C)
\[m=\frac{1}{2}\] done
clear
D)
\[m=\frac{1}{2}\] done
clear
View Solution play_arrow

The solution of the pair of equations \[x+y=14\] and \[xy=4\] is:
A)
\[\text{x}=\text{9},\text{y}=\text{5}\] done
clear
B)
\[\text{x}=\text{5},\text{y}=\text{9}\] done
clear
C)
\[\text{x}=\text{9,y}=\text{9}\] done
clear
D)
\[\text{x}=\text{5,y}=\text{5}\] done
clear
View Solution play_arrow

The length of a room exceeds its breadth by\[3m\]. If the Length is increased by \[3m\] and the breadth is decreased by \[2m,\] the area remains the same. Find the length and the breadth of the room.
A)
\[12m,\,9m\] done
clear
B)
\[17m,\,14m\] done
clear
C)
\[15m,\,12m\] done
clear
D)
\[14m,\,11m\] done
clear
View Solution play_arrow

Aruna has only Rs.1 and Rs.2 coins with her. If the total number of coins that she has 50 and the amount of money with her is Rs.75, then the number of Rs.1 and Rs.2 coins are, respectively. (NCERT EXEMPLAR)
A)
35 and 15 done
clear
B)
35 and 20 done
clear
C)
15 and 35 done
clear
D)
25 and 25 done
clear
View Solution play_arrow

The father's age is six times his son's age. Four years hence, the age of the father. will be four times his son's age. The present ages, in years of the son and the father are, respectively: (NCERT EXEMPLAR)
A)
4 and 24 done
clear
B)
5 and 30 done
clear
C)
6 and 36 done
clear
D)
3 and 24 done
clear
View Solution play_arrow

The sum of the digits of a two digit number is 9. If 27 is added to the number, its digits reverse. The number is: (NCERT EXEMPLAR)
A)
25 done
clear
B)
72 done
clear
C)
63 done
clear
D)
36 done
clear
View Solution play_arrow

Aseem went to a stationery shop and purchased 3 pens and 5 pencils for Rs.40. His cousin Manik bought 4 pencils and 5 pens for Rs.58. If cost of 1 pen is Rs.x and 1 pencil is Rs.y, then which of the following represent the situation algebraically?
A)
\[3x+5y=40,\,\,4x+5y=58\] done
clear
B)
\[3x+4y=40,\,\,5x+5y=58\] done
clear
C)
\[3x+5y=40,\,\,5x+4y=58\] done
clear
D)
\[3x+5y=40,\,\,4x+3y=58\] done
clear
View Solution play_arrow

There are two positive numbers such that sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is:
A)
6 done
clear
B)
8 done
clear
C)
9 done
clear
D)
10 done
clear
View Solution play_arrow

The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference between the two digits of the number?
A)
9 done
clear
B)
6 done
clear
C)
12 done
clear
D)
3 done
clear
View Solution play_arrow

Which of the following cannot be the difference between a two digit number and the number obtained by interchanging the digits?
A)
72 done
clear
B)
36 done
clear
C)
54 done
clear
D)
48 done
clear
View Solution play_arrow

The area of a trapezium is \[\text{14}00\text{ c}{{\text{m}}^{\text{2}}}\]. Its altitude is 50 cm. Find the two bases, if the number of cms in each base is an integer divisible by 9. The number of solution to this problem is:
A)
one done
clear
B)
two done
clear
C)
three done
clear
D)
None of these done
clear
View Solution play_arrow

A two digit number is k times the sum of its digits. The number formed by interchanging the digits is the sum of digits multiplied by:
A)
\[9k\] done
clear
B)
\[11k\] done
clear
C)
\[k1\] done
clear
D)
\[k+1\] done
clear
View Solution play_arrow

A can do a piece of work in 24 days. If B is \[60%\] more efficient than A, then the number of days required by B to do the twice as Large as the earlier work is:
A)
24 done
clear
B)
36 done
clear
C)
15 done
clear
D)
30 done
clear
View Solution play_arrow

A motor boat takes 2 hours to travel a distance 9 km down the current and it takes 6 hours to travel the same distance against the current The speed of the boat in still water and that of the current (in km/hour) respectively are:
A)
\[3,1.5\] done
clear
B)
\[3,2\] done
clear
C)
\[\text{3}.\text{5},\text{2}.\text{5}\] done
clear
D)
\[3,1\] done
clear
View Solution play_arrow

X's salary is half that of r's. If X got a \[50%\]rise in his salary and Y got \[25%\] rise in his salary, then the percentage increase in combined salaries of both is:
A)
\[30\] done
clear
B)
\[33\frac{1}{3}\] done
clear
C)
\[37\frac{1}{2}\] done
clear
D)
\[75\] done
clear
View Solution play_arrow

The 2 digit number which becomes \[(5/6)th\] of itself when its digits are reversed. The difference in the digits of the number being 1, then the two digits number is:
A)
\[45\] done
clear
B)
\[54\] done
clear
C)
\[36\] done
clear
D)
None of these done
clear
View Solution play_arrow

In a number of two digits, unit's digit is twice the tens digit If 36 be added to the number, the digits are reversed. The number is:
A)
36 done
clear
B)
63 done
clear
C)
48 done
clear
D)
84 done
clear
View Solution play_arrow

At present ages of a father and his son are in the ratio \[7:3,\] and they will be in the ratio \[2:1\] after 10 years. Then the present age of father (in years) is:
A)
42 done
clear
B)
56 done
clear
C)
70 done
clear
D)
77 done
clear
View Solution play_arrow

A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is:
A)
2 done
clear
B)
3 done
clear
C)
5 done
clear
D)
15 done
clear
View Solution play_arrow

x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of \[\text{x}+\text{y}\] is:
A)
10 done
clear
B)
11 done
clear
C)
12 done
clear
D)
13 done
clear
View Solution play_arrow

A man can row a boat in still water at the rate of 6 km per hour. If the stream flows at the rate of 2 km/hour, he takes half the time going downstream than going upstream the same distance. His average speed for upstream and down stream trip is:
A)
6 km/hour done
clear
B)
16/3 km/hour done
clear
C)
Insufficient data to arrive at the answer done
clear
D)
None of the above done
clear
View Solution play_arrow

A boat travels with a speed of \[\text{15 km}/\text{h}\] in still water. In a river flowing at \[\text{5 km}/\text{hr},\]the boat travels some distance downstream and them returns. The ratio of average speed to the speed in still water is:
A)
\[8:3\] done
clear
B)
\[3:8\] done
clear
C)
\[8:9\] done
clear
D)
\[9:8\] done
clear
View Solution play_arrow

A shopkeeper sells a saree at \[8%\] profit and a sweater at \[10%\] discount, thereby, getting a sum of Rs.1008. If she had sold the saree at \[\text{1}0%\] profit and the sweater at \[\text{8}%\]discount, she would have got Rs.1028, then the cost of the saree and the List price (price before discount) of the sweater is:
A)
\[\text{3}00,\text{ 4}00\] done
clear
B)
\[\text{4}00,\text{ 3}00\] done
clear
C)
\[\text{4}00,\text{ 6}00\] done
clear
D)
\[\text{6}00,\text{ 4}00\] done
clear
View Solution play_arrow

A fraction becomes \[\text{4}/\text{5}\] when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each of them, it becomes \[\text{1}/\text{2}\]. Then, numerator of the fraction is:
A)
6 done
clear
B)
7 done
clear
C)
8 done
clear
D)
9 done
clear
View Solution play_arrow

Vijay had some bananas and he divided them into two Lots A and B. He sold the first lot at the rate of Rs.2 for 3 bananas and the second lot at the rate of Rs.1 per banana and got a total of Rs.400. If he had sold the first lot at the rate of Rs.1 per banana and the second lot at the rate of Rs.4 for 5 bananas, his total collection would have been Rs.460. Total number of bananas, he had is:
A)
200 done
clear
B)
300 done
clear
C)
400 done
clear
D)
500 done
clear
View Solution play_arrow

Shashi is decided fixed distance to walk on a tread mill. First day, she walks at a certain speed. Next day, she increases the speed of the tread mill by \[\text{1 km}/\text{h},\]she takes 6 min Less and if she reduces the speed by \[\text{1 km}/\text{h},\]then she takes 9 min more. What is the distance that she has decided to walk everyday?
A)
4 km done
clear
B)
6 km done
clear
C)
5 km done
clear
D)
3 km done
clear
View Solution play_arrow

A vessel contain a mixture of \[\text{24 L}\] milk and \[\text{6 L}\] water and second vessel contains a mixture of \[\text{15 L}\] milk and \[\text{1}0\text{ L}\]water, then how much mixture of milk and water should be taken from the first and the second veseel separately and kept in a third vessel so that the third vessel may contain a mixture of \[\text{25 L}\] milk and \[\text{1}0\text{ L}\] water.
A)
\[\text{15 L}\] and \[\text{15 L}\] done
clear
B)
\[\text{20 L}\] and \[\text{10 L}\] done
clear
C)
\[\text{20 L}\] and \[\text{15 L}\] done
clear
D)
None of these done
clear
View Solution play_arrow

The value of y, when \[\frac{x+y}{xy}=3\]and \[\frac{xy}{xy}=7,\] is:
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{5}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow

Solve the pair of the equations: \[\frac{2}{x}+\frac{3}{y}=13,\] \[\frac{3}{x}+\frac{6}{y}=21\]
A)
\[x=\frac{2}{5},y=1\] done
clear
B)
\[x=\frac{1}{2},y=\frac{1}{3}\] done
clear
C)
\[x=\frac{1}{5},y=1\] done
clear
D)
\[x=\frac{2}{3},y=3\] done
clear
View Solution play_arrow

Solve: \[x+\frac{6}{y}=11,\] \[3x+\frac{8}{y}=28\]
A)
\[x=5,\,\,y=1\] done
clear
B)
\[x=8,\,\,y=2\] done
clear
C)
\[x=4,\,\,y=\frac{1}{2}\] done
clear
D)
\[x=9,\,\,y=3\] done
clear
View Solution play_arrow

If \[{{2}^{x+y}}={{2}^{xy}}=\sqrt{8},\] then the value of x and y are:
A)
\[\frac{3}{2},0\] done
clear
B)
\[0,\frac{3}{2}\] done
clear
C)
\[\frac{2}{3},1\] done
clear
D)
\[1,\frac{2}{3}\] done
clear
View Solution play_arrow

The pair of equations \[{{3}^{x+y}}=81,\] \[{{81}^{xy}}=3\] has:
A)
no solution done
clear
B)
unique solution done
clear
C)
infinitely many solutions done
clear
D)
\[x=2\frac{1}{8},\,\,y=1\frac{7}{8}\] done
clear
View Solution play_arrow

A and B together can do a piece of work in 12 days, B and C together in 15 days. If A is twice as good a workman as C, then in how many days will B alone do it?
A)
10 days done
clear
B)
15 days done
clear
C)
20 days done
clear
D)
25 days done
clear
View Solution play_arrow

When a man travels equal distance at speed \[\text{x km}/\text{h}\] and \[\text{y km}/\text{h},\]his average speed is\[\text{4 km}/\text{h}\]. But when he travels at these speed for equal time, his average speed is\[\text{4}.\text{5 km}/\text{h}\]. The difference of the two speed is:
A)
\[\text{2 km}/\text{h}\] done
clear
B)
\[\text{4 km}/\text{h}\] done
clear
C)
\[\text{3 km}/\text{h}\] done
clear
D)
\[\text{5 km}/\text{h}\] done
clear
View Solution play_arrow