Q1. A
lending library has a fixed charge for the first two days and an additional
charge for each day thereafter. Sunil paid Rs. 28 for a book kept for five
days, while Sohail paid Rs. 32 for the book he kept for seven days. Find the
charge for each extra day.
Rs. 18
Rs. 2
Rs. 20
Rs. 3
Q2. The
larger of two supplementary angles exceeds the smaller by 22 degrees. What is
the smaller angle?
79o
69o
89o
49o
z3. Which of the
following equations has x = 3, y = - 4 as solution?
3x
- 4y = 21
x
+ y = -100
-x
+ y = 100
3x
- y = 13
Q4. The
sum of two numbers is 45 and one is twice the other. What is the smaller
number?
30
15
25
35
Q5. The
value of x in the system x - 3y = 7; 3x - 3y = 15 is:
x
= 4
x
= -4
x
= 11
x
= - 11
Q6.
Anita has only 20 paise and 25 paise coins in her purse. She has 50 coins in
all total to Rs. 11.25. The linear equation representing the situations is
20x
+ 25y = 11.25; 20x + 25y = 50
20x
+ 25y = 50; x + y = 11.25
25x
+ 20y = 11.25; 25x + 20y = 50
20x
+ 25y = 1125; x + y = 50
Q7. How
many solutions do the given equations have? 2x + 3y = 8, 4x + 6y = 7
2
1
0
3
Q8. The
value of x, y in the following 2x + 2 - 3y + 1 = 5 ………(1) 2x + 3y = 17 ………(2)
2,
3
-2,3
3,2
2,
-3
Q9. What
kind of solution does the equation of a pair of parallel lines have?
Unique
Infinite
No
solution
Two
possible solution
Q10. If
the given system of equation is 3x + 2y = 2xy; 6x + 2y = 3xy, then the first
step to solve such eqs is
To
equate the coefficients of x
To
equate the coefficients of y
To
divide the complete equation by xy.
Add
or subtract the two equations.
Q11.
Solve x + y = 10 ;x - y = 2, by the method of substitution.
x = 6 , y = 4
x = 4 , y = 6
x = -6 , y = 4
x = 6 , y = -4
Q12.
Find the solution to the following system of linear equations: 0.2x + 0.3y =
1.2 0.1x - 0.1y = 0.1
(1,2)
(2,1)
(3,2)
(2,3)
Q13. The
pair of linear equations 3x + 2y = 5 and 2x - 3y = 7 will have
unique
solution
no
solution
infinite
solution
none
of the above
Q14. The
pair of linear equations x + y + 10 = 0 and x + y - 7 = 0 has:
One
solution
Two solutions
Infinitely
many solutions
No
solutions
Q15. The
number of solutions of the pair of linear equations x + 2y - 8 = 0 and 2x + 4y
= 16 are:
0
1
Infinitely
many
None
Q16. A
system of simultaneous linear equations has infinitely many solutions if two
lines:
intersect
at one point
are
parallel
are
coincident
intersect
at two points
Q17. 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
17
18
81
Q18.
Pair of linear equations x+2y+5 =0 and 3x+6y -1 =0 have
unique
solution
exactly
two solutions
infinitely
many solutions
no
solution
Q19. 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
Q20.
Find the solution to the following system of linear equations: 2p+3q=9 p
- q = 2
(-4,1)
(2,-3)
(3,1)
(4,2)
Q21.
What is the solution of the following system of linear equations? 2x+3y=12
x-y=1
(3,2)
(3,-2)
(2,-3)
(-3,2)
Q22.
Find the solution to the following system of linear equations: 3x-y+9=0
3x+4y-6=0
(1,3)
(2,-3)
(-2,3)
(-2,-3)
Q23.
Find the point on the Cartesian plane where the line 3x - 2y = 6 intersects the
y - axis.
(3,
2)
(0,
-3)
(1,
2)
(-1,
-2)
Q24. The
pair of equations y = 0 and y = -7 has :
one
solution
two
solutions
infinitely
many solutions
no
solution
Q25.
Which of the following coordinates lies on the line 2x - 3y = 12?
(1,
2)
(1,
3)
(3,
-2)
(3,
2)
Q26. If
x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then the
values of a and b are, respectively.
3
and 5
5
and 3
3
and 1
-1
and -3
Q27. At
a closing down sale, a book store was selling 3 books and 5 notebooks for Rs.
309 or 6 books and 2 notebooks for Rs. 282. How much would one book and 1
notebook cost?
Rs. 33
Rs. 42
Rs. 75
Rs. 57
Q28.
Find the solution to the following system of linear equations: x-2y=6 2x+y=17
(1,2)
(10,2)
(12,3)
(8,1)
Q29. If
two lines are parallel to each other the system of equation is
consistent
Inconsistent
Consistent
dependent
Inconsistent
dependent
Q30.
Which of the following is not a solution of the pair of equations 3x - 2y = 4
and 6x - 4y = 8?
x
= 2, y = 1
x
= 4, y = 4
x
= 6, y = 7
x
= 5, y = 3
Q31. The
following pair of linear equations 3x - 2y + 5 = 0, 5x + 7y = 2 will have
infinite
solution
no
solution
a
unique solution
none
of the above
Q32. How
many solutions of the equation 15x - 14y + 11 = 0 are possible?
1
Infinite
2
No
solution
Q33.
Five liters of 31.2% acid solution has to be made out of a 40% and a 18% acid
solution. How many litres of each of the 40% and 18% solution need to be mixed?
2 and 3
4 and 5
3 and 2
5 and 4
Q34.
Which of following is not a solution of 3a + b = 12?
(4,
0)
(5,
-3)
(3,
3)
(2,
4)
Q35.
Find a and b for which (a-1)x + 3y = 2, 6x + (1-2b)y = 6 has an infinite
solution.
a
= 3, b = -4
a
= 3, b = -1
a
= -7, b= -4
a
= -1, b = -4
Q36. The
pair of linear equations 8x - 5y = 7 and 5x - 8y = -7 have :
One
solution
Two
solutions
No
solution
Many
solutions
Q37. The
present age of a father is the sum of the ages of his three sons. Ten years
from now his age will be a three quarter of the sum of their ages then. How old
is the father?
30
years
40
years
50
years
60
years
Q38.
Find the point on the Cartesian plane where the line 5x - y = 10 intersects the
x - axis.
x
= 0, y = 0
x
= 2, y = 0
x
= 0, y = 2
x
= 2, y = 5
Q39. One
equation of a pair of dependent linear equations is -5x + 7y = 2, the second
equation can be :
10x
+ 14y + 4 =0
-10x
- 14x + 4 = 0
-10x
+ 14y + 4 = 0
10x
- 14y = -4
Q40.
What would be the graphical representation of the pair of linear equations 3x -
5y = -9 and 6x - 10y = -8?
intersecting
lines
coincident
lines
parallel
lines
none
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