Sample QuestionsLinear Equations in One Variable questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The sum of three consecutive multiples of $‘5’$ is $45.$ Which is the smallest of the three multiples.
Answer: A.
View full solution →A linear equation in one variable has:
Answer: A.
View full solution →The root of the equation $\frac{\text{4x}}{3}-12=0$ is:
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer: If $\frac{\text{n}}{2}-\frac{3\text{n}}{4}+\frac{5\text{n}}{6}=21,$ then $\text{n}=?$
Answer: C.
View full solution →What is the solution of the given equation: $3(x - 3) = 4(2x + 4)$
Answer: D.
View full solution →$3$ years ago, the age of a boy was $y$ years. His age $2$ years ago was $(y - 2)$ years.
View full solution →$8r - 23 = - 7,$ then $r = 2.$
View full solution →Twice a number e reduced by $2$ is $36,$ then $c = 17.$
View full solution →Solution of $\frac{x+1}{3}=5$ and $3 x-1=5$ is same.
View full solution →Solution of $\frac{x}{3}=4$ and $x+1=13$ is same.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): Seven times a number is $42.$ This statement in the form of an equation is $7x = 42.$
Reason (R): Standard form for linear equation in one variable is $ax + b = 0.$ where $x$ is variable and $a, b$ are arbitrary constants
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- ✓
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- C
$A$ is true but $R$ is false
- D
$A$ is false but $R$ is true
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): A number when divided by $5$ gives $6.$ This statement in the form of an equation is $5x = 6.$
Reason (R): Standard form for linear equation in one variable is $ax + b = 0.$ where $x$ is variable and $a, b$ are arbitrary constants
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- C
$A$ is true but $R$ is false
- ✓
$A$ is false but $R$ is true
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The largest number of the three consecutive numbers is $x + 1.$ Then, the smallest number is $x - 1.$
Reason (R): The value of the variable which makes left hand side equal to right hand side in the given equation is called the solution or the root of the equation
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- ✓
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- C
$A$ is true but $R$ is false
- D
$A$ is false but $R$ is true
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If $6$ is added to $3$ times of a number, it becomes $15.$ This statement in the form of an equation is $3x + 6 = 15.$
Reason (R): the linear equation involves only one unknown, it is called “univariate”. The quadratic equation contains only powers of $x$ that are non-negative
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- ✓
$A$ is true but $R$ is false
- D
$A$ is false but $R$ is true
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The root of the equation $\frac{7\text{x}}{3} = {3}$ is $\frac{5\text{x}}{3}$
Reason (R): The value of the variable which makes left hand side equal to right hand side in the given equation is called the solution or the root of the equation
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- C
$A$ is true but $R$ is false
- D
$A$ is false but $R$ is true
Answer: A.
View full solution →Simplify and solve the linear equation: $3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17$
View full solution →Simplify and solve the linear equation $0.25(4f – 3) = 0.05 (10f – 9).$
View full solution →Solve the equations and check your result: $2x - 1 = 14 - x.$
View full solution →Solve the equation and check your result: $4z + 3 = 6 + 2z$
View full solution →Solve the equation and check your result: $5x + 9 = 5 + 3x$
View full solution →Simplify and solve the linear equation:$15(y – 4 ) – 2(y – 9) + 5(y + 6) = 0.$
View full solution →Simplify and solve the linear equation $3(t – 3) = 5(2t + 1).$
View full solution →Solve the linear equation: $m - \frac{{m - 1}}{2} = 1 - \frac{{m - 2}}{3}$
View full solution →Solve the linear equation $\frac{{3t - 2}}{4} - \frac{{2t + 3}}{3} = \frac{2}{3} - t$.
View full solution →Solve the linear equation $\frac{{x - 5}}{3} = \frac{{x - 3}}{5}$.
View full solution →Breadth of a rectangle is $3$ unit less than its length. If its breadth is $b-3,$ perimeter of that rectangle is$ ............ (2b-3, 2b-6, 4b-6)$
View full solution →Sum of two odd numbers is $12.$ If the smaller number is $5,$ the greater number is$............(12. 5, 7)$
View full solution →A number decreased by $2$ and then divided by $3$ is $6.$ That number is $.......... (10, 20, 30)$
View full solution →Sum of present ages of father and son is $60$ years. Sum of their ages after $x$ years will be$............( 30 + x, 30 + 2x, 60 + 2x )$
View full solution →Sum of two numbers is $25.$ The smaller number is ............. if the greater number is x. ( x - 25, x + 25, 25 - x )
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