MULTIPLE CHOICE QUESTIONS ( MCQ’s )
1. Graphically, the pair of equations 6 x – 3 y + 10 = 0 and
2 x – y + 9 = 0 represents two lines which are____
(a) Intersecting at exactly one point.
(b) Intersecting at exactly two points.
(c) Coincident.
(d) Parallel
2. The pair of equations x + 2 y –5 = 0 and −3 x – 6 y +15 = 0 have____
( a) A unique solution
( b) Exactly two solutions
( c) Infinitely many solutions
( d) No solution
3. If a pair of linear equations is consistent, then the lines will be ____
(a) Parallel
(b) Always coincident
(c) Intersecting or coincident
(d) Always intersecting
4. The pair of equations y = 0 and y = – 7 has_____
(a) One solution
(b) Two solutions
(c) Infinitely many solutions
(d) No solution
5. If the lines given by 3 x + 2 k y = 2 and 2 x + 5 y + 1 = 0 are parallel,
then the value of k is_____
(a) 5 / 4
(b) 2 / 5
(c) 15 / 4
(d) 3 / 2
6. The value of c for which the pair of equations c x – y = 2 and 6x– 2 y = 3
will have infinitely many solutions is______
(a) 3
(b) – 3
(c) – 12
(d) No value
7. One equation of a pair of dependent linear equations is – 5 x + 7 y – 2 = 0.
The second equation can be_____
(a) 10 x + 14 y + 4 = 0
(b) – 10 x – 14 y + 4 = 0
(c) – 10 x + 14 y + 4 = 0
(d) 10 x – 14 y = – 4
8. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers,
the ratio becomes 4 : 5. Then the numbers are______
(a) 40, 42
(b) 42, 48
(c) 40, 48
(d) 44, 50
9.The solution of the equations x – y = 2 and x + y = 4 is______
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) – 1 and – 3
10. For which values of a and b, will the following pair of linear equations have infinitely many solutions. x + 2 y = 1 and ( a – b ) x + ( a + b ) y = a + b – 2
(a) a = 2 and b = 1
(b) a = 2 and b = 2
(c) a = ̶ 3 and b = 1
(d) a = 3 and b = 1
11. Find the value of ‘k’ so that the graph will be parallel 2x − ky = 7 , 3x – 7y = 10.
(a) 11/3
(b) 14/3
(c) 10/3
(d) −14/3
12. What is the point of intersecting of the line 3x + 7y = 10 and the y axis
(a) 0 , 10/7
(b) 0, 7/10
(c) 10/7 , 0
(d) 7/10, 0
13. A fraction becomes \frac { 3 }{ 8 } if 2 is added to both numerator (x) and denominator (y) the equation will look like ____ .
(a) \frac { x + 2 }{ y+2 } =\frac { 8 }{ 3 }
(b)\frac { x−2 }{ y−2 } =\frac { 8 }{ 3 }
(c)\frac { x−2 }{ y−2 } =\frac { 3 }{ 8 }
(d)\frac { x−2 }{ y−2 } =\frac { 3 }{ 8 }
14. The sum of two numbers is 12. Find the equation if the sum of their reciprocals is \frac { 3 }{ 17 } .
(a) x − y = 12, \frac { 1 }{ x } +\frac { 1 }{ y } =\frac { 3 }{ 17 }
(b) x + y = 12 \frac { 1 }{ x } +\frac { 1 }{ y } =\frac { 3 }{ 17 }
(c) x + y = 17, \frac { 1 }{ x } +\frac { 1 }{ y } =\frac { 3 }{ 12 }
(d) x + y = 3 \frac { 1 }{ x } +\frac { 1 }{ y } =\frac { 12 }{ 17 }
15. x+\frac { 7 }{ y } can also be written as ____ .
(a) xy − 7 = 5y
(b) xy + 7 = 5y
(c) xy − 7 = −7
(d) xy + 5y = 7
16. A pair of linear equations in two variables can be represented and solved by two methods they are :
(a) Mathematical , geometrical
(b) Mathematical , algebraic
(c) Graphical , algebraic
(d) Mathematical , graphical
17. If a1/a2 ≠ b1/b2 then pair of linear equation is ____
(a) Dependent
(b) Inconsistent
(c) Parallel
(d) Consistent
18. The ages of A and B are 10 and 5 respectively now, after 5 years the sum of their ages will be _________ .
(a) 35
(b) 25
(c) 30
(d) 20
19. 2u2 + 8u = 0 ∴ u = ___
(a) 0 , −4
(b) 0 , 4
(c) 0 , −2
(d) 0 , 2
20.If 3x + 2y = 10 and 2x + 3y = 5 then x = _____
(a) 2
(b) 12
(c) 5
(d) 10
21.Linear equations can be represented algebraically as a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 where a1, a2, b1, b2, c1, c2 are ______
(a) Equations
(b) Factors
(c) Real numbers
(d) Whole numbers
22. A pair of linear equations in two variables can be solved by two methods . they are ______
(a) Real ,consistent
(b) Graphical, algebraic
(c) Unique ,real
(d) Graphical, real.
23. If the pair of the lines in a graph are coincident then it has _____ solutions .
(a) Infinite
(b) No
(c) Limited
(d) Only one
24. A pair of linear equation will be ———— if a1/a2 ≠ b1/b2
(a) Curved
(b) Parallel
(c) Coincident.
(d) Intersecting
25. A pair of linear equation is said to be ————– if it has at least one solution.
(a) Parallel
(b) Coincident
(c) Interesting
(d) Consistent
26. If the linear equation x + y = 10 and x−y = 6 the value of (x + y)2= ___
(a) 64
(b) 100
(c) 36
(d) 49
27. 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 of the son and the father, in years, are respectively
(a) 4 and 24
(b) 5 and 30
(c) 6 and 36
(d) 3 and 24
28. The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are
(a) 45°, 75°
(b) 50°, 80°
(c) 55°, 85°
(d) 55°, 95°
29. Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Rs 1 and Rs 2 coins are respectively
(a) 35 and 15
(b) 35 and 20
(c) 15 and 35
(d) 25 and 25
30. For what value of k the graph 2x − ky = 9 and 6x − 9y = 18 will be parallel
(a) 3
(b) 5
(c) 4
(d) 7
31. If 4x + y = 7 and x + 4y + −2 .Then x −y + ____
(a) 3
(b) 5
(c) 4
(d) 7
32. The solution of the equation 2x + 3y = 2 and x + y = 2 is ___
(a) x = 4 ,y = −8
(b) x = 6 ,y = −2
(c) x = 4 ,y = −2
(d) x = 5 , y = −2
33. The angles of a triangle are x, 105° and 40°. Then x + ___
(a) 35°
(b) 55°
(c) 45°
(d) 70°
34. If 2x2 +7x2 = 900. Then x = ____
(a) 35
(b) 50
(c) 10
(d) 30
35.The ages of M and N are 14 and 15 respectively now, after 3 years the sum of their ages will be ______years .
(a) 35
(b) 50
(c) 10
(d) 30
Answers. + Clues.
1: (d) ⇒ Refer table (3.4) text book
2: (c) ⇒ Refer table (3.4) text book
3: (c) ⇒ Refer table (3.4) text book
4: (d) ⇒Refer table (3.4) text book
5: (c) ⇒ If parallel then \frac { a1 }{ a2 } =\frac { b1 }{ b2 } +\frac { c1 }{ c2 }
6: (a)⇒ If infinite solutions \frac { a1 }{ a2 } =\frac { b1 }{ b2 } =\frac { c1 }{ c2 }
7 : (d) ⇒ Dependent linear equations have one solution \frac { a1 }{ a2 } =\frac { b1 }{ b2 } =\frac { c1 }{ c2 }
8: (c) ⇒ \frac { x }{ y } =\frac { 5 }{ 6 } \Longrightarrow 6x−5y=0 if 8 is subtracted = \frac { x−8 }{ y−8 } =\frac { 4 }{ 5 } we have two equations then solve it
9: (c) ⇒ Solve the equation.
10: (d) ⇒ Use table (3.4) on text book. \frac { a1 }{ a2 } =\frac { b1 }{ b2 } =\frac { c1 }{ c2 }
11. (b) ⇒ Refer table (3.4) text book
12 . (a) ⇒ Put (x = 0) and solve
13. (d) ⇒ Form the equation from the given data
14. (b) ⇒ Let the two numbers be x and y. Then form the equation from the given data
15. (b) ⇒ Put it as \frac { x }{ 1 } +\frac { 7 }{ y } =\frac { 5 }{ 2 } and solve as a simple fraction
16. (c)⇒ Textbook
17. (d) ⇒ Textbook
18. (a) ⇒ Add 5 years to their present ages
19. (a) ⇒ Take ‘u’ as common & then solve it
20.(c) ⇒ First add the two equations and get equation (1).then subtract the rwo equations and get equation (2).then solve equation (1) and (2)
21.(c) ⇒ Text book
22.(b) ⇒ Text book
23.(a) ⇒ Text book (table 3.4)
24.(d) ⇒ Text book (table 3.4)
25.(d) ⇒ Summary
26 (b) ⇒ Solve the equations.
27 (c) ⇒ Let the son’s age be x years.So father will be 6x
28 (c) ⇒ x + y + 40 = 180 and x−y = 30
29 (d) ⇒ Let the Re 1 coins be x and the Rs 2 coins be y
30 (a) ⇒ Solve using the parallel condition of lines
31. (a) ⇒ Solve the equations.
32. (c) ⇒ Solve the equations.
33.(a) ⇒ Angles of a triangle +180°
34. (c) ⇒ Solve the equation.
35. (a) ⇒ Add 3 years to their present ages