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Test: Formation Of Linear Equations - Class 9 MCQ


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15 Questions MCQ Test - Test: Formation Of Linear Equations

Test: Formation Of Linear Equations for Class 9 2024 is part of Class 9 preparation. The Test: Formation Of Linear Equations questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Formation Of Linear Equations MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Formation Of Linear Equations below.
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Test: Formation Of Linear Equations - Question 1

Geeta’s age is 3 years more than thrice m, the age of Meeta. Write an equation of first degree to display this information.

Detailed Solution for Test: Formation Of Linear Equations - Question 1

Let Geeta's age be G and Meeta's age be m. According to the given information:

  • Geeta’s age is 3 years more than thrice Meeta's age.

This can be written as the equation:

G=3m+3

This is a first-degree equation that represents the relationship between Geeta's and Meeta's ages.

Test: Formation Of Linear Equations - Question 2

Which of the following is not a linear equation?

Detailed Solution for Test: Formation Of Linear Equations - Question 2

The equation (a) 1/x + 1/y = 4 is not a linear equation because the variables x and y are in the denominator.

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Test: Formation Of Linear Equations - Question 3

A linear equation in one variable is an equation of the form ………..

Detailed Solution for Test: Formation Of Linear Equations - Question 3

A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form a x + b = 0, ax+b=0, ax+b=0 and are solved using basic algebraic operations

Test: Formation Of Linear Equations - Question 4

The Equation y = – 5, in two variables can be written in the form of ax + by + c = 0 as​

Detailed Solution for Test: Formation Of Linear Equations - Question 4

The equation y = - 5 in the form ax + by + c = 0 is:
C: 0.x + 1.y + 5 = 0

Test: Formation Of Linear Equations - Question 5

Which of the following equations is linear equation in two variables?

Detailed Solution for Test: Formation Of Linear Equations - Question 5

Option A, 2.4s + 3t = 7, is a linear equation because it has two variables sss and ttt, both with a power of 1, and follows the standard form of a linear equation ax + by + c = 0.
Option B contains t2, which makes it non-linear. Option C has x2, which violates the linear condition.
Option D includes 7/x, a rational term, which also disqualifies it as a linear equation.
Thus, the correct answer is Option A.

Test: Formation Of Linear Equations - Question 6

The number of girls x in a class is 5 less than twice the number of boys y of the same class. The linear equation in two variables for this information is

Detailed Solution for Test: Formation Of Linear Equations - Question 6

Correct Answer :- a

Explanation : Let number of girls in class = x

Boys = 2y - 5

Equation will be : x + 5 = 2y

Test: Formation Of Linear Equations - Question 7

The speed x of train A is twice the speed y of the train B. Express this in the form of a linear equation.

Detailed Solution for Test: Formation Of Linear Equations - Question 7

The speed x of train A is twice the speed y of train B. This can be expressed as:

x = 2y

Answer: B) x = 2y

Test: Formation Of Linear Equations - Question 8

The cost of a pencil is thrice the cost of rubber.The equivalent linear equation in two variables of above statement is:

Detailed Solution for Test: Formation Of Linear Equations - Question 8

The cost of a pencil p is thrice the cost of a rubber r. The equation can be written as:
p = 3r
Answer: C) p = 3r

Test: Formation Of Linear Equations - Question 9

The equation - (9/5) x = 1/2 in two variables is expressed as:

Detailed Solution for Test: Formation Of Linear Equations - Question 9

The given equation is: - (9/5) x = 1/2
To express it in the standard form of a linear equation in two variables ax + by + c = 0, we rearrange:
- 9/5x + 0.y - 1/2 = 0
Here:

  • Coefficient of x is = - 9/5.
  • Coefficient of y is 0 (no y-term is present).
  • Coeficient term is -1/2.

Thus, the correct answer is Option D.

Test: Formation Of Linear Equations - Question 10

Which of the following is a linear equation in one variable?

Detailed Solution for Test: Formation Of Linear Equations - Question 10

A linear equation with one variable consists of numbers or constants and multiplies of a variable. The standard form of such an equation is ax + b = 0, where a and b are constants and x is the variable.
Hence, 2x + 7 = 8  is a linear equation in one variable.

Test: Formation Of Linear Equations - Question 11

The coefficients a,b, c in the following linear equation of the form ax + by + c = 0 is of the equation - 7/2 x + 5/4 y = - 9 are

Detailed Solution for Test: Formation Of Linear Equations - Question 11

a = - 7/2 (coefficient of x), 
b = 5/4 (coefficient of y), 
c = 9 (constant term) .

Test: Formation Of Linear Equations - Question 12

Check which of the following are solutions of the equation 3x + 2y = 10.

Detailed Solution for Test: Formation Of Linear Equations - Question 12

(i) Not a solution: Substituting (2, 2), 3(2) + 2(2) = 6 + 4 = 10 (True).
(ii) Not a solution: Substituting (1, 4), 3(1) + 2(4) = 3 + 8 = 11 (False).
(iii) Is a solution: Substituting (0, 5), 3(0) + 2(5) = 0 + 10 = 10 (True).
(iv) Not a solution: Substituting (3, 1), 3(3) + 2(1) = 9 + 2 = 11 (False).

Test: Formation Of Linear Equations - Question 13

Which of the following is linear equation?

Detailed Solution for Test: Formation Of Linear Equations - Question 13

[√x]2 + [√y]2 = √2
Step 1: Simplify the terms
• [√x]2 = x
• [√y]2 = y
Thus, the equation becomes:
x + y = √2
Step 2: Check for linearity
• The variables  x and y both have degree 1.
• The constant √2 does not affect the linearity of the equation.
Conclusion:
This is a linear equation because it is of the form ax + by + c = 0, where a = 1, b = 1, and c = - √2.
Answer: The equation is linear.

Test: Formation Of Linear Equations - Question 14

Difference between the cost of a carpet(C) and a durries(D) is Rs.200. If the carpet is the costlier one of the two, which of the following represents this information?

Detailed Solution for Test: Formation Of Linear Equations - Question 14

The difference in costs of two articles is 200 and since the carpet is more costlier than durry. So the equation will be C - D = 200

Test: Formation Of Linear Equations - Question 15

Four times B’s age exceeds A’s age by twenty years.

Detailed Solution for Test: Formation Of Linear Equations - Question 15

Four times B's age: 4B
Exceeds A's age: - A
By twenty years: = 20
4B - A = 20

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