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Published on: 26/10/2025
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1.
The value of k for which the system of equstions kx + 2y = 5 and 3x + 4y = 1 have no solution is
\(k=\frac{3}{2}\)
\(k \neq \frac{3}{2}\)
\(k \neq \frac{2}{3}\)
k = 15
2.
The pair of linear equations x + 2y + 5 = 0 and -3x = 6y - 1 has
unique solution
exactly two solutions
infinitely many solutions
no solution
3.
If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is
\(-\frac{5}{4}\)
\(\frac{2}{5}\)
\(\frac{15}{4}\)
\(\frac{3}{2}\)
4.
The pair of equations y = 0 and y = - 7 has
one solution
two solutions
infinitelymany solutions
no solution
5.
Which of the following pair of equations are inconsistent?
3x - y = 9, x - \(\frac{y}{3}\)=3
4x.+ 3y = 24, - 2x+ 3y = 6
5x - y = 10,10x-2y = 20
2x+ y=3,-4x+2y=10
6.
A fraction becomes 4/5 when 1 is added to each of the numerator and denominator. However, if..we subtract 5 from each of them, it becomes 1/2. Then, numerator of the fraction is
6
7
8
9
7.
If a pair of linear equations is consistent, then the lines will be
parallel
always coincident
intersecting or coinciden
always intersecting
8.
The pair of equations x + 2y + 5 = 0 and - 3x - 6y + 1= 0 has
a unique solution
exactlytwo solutions
infinitely many solutions
no solution
9.
A and B together can do a piece of work in 12 days, Band 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?
10 days,
15 days,
20 days,
25 days,
10.
The values of x and y which satisfy the equations: 47x + 31y = 63 and 31x + 47y=15 are ____________
2 and -1
-2 and 1
-2 and -1
2 and 1
11.
The sum of the digits of a two-digit number is 9. Also, twice this number is nine times the number obtained by reversing the order of the digits. Find the number
71
81
17
18
12.
Find the point on Cartesian plane where the line 3x – 2y = 6 intersects the y axis
(3, 2)
(-1, -2)
(0, -3)
(1, 2)
13.
The pair of equations y = 0 and y = -7 has :
one solution
infinitely many solutions
no solution
two solutions
14.
2 apples & 3 bananas cost Rs.15 and 2 apples & 2 bananas cost Rs 12. What is the cost of an apple & a banana?
An apple is for Rs.6 and banana for Rs.1
An apple for Rs.3 & a banana for Rs.3.
An apple for Rs.4 & a banana for Rs.2.50
An apple for Rs.2 & a banana for Rs.2
15.
A boat goes 35 km upstream and 42 km downstream in 11 hours. In 14 hours, it can go 43 km upstream and 59 km down-stream. To determine the speed of the stream and that of the boat in still water , express the information in the form of equations of the type ax + by + c = 0
35u + 42v -14 = 0, 43u + 59v-11=0
35u + 42v -14 = 0, 43x + 59y-11=0
35u + 42v -14 = 0, 43u + 59v-14=0
35x + 42y -14 = 0, 43x + 59y-14=0
16.
The difference between two numbers is 45 and one number is six times the other. Find them
7,42
8,48
6,36
9,54
17.
Adding 1 to the numerator and subtracting 1 from the denominator of a fraction makes it 1. However, if 1 is added only to the denominator of the fraction it becomes ½ . The fraction is______
2/3
3/5
5/3
3/2
18.
What is the solution of the equations \(\sqrt { 2 } x-\sqrt { 3 } y\ =\ 0\ and\ \sqrt { 5 } x+\sqrt { 2 } y=0\)
0, 2
2, 0
0, 0
None
19.
The values of x and y that satisfy the pair of equations:
\(\frac { 5 }{ x-1 } +\frac { 1 }{ y-2 } =2;\frac { 6 }{ x-1 } -\frac { 3 }{ y-2 } =1\)
4 and 5
1/3, 1/5
5 and 4
1/5, 1/3
20.
The value of x in the system x – 3y = 7; 3x – 3y = 15 is
x = – 11
x = – 4
x = 11
x = 4
21.
The pair of linear equations 8x – 5y = 7 and 5x – 8y = -7 have
One solution
Two solutions
Many solutions
No solution
22.
The following pairs of linear equations 2x + 5y = 3 and 6x + 15y = 12 represent
Intersecting
Parallel lines
Coincident lines
None from a, b, c
23.
Find the solution to the following system of linear equations:
2p+3q=9
p-q=2
(4,2)
(-4,1)
(2,-3)
(3,1)
24.
How many solutions of the equation 15x – 14y + 11 = 0 are possible?
2
No solution
Infinite
1
25.
Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?
a ≠ 2
a = -2
a = 2
a ≠ -2
26.
Find the value of ‘a” for which the system of equations 3x + 2y – 4 = 0 and ax – y – 3 = 0, will represent intersecting lines
a = 3/2
a ≠ 2/3
a = 2/3
a ≠ 3/2
27.
The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 are
Infinitely many
1
0
None
28.
If two lines are parallel to each other the system of equation is
Consistent dependent
Inconsistent
Inconsistent dependent
consistent
29.
Find the solution to the following system of linear equations
0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1
(2,1)
(2,3)
(1,2)
(3,2)
30.
If the pair of equation has no solution, then the pair of equation is
inconsistent
none of these
coincident
consistent
31.
Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?
6km/hr
4km/hr
3km/hr
7km/hr
32.
If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and b
2,1
3,1
4,6
1,2
33.
Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.
20
50
60
40
34.
A fraction becomes when subtracted from the numerator and it becomes . when 8 is added to its denominator. Find the fraction
4/12
3/13
5/12
11/7
35.
8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.
120, 130
140,280
240,280
100,120
1.
(a)
\(k=\frac{3}{2}\)
2.
(d)
no solution
3.
(c)
\(\frac{15}{4}\)
4.
(d)
no solution
5.
(d)
2x+ y=3,-4x+2y=10
6.
(b)
7
7.
(c)
intersecting or coinciden
8.
(d)
no solution
9.
(c)
20 days,
10.
(a)
2 and -1
11.
(b)
81
12.
(c)
(0, -3)
13.
(c)
no solution
14.
15.
(c)
35u + 42v -14 = 0, 43u + 59v-14=0
16.
(d)
9,54
17.
(b)
3/5
18.
(c)
0, 0
19.
(a)
4 and 5
20.
(d)
x = 4
21.
(a)
One solution
22.
(b)
Parallel lines
23.
(d)
(3,1)
24.
(c)
Infinite
25.
26.
(d)
a ≠ 3/2
27.
(a)
Infinitely many
28.
(b)
Inconsistent
29.
(d)
(3,2)
30.
(a)
inconsistent
31.
(a)
6km/hr
32.
(b)
3,1
33.
(b)
50
34.
(c)
5/12
35.
(b)
140,280
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