M.C.Q. [1 Marks Each]

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

$p$

$1^2$
$2^2$ $3^2$ $4^2$

$q$

$1^3$

$2^3$

$2^3$

$4^3$

$r$	$2$	$5$	$10$	$25$	$50$
$s$	$25$	$10$	$5$	$2$	$0.5$

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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$p$	$1^2$	$2^2$	$3^2$	$4^2$
$q$	$1^3$	$2^3$	$2^3$	$4^3$

$u$	$2$	$4$	$6$	$9$	$12$
$v$	$18$	$9$	$6$	$4$	$3$

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

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