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Pair of Linear Equations in Two variables Maths - Pair of Linear Equations in Two variables

Jharkhand Board (JAC) - STD 10 - Maths (Jharkhand - English Medium). 73 questions in this chapter.

Question types

Pair of Linear Equations in Two variables question types

73 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

73
Questions
5
Question groups
5
Question types
Sample Questions

Pair of 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
Choose the correct answer from the given four options:
The pair of equations x = a and y = b graphically represents lines which are:
  • A
    Parallel.
  • B
    Intersecting at (b, a).
  • C
    Coincident.
  • ✓
    Intersecting at (a, b).

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options:
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, in years, of the son and the father are, respectively:
  • A
    4 and 24.
  • B
    5 and 30.
  • ✓
    6 and 36.
  • D
    3 and 24.

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options:
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.
  • ✓
    25 and 25.

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options:
The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is:
  • A
    3.
  • B
    -3.
  • ✓
    -12.
  • D
    No value.

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options:
Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are:
  • A
    Intersecting at exactly one point.
  • ✓
    Intersecting at exactly two points.
  • C
    Coincident.
  • D
    Parallel.

Answer: B.

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Q 91 Marks Question1 Mark
Are the following pair of linear equations consistent? Justify your answer:
$\frac{3}{5}\text{x}-\text{y}=\frac{1}{2}$ and $\frac{1}{5}\text{x}-3\text{y}=\frac{1}{6}$
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Q 122 Marks Questions2 Marks
For the pair of equations λx + 3y = -7 and 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true? Give reasons.
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Q 153 Marks Question3 Marks
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
$3x - y - 5 = 0$ and $6x - 2y - p = 0,$
If the lines represented by these equations are parallel.
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Q 163 Marks Question3 Marks
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
$-x + py = 1$ and $px - y = 1,$
if the pair of equations has no solution.
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Q 173 Marks Question3 Marks
Solve the following pairs of equations:
$\frac{\text{x}}{\text{a}}-\frac{1}{\text{y}}=-1,\frac{1}{\text{x}}+\frac{1}{2\text{y}}=8,\text{ x},\text{ y}\neq0$.
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Q 183 Marks Question3 Marks
Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?
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Q 205 Marks Questions5 Marks
The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
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Q 215 Marks Questions5 Marks
Ankita travels 14km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.
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Q 225 Marks Questions5 Marks
Graphically, solve the following pair of equations:
2x + y = 6
2x - y + 2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.
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