1. A pair of linear equations a_{1}x + b_{1}y + c_{1} = 0; a_{2}x + b_{2}y + c_{2} = 0 is said to be inconsistent, if

Answer: b

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2. Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which are

(a) intersecting at one point

(b) parallel

(c) intersecting at two points

(d) coincident

Answer: b

3. The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have

(a) a unique solution

(b) infinitely many solutions

(c) no solution

(d) two solutions

Answer: c

4. If a pair of linear equations is consistent, then the lines will be

(a) always coincident

(b) parallel

(c) always intersecting

(d) intersecting or coincident

Answer: d

5. The pair of equations x = 0 and x = 5 has

(a) no solution

(b) unique/one solution

(c) two solutions

(d) infinitely many solutions

Answer: c

6. The pair of equation x = – 4 and y = – 5 graphically represents lines which are

(a) intersecting at (- 5, – 4)

(b) intersecting at (- 4, – 5)

(c) intersecting at (5, 4)

(d) intersecting at (4, 5)

Answer: b

7. For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines

Answer: a

8. If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is

Answer: a

9. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be

(a) 2x + 5y = 6

(b) 3x + 5y = 3

(c) -10x – 25y + 15 = 0

(d) 10x + 25y = 15

Answer: c

10. If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are respectively

(a) 6, -1

(b) 2, 3

(c) 1, 4

(d) 19/5, 6/5

Answer: d

11. The graph of x = -2 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both x- and y-axis

(d) none of these

Answer: b

12. The graph of y = 4x is a line

(a) parallel to x-axis

(b) parallel to y-axis

(c) perpendicular to y-axis

(d) passing through the origin

Answer: d

13. The graph of y = 5 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both axis

(d) none of these

Answer: a

14. Two equations in two variables taken together are called

(a) linear equations

(b) quadratic equations

(c) simultaneous equations

(d) none of these

Answer: c

15. If am bl then the system of equations ax + by = c, lx + my = n, has

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) none of these

Answer: a

16. If in the equation x + 2y = 10, the value of y is 6, then the value of x will be

(a) -2

(b) 2

(c) 4

(d) 5

Answer: a

17. The graph of the equation 2x + 3y = 5 is a

(a) vertical line

(b) straight line

(c) horizontal line

(d) none of these

Answer: b

18. The value of k, for which equations 3x + 5y = 0 and kx + lOy = 0 has a non-zero solution is

(a) 6

(b) 0

(c) 2

(d) 5

Answer: a

19. The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1 has infinitely many solutions is

(a) 2

(b) 3

(c) 4

(d) 5

Answer: a

20. The value of k for which the equations (3k + l)x + 3y = 2; (k2 + l)x + (k – 2)y = 5 has no solution, then k is equal to

(a) 2

(b) 3

(c) 1

(d) -1

Answer: d

21. The pair of equations x = a and y = b graphically represents lines which are

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

Answer: d

22. Asha has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively

(a) 35 and 15

(b) 15 and 35

(c) 35 and 20

(d) 25 and 25

Answer: d

23. 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 are, respectively

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

Answer: c

24. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

(a) 27

(b) 72

(c) 45

(d) 36

Answer: d

25. The pair of linear equations 2x + 3y = 5 and 4x + 6y= 10 is

(a) inconsistent

(b) consistent

(c) dependent consistent

(d) none of these

Answer: c

Explaination:

26. The pair of equations y = 0 and v = -7 has [NCERT Exemplar Problems]

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

Answer: d

Explaination: (d) No solution (parallel lines)

27. The pair of equations x = a and y = b graphically represents lines which are

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

Answer: d

Explaination: (d) Intersecting at (a, b)

28. Match the Column:

(a) 1 – A, 2 – B, 3 – C

(b) 1 – B, 2 – C, 3 – A

(c) 1 – C, 2 – B, 3 – A

(d) 1 – A, 2 – C, 3 – B

Answer: d

Explaination:

29. The pair of equations x = 4 and y = 3 graphically represents lines which are

(a) parallel

(b) intersecting at (3, 4)

(c) coincident

(d) intersecting at (4, 3)

Answer: d

Explaination:

(d) When lines x = 4, y = 3 will intersect, then x coordinate = 4, y-coordinate = 3

30. a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0, where a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2} are all real numbers and a_{1}^{2}+ b_{1}^{2} ≠ 0, a_{2}^{2} + b_{2}^{2} ≠ 0, is called a

(a) family of two different straight lines

(b) family of two coincident lines

(c) pair of linear equations in two variables

(d) none of these

Answer: c

Explaination:

(c) Definition of pair of linear equations in two variables.

31. Match the Column:

(a) 1 – A, 2 – B, 3 – C

(b) 1 – B, 2 – A, 3 – C

(c) 1 – B, 2 – C, 3 – A

(d) 1 – C, 2 – A, 3 – B

Answer: c

Explaination:

32. A pair of linear equations which has a unique solution x = 2, y = -3 is [NCERT Exemplar Problems]

(a) x + y = —1; 2x – 3y = -5

(b) 2x + 5y = -11; 4x + 10y = -22

(c) 2x – y = 1 ; 3x + 2y = 0

(d) x-4y- 14 = 0; 5x-y- 13 = 0

Answer: b

Explaination:

(b) 2x + 5y = – 11; 4x + 10y = – 22

33. The father’s age is six times of his son’s age. Four years hence, the age of the father will be four times of his son’s age. The present ages, in years, of the son and the father are, respectively. [NCERT Exemplar Problems]

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

Answer: c

Explaination:

Let F and S be the ages of father and sos respectively.

ATQ F = 6S …(i)

F + 4 = 4(S + 4)

⇒ F + 4 = 4S + 16 …(ii)

Substituting F = 6S in (ii), we get

6S + 4 = 4S + 16

2S = 12 .

⇒ S = 6; F = 36

34. If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then the respective values of a and b are

[CBSE 2018(C)]

(a) 3, 5

(b) 5, 3

(c) 3, 1

(d) -1, -3

Answer: c

Explaination:

35. The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference betw een the two digits of the number?

(a) 9

(b) 6

(c) 12

(d) 3

Answer: d

Explaination:

Let number is 10x + y (x, y are the digits).

Number obtained by interchanging the digits = 10y+x

∴ 10x + y – (10y + x) = 27

9(x -y) = 27

∴ x – y = 3

36. The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if

(a) a = b

(b) 3a = 2b

(c) 2 a = 3 b

(d) ab = 6

Answer: c

Explaination:

37. The equations ax + by + c = 0 and dx + ey + c = 0 represent the same straight line if

(a) ad = be

(b) ac = bd

(c) be = ad

(d) ab = de

Answer: d

Explaination:

38. Using the following equations:

\(\frac{4}{x}\) + 6y = 10

\(\frac{1}{x}\) – 6y = 5

find the value of p if p = 5x.

(a) 1

(b) 2

(c) 3

(d) 4

Answer: a

Explaination:

39. Find the number of solutions of the following pair of linear equations:

x + 2y — 8 = 0

2x + 4 v =16

Answer:

Explaination:

∴ Given pair of linear equations has infinite many solutions.

40. Write whether the following pair of linear equations is consistent or not. x + y = 14, x – y = 4

Answer:

Explaination:

⇒ The equations have unique solution.

∴ Pair of linear equations is consistent.

41. Given the linear equation 3x + 4y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines.

Answer:

Explaination:

Lines are parallel when \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\)

∴ One of the linear equation in two variables can be 6x + 8y + k = 0 where k is constant not equal to -16.

42. Find the value of k for which the given pair of linear equations has no common solution.

4x + Ay = 5

8x + 12y = 10

Answer:

Explaination:

43. Find the value of p for which the given pair of linear equations has infinite many solutions.

4x + 3y – 4=0

px + 9y + 12 = 0

Answer:

Explaination:

44. The larger of two supplementary angles exceeds the smaller by 20 degrees. Find the angles.

Answer: c

Explaination:

Let larger angle = x° and smaller angle =y° Now x -y = 20 andx +y = 180

∴ Algebraic representation is x – y = 20, x+y= 180

45. On solving the following pair of linear equations: 2x – y = 2; 5x + 2y = 14 by substitution method, values of x and y are _____ and _____ respectively.

Answer:

Explaination:

2x – y = 2 …(i)

5x + 2y = 14 …(ii)

Substituting y = 2x – 2 in (ii), we get 5x + 2(2x – 2)=14

9x – 4 = 14

⇒ x= \(\frac{18}{9}\) = 2

⇒ x = 2, y = 2

46. Solve the following pair of linear equations by substitution method 2x – 3y +15 = 0; 3x – 5 = 0.

Answer: c

Explaination:

47. There are two positive numbers such

that sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is _____ .

Answer: c

Explaination:

48. Solve for x and y by the method of elimination:

4x -3 y = 1; 5x – 7y = 2.

Answer:

Explaination:

Given equations are

4x – 3y = 1 …(i)

5x – 7y = -2 …(ii)

For making coefficient of y equal in both the equations multiplying equation (/) with 7, we get

7 × (4x – 3y) = 7 × 1

⇒ 28x – 21y = 7 …(iii)

Multiplying equation (ii) with 3, we get

3 × (5x – 7y) = 3 × -2

⇒ 15x – 21y = -6 …(iv)

Subtracting equation (iv) from (iii), we get

when x – 1, equation (i) becomes

4 × – 3y = 1

⇒ -3y = -3

⇒ y = 1

∴ x= 1, y= 1

49. If the pair of equations x + y = √2 and x sin θ + y cos θ = 1 has infinitely many solutions, then θ = _____ .

Answer:

Explaination:

50. Find the value of k so that the following system of equation has infinite solutions: 3x – y – 5 = 0, 6x – 2y + k = 0

Answer:

Explaination:

51. For which values of p, does the pair of equations given below has unique solution? 4x + py + 8 = 0 and 2x + 2y + 2 = 0

Answer:

Explaination:

For unique solution, \(\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \Rightarrow \frac{4}{2} \neq \frac{p}{2}\)

⇒ p ≠ 4

52. The equations \(\frac{x y}{x+y}=\frac{1}{9}\) and \(\frac{x y}{x-y}=\frac{1}{4}\) are equivalent to the equations:

Answer: d

Explaination:

53. On solving the following equations: \(\frac{5}{x}\) + 6y = 3; \(\frac{-5}{x}\) + 3y = 6, values of x and y are ____ and ____ respectively.

Answer:

Explaination:

54. Solve forx andy : x + \(\frac{6}{y}\) = 6, 3x – \(\frac{8}{y}\) = 5

Answer:

Explaination: