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 4 of 8 pages

Question 31. If the cost of a bike

x

is twice the cost of a scooter

y

, the representation using equations in 2 variables in the form

a x + b y + c = 0

will be

x - 2 y = 0

True
False
Dependent, infinite
None of these

Discuss Question

Answer: Option A. -> True
:
A
Let, the cost of a bike be

x

.
Thecost of scooter be

y

.
According to question

x = 2 y

Therefore linear equation will be:

\Rightarrow x - 2 y = 0

Question 32. Find the solution of the given system of equations.

\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{8} = \frac{3 x + y - 12}{11}

(1, -1)
(2, 6)
(2, 2)
(0, 1)

Discuss Question

Answer: Option B. -> (2, 6)
:
B
Take first two components,

\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{8}

\Rightarrow 8 (x + y - 8) = 2 (x + 2 y - 14)

\Rightarrow 8 x + 8 y - 64 = 2 x + 4 y - 28

\Rightarrow 6 x + 4 y - 36 = 0

\Rightarrow 3 x + 2 y - 18 = 0 . . . . . (i)

Take last two components,

\frac{x + 2 y - 14}{8} = \frac{3 x + y - 12}{11}

\Rightarrow 11 (x + 2 y - 14) = 8 (3 x + y - 12)

\Rightarrow 11 x + 22 y - 154 = 24 x + 8 y - 96

\Rightarrow - 13 x + 14 y - 58 = 0 . . . . . (i i)

On multiplying equation

(i)

by 7, we get

\Rightarrow 21 x + 14 y - 126 = 0... (i i i)

,
On subtracting equation (ii) from (iii), we get

\Rightarrow 34 x = 68

\Rightarrow x = 2

On substituting value of

x = 2

in equation

(i)

, we get

3 \times 2 + 2 y - 18 = 0

\Rightarrow y = 6

∴

The solutionis (2, 6).

Question 33. A man starts his job with a certain salary and earns a fixed increment every year. If his salary was ₹ 15000 after 4 years of service and ₹ 18000 after 10 years of service, then find his starting salary and annual increment respectively.

₹ 11000, ₹ 700
₹ 13000, ₹ 500
₹ 13000, ₹ 700
₹ 11000, ₹ 500

Discuss Question

Answer: Option B. -> ₹ 13000, ₹ 500
:
B
Let starting salary be ₹x
and annual increment be ₹ y
According to the first condition:
x + 4y = 15000 ......(i)
According to the second condition:
x + 10y = 18000 ......(ii)
Subtracting (i) from (ii), we get
6y = 3000
y = 500
Substituiting y = 500 in equation (i), we get
x + (4

\times

500) = 15000
x = 15000 - 2000
x = 13000
Hence starting salary is ₹ 13000 and annual increment is ₹ 500.

Question 34. If the numerator of a fraction is increased by 2 and its denominator is decreased by 1, it becomes

\frac{2}{3}

. If the numerator is increased by 1 and the denominator is increased by 2, it becomes

\frac{1}{3}

. Find the fraction.

x=2 and y=7
x=−2 and y=−7
x=3 and y=7
x=2 and y=6

Discuss Question

Answer: Option A. -> x=2 and y=7
:
A
Let the fraction be

\frac{x}{y}

∴ \frac{x + 2}{y - 1} = \frac{2}{3} a n d \frac{x + 1}{y + 2} = \frac{1}{3}

\Rightarrow 3 x - 2 y = - 8 . . . . (i)

a n d 3 x - y = - 1...... (i i)

\Rightarrow 3 x - 2 y = - 8

- (3 x - y = - 1)

\Rightarrow 3 x - 2 y = - 8

- 3 x + y = 1

______________________

- y = - 7

______________________

\Rightarrow y = 7

Substitutingy = 7 in equation (ii), we get

3 x - (14) = - 8

3 x = - 8 + 14 = 6

∴ x = 2

\Rightarrow x = 2 a n d y = 7

Question 35. Given graph represents _______________ pair of linear equation having _____________solution(s).

Consistent, unique
Inconsistent ,zero
Dependent, infinite
None of these

Discuss Question

Answer: Option B. -> Inconsistent ,zero
:
B
In the given graph, lines of the equations 2x + 4y - 12 = 0 and x + 2y - 4 = 0 are parallel to each other which gives no solution; hence it is an inconsistent pair of linear equation.

Question 36. If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right angle triangle AOB is of length ___. (O is origin)

4 units
3 units
5 units
None of these

Discuss Question

Answer: Option C. -> 5 units
:
C

4 x + 3 y = 12 P u t y = 0 t h e n, w e g e t 4 x + 3 (0) = 12 \Rightarrow x = 3 ∴ A (3, 0) c u t s t h e x - a x i s P u t x = 0 t h e n, w e g e t 4 (0) + 3 y = 12 \Rightarrow y = 4 ∴ B (0, 4) c u t s t h e y - a x i s

If The Graph Of The Equation 4x + 3y = 12 cuts The Coordina...

I n △ A O B, AB is the hypotenuse of the given triangle. T h e l e n g t h O A = 3 u n i t s a n d O B = 4 u n i t s B y p y t h o g o r a s t h e o r e m, A B = \sqrt{O A^{2} + O B^{2}} = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 u n i t s

Question 37. A linear equation in two variables

Has no solution
Has one solution
Has two solutions
Has infinitely many solutions

Discuss Question

Answer: Option D. -> Has infinitely many solutions
:
D
A linear equation in two variables is of the form

x + b y + c = 0

\Rightarrow x = - c - b y

For every unique value of x, we get a unique value of y satisfying the above equation. Therefore, a linear equation in two variables can have infinitely many solutions.

Question 38. A point on the line x + y = 0 can be represented as (a,-a).

True
False
5 units
None of these

Discuss Question

Answer: Option A. -> True
:
A
x + y = 0

\Rightarrow

x = - y or y = - x
If x = a, y = -a

∴

Any point on the line x + y = 0 can be represented as(a,-a)

Question 39. Co-ordinates of P and Q are _______ respectively:

(1, 1) & (2, 0)
(1, 1) & (0, 2)
(1, 2) & (0, 1)
(2, 0) & (1,2)

Discuss Question

Answer: Option B. -> (1, 1) & (0, 2)
:
B

CoordinateP is (1, 1) and Q is (0, 2)

Question 40. The geometrical representation of a linear equation is a

Straight line
curve
circle
parabola

Discuss Question

Answer: Option A. -> Straight line
:
A
A linear relation between two variablesis geometrically represented by a straight line on the Cartesian plane.