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

Direct and Inverse Proportion · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 15 questions.

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M.C.Q. [1 Marks Each]

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15 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Both x and y are in direct proportion, then$\frac{1}{\text{x}}$ and $\frac{1}{\text{y}}$ are:
  • A
    In indirect proportion.
  • ✓
    In indirect proportion.
  • C
    Neither in direct nor in inverse proportion.
  • D
    Sometimes in direct and sometimes in inverse proportion.
Answer
Correct option: B.
In indirect proportion.
If both x arid y are in directly proportion, then and are in inverse proportion.
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MCQ 21 Mark
Both $u$ and $v$ vary directly with each other. When $u$ is $10, v$ is $15,$ which of the following is not a possible pair of corresponding values of $u$ and $v?$
  • A
    $2$ and $3$
  • B
    $8$ and $12$
  • ✓
    $15$ and $20$
  • D
    $25$ and $37.5$
Answer
Correct option: C.
$15$ and $20$
Since,$u$ & $v$ vary directly, i.e., $\frac{\text{u}}{\text{v}}=\text{k} $ (constant)
If $u = 10$ and $v = 15$ then,$\frac{\text{u}}{\text{v}}=\frac{10}{15}=\frac{2}{3}$
In option $(b), \frac{8}{12} = \frac{2}{3}$
In option $(c), \frac{15}{20} = \frac{3}{4}$
In option $(d), \frac{25}{37.5} = \frac{2}{3}$
So, option $(c)$ is not possible pair of corresponding values $u$ & $v.$
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MCQ 31 Mark
100 persons had food provision for $24$ days. If $20$ persons left the place, the provision will last for
  • ✓
    $30$ days
  • B
    $\frac{96}{5}$days
  • C
    $120$ days
  • D
    $40$ days
Answer
Correct option: A.
$30$ days
$100$ persons had food provision for $24$ days $1$ person had food provision for $24 × 100$ i.e., $2400$ days.
If $20$ persons left the place, then remaining persons $= (100 − 20) = 80$
$80$ persons had food provision for$\frac{2400}{80}$ i.e,$30$ days.
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MCQ 41 Mark
Both $x$ and $y$ vary inversely with each other. When $x$ is $10, y$ is $6,$ which of the following is not a possible pair of corresponding values of $x$ and $y?$
  • A
    $12$ and $5$
  • B
    $15$ and $4$
  • C
    $25$ and $2.4$
  • ✓
    $45$ and $1.3$
Answer
Correct option: D.
$45$ and $1.3$
Since,$x$ & $y$ vary inversely,i.e., $\text{x}\times\text{y} = \text{k}$ (constant)
If $x = 10$ and $y= 6$
$xy=10×6=60$
In option $(a),12 × 5 = 60$
In option $(b),15 × 4 = 60$
In option $(c),25 × 2.4 = 60$
But in option$(d),45 × 1.3 = 58.3$
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MCQ 51 Mark
If the distance travelled by a rickshaw in one hour is $10\ km,$ then the distance travelled by the same rickshaw with the same speed in one minute is:
  • A
    $\frac{250}{9}\text{m}$
  • B
    $\frac{500}{9}\text{m}$
  • C
    $1000\text{m} $
  • ✓
    $\frac{500}{3}\text{m}$
Answer
Correct option: D.
$\frac{500}{3}\text{m}$
The distance travelled by a rickshaw in $1h = 10\ km$ The distance travelled by a rickshaw in $=\frac{10}{60}\text{km}=\frac{10\times1000}{60}\text{m}$ $=\frac{1000}{6}=\frac{500}{3}$
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MCQ 61 Mark
The number of teeth and the age of a person vary:
  • A
    Directly with each other.
  • B
    Inversely with each other.
  • C
    Neither directly nor inversely with each other.
  • ✓
    Sometimes directly and sometimes inversely with each other.
Answer
Correct option: D.
Sometimes directly and sometimes inversely with each other.
The number of teeth and the age of a person vary sometimes directly and sometimes inversely with each other, we cannot predict about the number of teeth wuth exactliy the age of aperson. it change with person-to-person.
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MCQ 71 Mark
In which of the following case, do the quantities vary directly with each other$?​​​​​$
  • ✓
    $x$
    $0.5$
    $2$
    $8$
    $32$
    $y$
    $2$
    $8$
    $32$
    $128$
  • B
    $p$
    $1^2$
    		 $2^2$ $3^2$ $4^2$
    $q$
    $1^3$
    $2^3$
    $2^3$
    $4^3$
  • C
    $r$
    $2$
    $5$
    $10$
    $25$
    $50$
    $s$
    $25$
    $10$
    $5$
    $2$
    $0.5$
  • D
    $u$
    $2$
    $4$
    $6$
    $9$
    $12$
    $v$
    $18$
    $9$
    $6$
    $4$
    $3$
Answer
Correct option: A.
$x$
$0.5$
$2$
$8$
$32$
$y$
$2$
$8$
$32$
$128$
​​​​​​
$x$
$0.5$
$2$
$8$
$32$
$y$
$2$
$8$
$32$
$128$

If we multiply $x$ with $4,$ we get the directly required result as same as shown in corresponding $y.$ In this case, as the value of $x$ increases, the value of $y$ also increases.
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MCQ 81 Mark
A truck needs $54$ litres of diesel for covering a distance of $297\ km.$ The diesel required by the truck to cover a distance of $550\ km$ is
  • ✓
    $100$ litres
  • B
    $50$ litres
  • C
    $25.16$ litres
  • D
    $25$ litres
Answer
Correct option: A.
$100$ litres
A truck needs 54 litres of diesel for covering a distance $= 297\ km$
in $1L,$ the truk can cover the distance $=\frac{297}{54} =5.5\text{Km}$
Thus, for $550\ km,$ the required diesel of truck $= \frac {550}{5.5}=100 \text{L}$
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MCQ 91 Mark
Which of the following vary inversely with each other?
  • A
    Speed and distance covered.
  • B
    Distance covered and taxi fare.
  • C
    Distance travelled and time taken.
  • ✓
    Speed and time taken.
Answer
Correct option: D.
Speed and time taken.
We know that, when we increases the speed, then the time taken by vehicle decrease.
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MCQ 101 Mark
Both $x$ and $y$ vary directly with each other and when $x$ is $10, y $ is $14,$ which of the following is not a possible pair of corresponding values of $x$ and $y?$
  • A
    $20$ and $35$
  • ✓
    $35$ and $25$
  • C
    $35$ and $49$
  • D
    $15$ and $21$
Answer
Correct option: B.
$35$ and $25$
Both $x$ and $y$ vary directly with each other. i.e.,$\text{x}\propto\text{y}$ If $x = 10$ and $y = 14$ so,$10 \propto 14 $ or $5 \propto 7$ This proportion is not follow in option.
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MCQ 111 Mark
Meenakshee cycles to her school at an average speed of $12\ km/h$ and takes $20$ minutes to reach her school. If she wants to reach her school in $12$ minutes, her average speed should be.
  • A
    $\frac{20}{3}$km/ h
  • B
    $16$km/ h
  • ✓
    $20$km/ h
  • D
    $15$km/ h
Answer
Correct option: C.
$20$km/ h
Given, speed of cycle $= 12\ km/ h$
Time taken by Meenakshee through cycle $= 20\ min$
Then, total distance cover $=\frac{12\times20}{60}= 4\ km = 4\ km [$distance $=$ time $\times$ speed$]$
If Meenakshee want to reach her school in $12\ min,$ then her cycle speed should be
$\frac{\frac{4}{12}}{60}$i.e., $20\ km/ h$
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MCQ 121 Mark
If two quantities $x$ and $y$ vary directly with each other, then
  • A
    $\frac{\text{x}}{\text{y}}$ remains constant.
  • B
    $x – y$ remains constant.
  • C
    $x + y$ remains constant.
  • ✓
    $x × y$ remains constant.
Answer
Correct option: D.
$x × y$ remains constant.
If two quantities $x$ and $y$ vary directly with each other, then$\frac{\text{x}}{\text{y}}= k =$ constant. Since, in direct proportion, both $x$ and $y$ increases or decreases together such a manner that the ratio of their corresponding value remains constant.
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MCQ 131 Mark
If two quantities $p$ and $q$ vary inversely with each other, then
  • A
    $\frac{\text{p}}{\text{q}}$ remains constant.
  • B
    $p+q$ remains constant.
  • ✓
    $p × q$ remains constant.
  • D
    $p – q$ remains constant.
Answer
Correct option: C.
$p × q$ remains constant.
If two quantities $p$ and $q$ vary inversely with each other, then $p × q$ remains constant. Since, in inverse proportion, an increase in $p$ cause a proportional decrease in $q$ and vice-versa.
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MCQ 141 Mark
By travelling at a speed of $48$ kilometres per hour, a car can finish a certain journey in $10$ hours. To cover the same distance in $8$ hours, the speed of the car should be
  • ✓
    $60\ km/ h$
  • B
    $80\ km/ h$
  • C
    $30\ km/ h$
  • D
    $40\ km/ h$
Answer
Correct option: A.
$60\ km/ h$
speed of the car $= 48 \ km/ h$ & times teken by car $= 10h$
Distence $=$ speed $×$ times $=48 \times 10=480\text{Km/ h}$
If car need to car $480\ km$ in $8h$, then
Requierd speed $=\frac{480}{8}=60\text{Km/ h}$
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MCQ 151 Mark
Assuming land to be uniformly fertile, the area of land and the yield on it vary
  • ✓
    Directly with each other.
  • B
    Inversely with each other.
  • C
    Neither directly nor inversely with each other.
  • D
    Sometimes directly and sometimes inversely with each other.
Answer
Correct option: A.
Directly with each other.
If land to be uniformly fertie,then the area of land and the yield on vary directly with each other.
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