LINEAR EQUATION IN TWO VARIABLES w - Ingenious Infinity

1 ✆ +91- 9971750366, 8447026670 :[email protected] : www.ingeniousinfinity.com

LINEAR EQUATION IN TWO VARIABLES MCQ

1. Which of the following is not a linear equation in two variable : (a) ax + by = c (b) ax2 + bx = c (c) 2x + 3y = 5 (d) 3x + 2y = 6

2. The graph of ax + by + c = 0 is :

(a) a straight line parallel to x-axis (b) a straight line parallel to y-axis

(c) a general straight line (d) a line in 2nd and 3rd quadrant

3. The solution of linear equation in two variable is :

(a) a number which satisfies the given equation

(b) an order pair which satisfies the given equation

(c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it

(d) None of these. 4. One of the solutions of linear equation 3x – 4y + 6 = 0 is:

(a) (3, 2) (b) (3, -2) (c) (2, 3) (d) (-2, -3)

5. The ordered pair (m, n) satisfies the equation ax + by + c = 0 if

(a) c = 0 (b) an + bm = 0 (c) am + bn + c = 0 (d) am + bn – c = 0

6. The equation of x-axis is :

(a) a = 0 (b) y = 0 (c) x = 0 (d) y = k

7. From the graph of a line we can find the coordinate of :

(a) Only one point lying on the line

(b) Only two point lying on the line

(c) Only finite number of point lying on the line

(d) Infinite number of point lying on the line

8. A linear equation in two variable has:

(a) No solution (b) Only one solution

(c) only two solutions (d) Infinite many solutions


9. An equation of the form ax + by + c =0 represent the linear equation in two variables if:

(a) a = 0, b ¹ 0 (b) a ¹ 0, b = 0 (c) a = 0, b = 0 (d) a ¹ 0, b ¹ 0

10. The graph of linear equation in two variables y = mx is:

(a) a line parallel to x-axis (b) a line parallel to y-axis

(c) a line passing through the origin (d) Not a straight line

11. If is written in standard form , then values of are

(a) (b)

(c) (d)

12. The equation is written in two variables as

(a) (b) (c) (d)

13. If x years, represents the present age of the father and y years represents the present age of the son, then the statement “present age of the father is 5 more than 6 times age of the son” in mathematical term equation is:

(a) (b)

(c) (d)

14. The equation has

(a) No solution (b) unique solution (c) infinitely many solutions (d) exactly two solutions

15. If , is a solution of the equation then the value of k is:

(a) – 1 (b) 2 (c) 1 (d) 3

16. The graph of linear equation is:

(a) parallel to x-axis (b) lie along x-axis

(c) parallel to y-axis (d) passes through origin

17. The linear equation , represented as has:

(a) a unique solution (b) infinitely many sol.

(c) two solutions (d) no solution

4 3x y- = 0ax by c+ + = , ,a b c

1, 4, 3a b c= = - = 1, 3, 4a b c= = = -

3, 1, 4a b c= = - = 1, 3, 4a b c= = - = -

5 2x =

5 2x y+ = 5 2xy = 5 2x y= 5 0 2 0x y+ - =

6 5x y+ + 30x y= +

6 5x y+ = 6 5x y- =

4 7y x= -

2x = 1y = 2 3x k y+ =

4 5x =

3 5 0y - = 0ax by c+ + =


18. The equation has a unique solution, if x and y are:

(a) natural no (b) positive real numbers

(c) real numbers (d) rational numbers

19. If point lies on the graph of the equation , the value of k is:

(a) 6 (b) 3 (c) 2 (d) 5

20. Any solution of the linear equation in two variables, is of the form

(a) (b) , n is a real number

(c) , n is a real number (d)

21. The graph of linear equation cut the x-axis at the point

(a) (b) (c) (d)

22. The equation in two variables can be written as

(a) (b)

(c) (d)

23. Any point on the line , is of the form

(a) (b) (c) (d)

24. The equation of x-axis is

(a) (b)

(c) (d)

25. The graph of the equation is a line

(a) parallel to x-axis, at a distance of 3 units from origin and below x-axis

(b) parallel to x-axis, at a distance of 3 units from the origin

(c) parallel to y-axis, at a distance of 3 units from origin to the left side of y-axis

(d) cuts intercept of 6 units on both axes

2 5 7x y+ =

( )3,0 2 3x y k+ =

2 0 9x y+ =

9 ,02æ öç ÷è ø

9 ,2næ ö

ç ÷è ø

9,2

næ öç ÷è ø

90,2

æ öç ÷è ø

3 5 15x y+ =

( )5,0 ( )3,0 ( )0,5 ( )0,3

5x =

1. 1. 5x y+ = 0. 1. 5x y+ =

0. 0. 5x y+ = 1. 0. 5x y+ =

y x=

( ),0m ( )0,m ( ),m m- ( ),m m

0x y+ = 0x y- =

0y = 0x =

3y = -


26. , is a solution of the linear equation

(a) (b)

(c) (d)

27. If linear equation has solutions , , then equation is

(a) (b)

(c) (d)

28. For one of the solutions of the equation , x is negative and y is positive then

surely a portion of the line lies in the

(a) first quadrant (b) second quadrant

(c) third quadrant (d) fourth quadrant

29. The graph of the linear equation passes through the point

(a) (b) (c) (d)

(2, 3, 4 Marks Questions)

1. The taxi fare in a city is as follows: Rs.15 for first km and Rs.8 for next subsequent km. Taking the total distance covered as x and total fare as y, write the above as linear equation.

2. If (4, 2) is a solution of the equation 4x + 3y – k = 0 find the value of k. 3. Find the coordinates of the points where the graph of the equation 3x + 4y = 24 intercept x – axis

and y- axis. 4. Draw the graph of the line 2x + 3y = 6 on the graph paper write the sum of the intercepts cut by

this line on two axis. 5. Do the point (1, 2), (-1, -16) and (0, - 7) lie on the linear equation y = 9x – 7. If no give reason for

the same. 6. The graphs of the equations 2x – y = 6 and 4x + y = 24 intersect x-axis at A and B. Find the

relationship between OA and OB where O is the origin. 7. By means of graph verify that the point (1, -1) is the solution of the equations 3x + 2y – 1 = 0 ,

2x + y – 1 = 0. 8. Draw the graph of the equation 2x – 3y = 5. From the graph, find (i) the value of y when x = 4, (ii)

the value of x when y = 3. 9. Draw the graph of the equation 2x + y = 6. Find the coordinates of the point where the graph cuts

the x-axis. 10. Draw the graph of the equation 3x + 2y = 6. Find the coordinates of the point where the graph

cuts the y-axis. 11. A part of monthly expenses of a family on milk is fixed which is Rs.500 and the remaining varies

with the quality of the milk taken extra of the rate Rs.20 per kg. Taking the quantity of the milk

5x = 2y = -

2 9x y+ = 2 12x y- =

3 1x y+ = 3 0x y+ =

( )5,5- ( )0,0 ( )5, 5-

0x y- = 0x y+ =

2 0x y- = 2 0x y+ =

0ax by c+ + =

2y x=

( )2,1 ( )2, 1- 3 , 32æ ö-ç ÷è ø

3 ,32æ öç ÷è ø


required extra as x kg and the total expenditure on milk Rs.y. Write a linear equation for this information and draw the graph.

12. When five times the larger of the two numbers is divided by the smaller, the quotient and remainder are 2 and 9 respectively. Form a linear equation in two variables for above and gives its two solutions.

13. “Two years later a father will be 8 years more than three times the age of the son” taking the present age of the father and son as x and y respectively. Write a linear equation for the above and draw its graph. From the graph find the age of the father when son’s age is 10 years.

14. Determine the point on the graph of the linear equation , whose ordinate is

times its abscissa. 15. Solve the equation, and represent the solution (a) number line (b) on the

Cartesian plane. 16. The following observed values of x and y are thought to fulfill the law . Find the values

of a and b x 1 2 -3 0 5

y 12 19 16 5 40

17. Find m if point lies on the equation .

18. Find coordinates of the points where the line represented by the linear equation intersect x-axis and y-axis.

19. Ram is half of his father’s age. Twenty years ago the age of father was six times age of Ram. Find age of Ram and his father.

20. Draw straight lines and on same graph paper. Find the point of intersection of these lines.

21. Water is following into a water tank at the rate of 20 . If the volume of water collected in x second is y then write a linear equation and (a) Draw the graph of linear equation (b) Find the volume of water after 5 seconds.

22. Draw the lines , and on the same graph paper and then identify what type of figure obtained? Also write the point of vertices of this figure formed.

ANSWERS

MCQ

1. (b) 2. (c) 3. (c) 4. (c) 5. (c) 6. (b)

7. (d) 8. (d) 9. (d) 10. (c) 11. (d) 12. (d)

13. (d) 14. (c) 15. (a) 16. (c) 17. (b) 18. (a)

19. (a) 20. (b) 21. (a) 22. (d) 23. (d) 24. (c)

25. (a) 26. (b) 27. (b) 28. (b) 29. (d)

2 5 19x y+ =112

5 2 3 8x x- = -

y ax b= +

( )7, 3- 3 27 7

y m xæ ö æ ö- = -ç ÷ ç ÷è ø è ø

2 4y x= -

2 3x y- = 3 2 1x y+ =

3 / seccm3cm

4x = 2y = x y=


2,3,4 marks Questions

1. y = 8x + 7 2. k = 22 3. (8, 0), (0, 6) 4. 5

6. OA = OB 8. (i) y = 1, (ii) x = 7 9. (3, 0) 10. (0, 3).

By Arun Kumar Shukla

LINEAR EQUATION IN TWO VARIABLES w - Ingenious Infinity

Documents

Transcript of LINEAR EQUATION IN TWO VARIABLES w - Ingenious Infinity