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Maths M.C.Q. [1 Marks Each]

Linear Equations in One Variable · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 14 questions.

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M.C.Q. [1 Marks Each]

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14 questions · auto-graded multiple-choice test.

MCQ 11 Mark
A linear equation in one variable has:
  • ✓
    Only one solution.
  • B
    Two solutions.
  • C
    More than two solutions.
  • D
    No solution.
Answer
Correct option: A.
Only one solution.
A linear equation in one variable has only one solution. e.g. Solution of the linear equation $ax + b = 0$ is unique, i.e. $\text{x}=-\frac{\text{b}}{\text{a}}.$
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MCQ 21 Mark
If $8x - 3 = 25 + 17x,$ then $x$ is:
  • A
    a fraction.
  • B
    an integer.
  • ✓
    a rational number.
  • D
    cannot be solved.
Answer
Correct option: C.
a rational number.
Given, $8x - 3 = 25 + 17x$
$8x - 17x = 25 + 3$
$-9x = 28$
$\text{x} = -\frac{28}{9}$
Hence, $x$ is a rational number.
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MCQ 31 Mark
The value of $x$ for which the expressions $3x - 4$ and $2x + 1$ become equal is:
  • A
    $-3$
  • B
    $0$
  • ✓
    $5$
  • D
    $1$
Answer
Correct option: C.
$5$
Given expresions $3x - 4$ and $2x + 1$ are equal.
Then, $3x - 4 = 2x + 13x - 2x = 1 + 4$ [transporting $2x$ to $LHS$ and $-4$ to $RHS$] $x = 5$
Hence, the value of $x$ is $5.$
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MCQ 41 Mark
Value of S in $\frac{1}{3}+\text{S}=\frac{2}{5}$
  • A
    $\frac{4}{5}$
  • ✓
    $\frac{1}{15}$
  • C
    $10$
  • D
    $0$
Answer
Correct option: B.
$\frac{1}{15}$
Given, $\frac{1}{3}+\text{S}=\frac{2}{5}$
$\text{S}=\frac{2}{5}-\frac{1}{3}$
$\text{S}=\frac{6-5}{15}$
$\text{S}=\frac{1}{15}$
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MCQ 51 Mark
If $\frac{5\text{x}}{3}-4=\frac{2\text{x}}{5}$ , then the numerical value of $2x - 7$ is:
  • A
    $\frac{19}{13}$
  • ✓
    $-\frac{13}{19}$
  • C
    $0$
  • D
    $\frac{13}{19}$
Answer
Correct option: B.
$-\frac{13}{19}$
Given, $\frac{5\text{x}}{3}-4=\frac{2\text{x}}{5}$
$\frac{5\text{x}}{3}-\frac{2\text{x}}{5}=4$
$\frac{25\text{x}-6\text{x}}{15}=4$
$19\text{x}=60$
$\frac{19\text{x}}{19}=\frac{60}{19}$
$\text{x}=\frac{60}{19}$
$\text{Now, }2\text{x}-7=2\times\frac{60}{19}-7$
$\frac{120-133}{19}=-\frac{13}{19}$
Hence, the numerical value of $2x - 7$ is $-\frac{13}{19}.$
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MCQ 61 Mark
Arpita’s present age is thrice of Shilpa. If Shilpa’s age three years ago was $x$. Then Arpita’s present age is:
  • A
    $3(x - 3)$
  • B
    $3x + 3$
  • C
    $3x - 9$
  • ✓
    $3(x + 3)$
Answer
Correct option: D.
$3(x + 3)$
Given, Shilpa’s age three years ago $= x$
Then, Shilpa’s present age $= (x + 3)$
Arpita’s present age $3 \times $ Shilpa’s present age $= 3 (x + 3)$
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MCQ 71 Mark
The solution of which of the following equations is neither a fraction nor an integer:
  • A
    $3x + 2 = 5x + 2$
  • B
    $4x - 18 = 2$
  • ✓
    $4x + 7 = x + 2$
  • D
    $5x - 8 = x + 4$
Answer
Correct option: C.
$4x + 7 = x + 2$
$a.$ Given linear equation is $3x + 2 = 5x + 2$
$3x - 5x = 2 - 2$
$-2x = 0$
$\frac{-2\text{x}}{-2}=\frac{0}{-2}$
$x = 0$
Hence, $x = 0$ is an integer.
$b.$ Given linear equation is
$4x - 18 = 2$
$4x = 2 + 18$
$4x = 20$
$\frac{4\text{x}}{4}=\frac{20}{4}$
$x = 5$
Hence, $x = 5 $is a positive integer.
$c.$ Given linear equation is
$4x + 7 = x + 2$
$4x - x = 2 - 7$
$3x = -5$
$\text{x}=-\frac{5}{3}$
Hence, $\text{x}=-\frac{5}{3}$ is neither a fraction nor an integer.
$d.$ Given linear equation is
$5x - 8 = x - 4$
$5x - x = 4 + 8$
$4x = 12$
$\frac{4\text{x}}{4}=\frac{12}{4}$
$x = 3$
Hence, $x = 3$ is a positive integer.
Option $(c)$, satisfies the condition.
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MCQ 81 Mark
The sum of three consecutive multiples of $7$ is $357$. Find the smallest multiple.
  • ✓
    $112$
  • B
    $126$
  • C
    $119$
  • D
    $116$
Answer
Correct option: A.
$112$
Let the three consecutive multiplies of $7$ be $7x, (7x + 7), (7x + 14)$ where $x$ is a natural number.
According to question,
$7x + (7x + 7) + (7x + 14) = 357$
$21x + 21 = 357$
$21(x + 1) = 357$
$\frac{21(\text{x}+1)}{21}=\frac{357}{21}$
$x + 1 = 17$
$x = 17 - 1$
$x = 16$
Hence, the smallest multiple of $7$ is $7 \times 16$ i.e., $112.$
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MCQ 91 Mark
$-\frac{4}{3}\text{y}=-\frac{3}{4}$, then $y = ?$
  • A
    $-\Big(\frac{3}{4}\Big)^2$
  • B
    $-\Big(\frac{4}{3}\Big)^2$
  • ✓
    $\Big(\frac{3}{4}\Big)^2$
  • D
    $\Big(\frac{4}{3}\Big)^2$
Answer
Correct option: C.
$\Big(\frac{3}{4}\Big)^2$
Given, $-\frac{4}{3}\text{y}=-\frac{3}{4}$
$\text{y}=-\frac{3}{4}\times-\frac{3}{4}$
$\text{y}=\Big(\frac{3}{4}\Big)^2$
Hence, the value of y is $\Big(\frac{3}{4}\Big)^2.$
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MCQ 101 Mark
Linear equation in one variable has:
  • A
    Only one variable with any power.
  • B
    Only one term with a variable.
  • ✓
    Only one variable with power 1.
  • D
    One constant term.
Answer
Correct option: C.
Only one variable with power 1.
Linear equation in one variable has only one variable with power $1.$
e.g. $3x + 1 = 0, 2y - 3 = 7$ and $z + 9 = -2$ are the linear equations in one variable.
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MCQ 111 Mark
If $a$ and $b$ are positive integers, then the solution of the equation $ax = b$ has to be always:
  • ✓
    Positive.
  • B
    Negative.
  • C
    One.
  • D
    Zero.
Answer
Correct option: A.
Positive.
If ax = b, then $\text{x}=\frac{\text{b}}{\text{a}}$
Since, a and b are positive integers. So, $\frac{\text{b}}{\text{a}}$ is also positive integer.
Hence, the solution of the given equation has to be always positive.
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MCQ 121 Mark
The solution of the equation $ax + b = 0$ is:
  • A
    $\text{x}=\frac{\text{a}}{\text{b}}$
  • B
    $\text{x}=-\text{b}$
  • ✓
    $\text{x}=-\frac{\text{b}}{\text{a}}$
  • D
    $\text{x}=\frac{\text{b}}{\text{a}}$
Answer
Correct option: C.
$\text{x}=-\frac{\text{b}}{\text{a}}$
Given equation is
$ax + b = 0$
$ax = -b$
$\frac{\text{ax}}{\text{a}}=-\frac{\text{b}}{\text{a}}$
$\text{x}=-\frac{\text{b}}{\text{a}}$
Hence, the solution of the equation $ax + b = 0$ is $\text{x}=-\frac{\text{b}}{\text{a}}$
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MCQ 131 Mark
The shifting of a number from one side of an equation to other is called:
  • ✓
    Transposition.
  • B
    Distributivity.
  • C
    Commutativity.
  • D
    Associativity.
Answer
Correct option: A.
Transposition.
The shifting of a number from one side of an equation to other side is called transposition.
e. g. $x + a = 0$ is the equation, $x = -a$
Here, number $'a'$ shifts from left hand side to right hand side.
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MCQ 141 Mark
Which of the following is a linear expression:
  • A
    $ x^2+1 $
  • B
    $ y+y^2 $
  • C
    $ 4 $
  • ✓
    $ 1+z $
Answer
Correct option: D.
$ 1+z $
We know that, the algebraic expression in one variable having the highest power of the variable as $1$, is known as the linear expression.
Here, $1 + z$ is the only linear expression, as the power of the variable $z$ is $1.$
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