Mathematics - Linear Equations in Two Variables
Exam Duration: 45 Mins Total Questions : 30
How many line(s) pass through the point (0,0)?
- (a)
Only one
- (b)
Two
- (c)
Infinitely many
- (d)
Three
If x = -2 and y = 3 is the solution of the equation 3x -5y = k, find 'k'.
- (a)
-21
- (b)
-9
- (c)
-18
- (d)
19
What does an equation of the form ax + by + C = 0, where a and b are nonzero numbers represent?
- (a)
A straight line
- (b)
A circle
- (c)
A triangle
- (d)
A quadrilateral
What is the equation of X-axis?
- (a)
x = 0
- (b)
x = -2
- (c)
Y = 0
- (d)
y = -2
Which of the following is correct with respect to the line x + 1 = 0?
- (a)
It is parallel to y-axis.
- (b)
It passes through (0, -1).
- (c)
It is parallel to x-axis.
- (d)
It passes through (0,0).
The cost of a shirt of a particular brand is Rs 800. What is the linear equation when the cost of x number of shirts is Rs y?
- (a)
x = 800y
- (b)
x = 800 + y
- (c)
y = 800x
- (d)
y = 800 + x
What are all the roots for the equation 3|w-14|-6=21?
- (a)
19
- (b)
23
- (c)
5 and 23
- (d)
9 and 19
What is the solution of the equation given in the box?
\(\frac{3y+4}{2}+\frac{2y-5}{3}=\frac{31}{2}\)
- (a)
y = 1
- (b)
y = 6
- (c)
y = 7
- (d)
y = 13
Which of the following equations represents a straight line passing through the points (1,6), (0,4) and (-2,0)?
- (a)
2x - y = - 4
- (b)
x - 2y = - 4
- (c)
2x + y = 4
- (d)
x + 2y = - 4
Identify the equation of line parallel to y-axis and 5-units away from the origin.
- (a)
y = 5
- (b)
x = -5
- (c)
x = 5
- (d)
y = -5
Which of the following is true?
- (a)
The equation of the x-axis is y = 0.
- (b)
The graph of every linear equation in two variable is a curve.
- (c)
y = 3x + 5 has a unique solution.
- (d)
The graph of the equation 2y - 5 = 0 is parallel to y-axis.
If the expressions y - 10 and 24 - yare equal, what is the value of y?
- (a)
34
- (b)
14
- (c)
17
- (d)
12
How many kilograms of tea at Rs 50 per kg should be mixed with 35 kg of tea costingRs 60 per kg so as to sell the mixture at Rs 57 per kg without gaining or losing anything in the transaction?
- (a)
5 kg
- (b)
7 kg
- (c)
25 kg
- (d)
15 kg
A man is five times as old as his son. After 2 years the man will be four times as old as his son. What is the present age of the man?
- (a)
35 years
- (b)
30 years
- (c)
6 years
- (d)
31 years
Megacity High School earned Rs 5100 on tickets sales for a play. The cost per ticket was Rs 12. If t represents the number of tickets sold to the play, which of the following equations could be used to determine the number of tickets sold for the play?
- (a)
12 = 5100t
- (b)
12t = 5100
- (c)
t=5100-12
- (d)
t=5100.12
The function f(x) = 35 + 15x represents the amount of money, in Rupees, Mr. Ramesh earns for working X hours. How much money does Mr. Ramesh earn for working 25 hours?
- (a)
Rs 75
- (b)
Rs 375
- (c)
Rs 410
- (d)
Rs 1250
Two planes start from a city and fly in opposite directions, one averaging a speed of 40 km/hour greater than the second. If they are 3400 km apart from 5 hours, find the sum of their average speeds.
- (a)
680 km/h
- (b)
360 km/h
- (c)
320 km/h
- (d)
640 km/h
Which equation represents the relationship between time, t1 and distance, d?
Time (hours) | Distance (km) |
2 | 90 |
3 | 135 |
4 | 180 |
5 | 225 |
- (a)
d = t + 45
- (b)
d = 45t
- (c)
t = 45d
- (d)
\(t=\frac{45}{d}\)
Straight lines represented by linear equations x + y = 2 and 5x - 3y = 2 intersect at which of the given points?
- (a)
(1, 2)
- (b)
(1, 1)
- (c)
(2, 1)
- (d)
(3, 2)
The course of an enemy submarine as plotted on a set of rectangular axes is 2x + 3y = 5. On the same axes the course of the destroyer is indicated by x - y = 10. What is the point (x, y) at which the submarine can be destroyed?
- (a)
(-7, 3)
- (b)
(-3, 7)
- (c)
(3,-7)
- (d)
(7,-3)
The breadth of a rectangular room is 2 m less than its length(l).lf the perimeter of the room is 14 m, find the length(l) and breadth(b) of the room.
- (a)
l= 2.5 m, b = 4.5 m
- (b)
l= 3.5 m, b = 3.5 m
- (c)
l= 4.5 m, b = 2.5 m
- (d)
l= 2.5 m, b = 5.5 m
The total value of a collection of coins of denominations Rs 1.00,50 paise, 25 paise, 10 paise and 5 paise, is Rs 380. If the number of coins of each denomination is the same, find the number of one-rupee coins.
- (a)
160
- (b)
180
- (c)
200
- (d)
220
The graph of y = 6 is a line
- (a)
Parallel to x-axis at a distance of 6 units from the origin.
- (b)
Parallel to y-axis at a distance of 6 units from the origin.
- (c)
Making an intercept of 6 units on the x-axis.
- (d)
Making an intercept of 6 units on both the axes.
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point
- (a)
(0, 2)
- (b)
(2, 0)
- (c)
(3, 0)
- (d)
(0, 3)
A straight line parallel to the y-axis has equation _________.
- (a)
x = a
- (b)
Y = a
- (c)
y = x
- (d)
y =-x
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is________.
- (a)
4
- (b)
6
- (c)
5
- (d)
2
Point (4, 1) lies on the line________
- (a)
x + 2y = 5
- (b)
2x + Y = - 6
- (c)
x+2y=6
- (d)
x+y=16
A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 respectively.
- (a)
50years, 25years, 20years
- (b)
40 years, 20 years, 15 years
- (c)
20 years, 15 years, 10 years
- (d)
25 years, 20 years, 10 years
The equations representing the given graph is______.
- (a)
7x + 2y = 11; Y - 2x = 3
- (b)
2x + 7y = 11; 5x + (35y/2) = 25
- (c)
3x-7y=10;8y-6x=4
- (d)
3x-4y=1;8y-6x=4
Match the linear equations in column-I with their solutions in column-II.
Column-I | Column-II |
(P) 4x + 3y = 24 | (i) (2, -3) |
(Q)\(\frac{X}{2}-\frac{Y}{3}\)=2 | (ii) (2, 3) |
(R) 3x + 5y = 15 | (iii)(3, 4) |
(S)\(\frac{X-2}{3}\)=y-3 | (iv)\(\left( \frac { 9 }{ 8 } ,\frac { 6 }{ 5 } \right) \) |
- (a)
(P) \(\rightarrow\) (ii), (Q) \(\rightarrow\) (i), (R) \(\rightarrow\) (iv), (S) \(\rightarrow\)(iii)
- (b)
(P) \(\rightarrow\) (iii), (Q) \(\rightarrow\) (i), (R) \(\rightarrow\) (iv), (S) \(\rightarrow\) (ii)
- (c)
(P) \(\rightarrow\) (ii), (Q) \(\rightarrow\) (iv), (R) \(\rightarrow\) (i), (S) \(\rightarrow\) (iii)
- (d)
(P) \(\rightarrow\) (iii), (Q) \(\rightarrow\) (iv), (R) \(\rightarrow\) (i), (S) \(\rightarrow\) (ii)