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Linear Equations In Two Variables Maths - Linear Equations In Two Variables

Maharashtra Board - STD 10 - Maths (MSBSHSE - English Medium). 322 questions in this chapter.

Question types

Linear Equations In Two Variables question types

322 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

322
Questions
4
Question groups
5
Question types
Sample Questions

Linear Equations In Two Variables questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If the system of equations has infinitely many solutions, then:
$2x + 3y = 7$
$(a + b)x + (2a - b)y = 21$
  • A
    $a = 1, b = 5$
  • ✓
    $a = 5, b = 1$
  • C
    $a = -1, b = 5$
  • D
    $a = 5, b = -1$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
The value of $k$ for which the system of equations $x + 2y - 3 = 0$ and $5x + ky + 7 = 0$ has no solution, is:
  • ✓
    $10.$
  • B
    $6.$
  • C
    $3.$
  • D
    $1.$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
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
    $25.$
  • B
    $72.$
  • C
    $63.$
  • ✓
    $36.$

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark
If $am ≠ bl$, then the system of equations $ax + by = clx + my = nax + by = clx + my = n.$
  • ✓
    Has a unique solution.
  • B
    Has no solution.
  • C
    Has infinitely many solutions.
  • D
    May or may not have a solution.

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
If $2x - 3y = 7$ and $(a + b)x - (a + b - 3)y = 4a + b$ represent coincident lines, then $a$ and $b$ satisfy the equation:
  • A
    $a + 5b = 0$
  • B
    $5a + b = 0$
  • ✓
    $a - 5b = 0$
  • D
    $5a - b = 0$

Answer: C.

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Q 62 Marks Questions2 Marks
Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
Infinitely many solutions?
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Q 72 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
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Q 82 Marks Questions2 Marks
Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
a unique solutions?
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Q 92 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$
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Q 102 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$
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Q 133 Marks Question3 Marks
Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.
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Q 143 Marks Question3 Marks
Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes Rs. 50 and Rs 100 she received.
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Q 153 Marks Question3 Marks
The cost of 4 pens and 4 pencil boxes is ₹ 100. Three times the cost of a pen is ₹ 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and pencil box.
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Q 174 Marks Questions4 Marks
Solve the following systems of equations:
$\frac{\text{xy}}{\text{x}+\text{y}}=\frac{6}{5}$
$\frac{\text{xy}}{\text{y}-\text{x}}=6$ where $\text{x}+\text{y}\neq0,\text{y}-\text{x}\neq0.$
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Q 184 Marks Questions4 Marks
In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
$x - 2y = 8$
$5x - 10y = 10$
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Q 194 Marks Questions4 Marks
Find the value of k for which each of the following system of equations have infinitely many solutions:
$2x + 3y = k$
$(k - 1)x + (k + 2)y = 3k$
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Q 204 Marks Questions4 Marks
Find the values of a and b for which the following system of equations has infinitely many solutions:
$2x + 3y = 7$ 
$(a - 1)x + (a + 2)y = 3a$
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