Linear Equations(10th Grade > Mathematics ) Questions and answers for exam Preparation

10th Grade > Mathematics

LINEAR EQUATIONS MCQs

Linear Equations In One Variable, Linear Equations In Two Variables, Pair Of Linear Equations In Two Variables (8th, 9th And 10th Grade)

Total Questions : 74 | Page 5 of 8 pages

Question 41. Find the value of

k

, when

a = - 1

and

b = 4

is the solution of the equation

- 2 a = - 5 b + k

Discuss Question

Answer: Option D. -> 22
:
D
If

a = - 1, b = 4

is the solutionof equation

- 2 a = - 5 b + k

, then they will satisfy the given equation.
Putting values of

a & b

in the given equation.
So,

- 2 (- 1) = - 5 (4) + k 2 = - 20 + k \Rightarrow k = 20 + 2 \Rightarrow k = 22

.
Therefore, the value of k is 22.

Question 42. The equation

y = m x

represents ___ ;
where,

(m \neq 0)

a line parallel to x-axis
a line parallel to y-axis
a line passing through the origin
a line cutting x-axis at the point (m,0)

Discuss Question

Answer: Option C. -> a line passing through the origin
:
C
Given equation:

y = m x

Substituting

x = 0

y = m \times 0 = 0

So, if x = 0, then y = 0.
i.e,

(0, 0)

is a point on the line.
Therefore, the line passes through the origin.

Question 43. What will be the linear equation for the given graph?

x=2y
y=2x+5
y=2x+3
2y=x+1

Discuss Question

Answer: Option C. -> y=2x+3
:
C
The coordinates of the points of the graph (0,3) & (-1.5,0) satisfy only the equation y=2x+3:
(0, 3):
3 = 2 x 1 + 3
(-1.5, 0):
0 = 2

\times

(-1.5) + 3

Question 44. If kx - 2ky + 15 = 0 passes through the point (3,-1), then k = -3.

True
False
x=−2, y=−5
x=9, y=1

Discuss Question

Answer: Option A. -> True
:
A
Putting x = 3 , y = -1 in the given equation,
k x 3 - 2 x k x -1 + 15 = 0

\Rightarrow

3k + 2k + 15 = 0

\Rightarrow

k = -3

Question 45. If x = 1, y = 2 is a solution of the equation 3x + 2y = k, the value of k is ___.

Discuss Question

:
Putting x = 1, y = 2 in the given equation,
3 x 1 + 2 x 2 = k

\Rightarrow

k = 7

Question 46. Which of following is a solution of the equation,

2 x + 3 y = 11 ?

x=1, y=3
x=0, y=5
x=−2, y=−5
x=9, y=1

Discuss Question

Answer: Option A. -> x=1, y=3
:
A
Substitutingeach set of the values for

x

and

y

in the equation

2 x + 3 y = 11

, we have

(i) x = 1, y = 3 L H S = (2 \times 1) + (3 \times 3) = 11 = R H S (i i) x = 0, y = 5 L H S = (2 \times 0) + (3 \times 5) = 15 \neq R H S (i i i) x = - 2, y = - 5 L H S = (2 \times - 2) + (3 \times - 5) = - 19 \neq R H S (i v) x = 9, y = 1 L H S = (2 \times 9) + (3 \times 1) = 21 \neq R H S

∴ x = 1, y = 3

is solution to the given equation.

Question 47. The standard form of a linear equation in two variables x and y, whose respective coefficients are 2 and -3 and has the constant as 4 is ____.

3x−2y+4=0
2x−3y−4=0
3x−2y−4=0
2x−3y+4=0

Discuss Question

Answer: Option D. -> 2x−3y+4=0
:
D
The standard form of a linear equation in 2 variables x and y is given by ax + by + c = 0.
It is given that a = 2, b = -3 and c = 4.
Therefore, the linear equation is

2 x - 3 y + 4 = 0

Question 48. If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.

True
False

Discuss Question

Answer: Option A. -> True
:
A
When

x = 1

2 + 5 y = 7

\Rightarrow

y = 1
When

x = 2

4 + 5 y = 7

\Rightarrow y = \frac{3}{5}

When

x = 3

6 + 5 y = 7

\Rightarrow y = \frac{1}{5}

When

x = 4

8 + 5 y = 7

\Rightarrow y = \frac{- 1}{5}

So, in natural numbers, when x>1, the value of y is <1 and progressivelydecreases, and then becomes negative at x = 4.
When

y = 2

2 x + 10 = 7

\Rightarrow y = \frac{- 3}{2}

When

y = 3

2 x + 15 = 7

\Rightarrow y = - 4

In natural numbers, when y>1, x<0 and progressively decreases.
Hence, in natural numbers, there is only one pair i.e., (1,1) which satisfy the given equation but in real numbers and rational numbers there are many pairs to satisfy the given linear equation.

Question 49. The distance between the lines x = -3 and x = 2 is _____.

5 units
3 units
2 units
1 units

Discuss Question

Answer: Option A. -> 5 units
:
A

The Distance Between The Lines X = -3 And X = 2 is _____.

Both the lines are parallel to y-axis.
The line x = -3 lies at a distance of 3 units to the left side of the origin and the line x = 2 lies at a distance of 2 units to the right side of the origin.
Therefore, the distance between the lines is (3 + 2) units or 5 units.

Question 50. If y = 4x is written in the form of ax + by + c = 0, then which of the following options represents the values of a, b and c respectively?