MCQ 11 Mark
Mark $(\checkmark )$ against the correct answer in the following: The area of a square lawn of side $15m$ is:
- A
$ 60 m^2 $
- ✓
$ 225 m^2 $
- C
$ 45 m^2 $
- D
$ 120 m^2 $
AnswerCorrect option: B. $ 225 m^2 $
Side of the square lawn $= 15m$
Area of the square lawn $= ($Side$)^2$
$= (15)^2m^2$
$= 225 m^2 $
View full question & answer→MCQ 21 Mark
Mark $(\checkmark)$ against the correct answer in the following: The area of a rectangular carpet is $120m^2$ and its perimeter is $46m$. The length of its diagonal is:
Hint: $l + b = 23$ and $lb = 120$ Diagonal $=\sqrt{\text{l}^2+\text{b}^2}=\sqrt{289}$ $=\sqrt{17\times17}=17$
AnswerArea of rectangular carpet $= 120cm^2$
Perimeter $= 46m$
Now $2(l + b)$
$= 46m$
$\Rightarrow \text{l}+\text{b}=\frac{46}{2}=23$
and $lb = 120$
$\therefore (\text{l}-\text{b})^2=(\text{l}+\text{b})^2-4\text{lb}$
$=(23)^2-4\times120$
$=529-480$
$=49=(7)^2$
$\therefore \text{l}-\text{b}=7$
and $l + b = 23$
Adding we get, $2l = 30$
$\Rightarrow \text{l}=\frac{30}{2}$
$=15$
$\therefore b = 23 - 15 = 8$
Now diagonal $=\sqrt{\text{l}^2+\text{b}^2}$
$=\sqrt{(15)^2+(8)^2}$
$=\sqrt{225+64}$
$=\sqrt{289}$
$=17\text{m}$
View full question & answer→MCQ 31 Mark
Mark $(\checkmark )$ against the correct answer in the following: The area of a square is $256\ cm^2$. The perimeter of the square is:'
- A
$16\ cm$
- B
$32\ cm$
- C
$48\ cm$
- ✓
$64\ cm$
AnswerCorrect option: D. $64\ cm$
Let one side of the square be $x \ cm.$
Area of the square $= (Side)^2\ cm^2$
$= x^2$ $cm^2$
It is given that the area of the square is $256\ cm^2$
$\Rightarrow \text{x}^2=256$
$\Rightarrow \text{x}=\sqrt{256}$
$=\pm16$
We know that the side of a square cannot be negative.
So, we will neglect $-16$
Therefore, the side of the square is $16\ cm$
Perimeter of the square $= (4 \times $ side)
$= (4 \times 16)cm$
$= 64\ cm$
View full question & answer→MCQ 41 Mark
Mark $(\checkmark)$ against the correct answer in the following: The length of the diagonal of a square is $20\ cm$. Its area is:
- A
$400cm^2$
- ✓
$200cm^2$
- C
$300cm^2$
- D
$100\sqrt{2}\text{cm}^2$
AnswerCorrect option: B. $200cm^2$
Length of diagonal of a square $= 20\ cm$
Its area $=\Big(\frac{\text{diagonal}}{\sqrt{2}}\Big)^2$
$=\frac{(20)^2}{2}=\frac{400}{2}$
$=200\text{cm}^2$
View full question & answer→MCQ 51 Mark
Mark $(\checkmark)$ against the correct answer in the following: A lane $150m$ long and $9m$ wide is to be paved with bricks, each measuring $22.5\ cm$ by $7.5\ cm$. How many bricks are required?
- A
$65000$
- B
$70000$
- C
$75000$
- ✓
$80000$
AnswerCorrect option: D. $80000$
Length of the lane $= 150m$
Breadth of the lane $= 9m$
Area of the lane $= (150 \times 9)m^2$
$= 1350m^2$
Area of the brick $= 22.5\ cm \times 7.5\ cm$
$= 168.75\ cm^2$
$=\frac{168.75}{10000}\text{m}^2$
$=0.016875\text{m}^2$
$\therefore$ Number of bricks required $=\frac{\text{Area of lane}}{\text{Area of brick}}$
$=\frac{1350}{0.016875}$
$=1350\times \frac{1000000}{46875}$
$=80000$
View full question & answer→MCQ 61 Mark
Mark $(\checkmark )$ against the correct answer in the following: The area of a rectangle is $126m^2$ and its length is $12m$. The breadth of the rectangle is:
- A
$10m$
- ✓
$10.5m$
- C
$11m$
- D
$11.5m$
AnswerCorrect option: B. $10.5m$
Let the breadth of the rectangle be $x m$
Length of the rectangle $= 12m$
Area of the rectangle $= 126m^2$
Area of the rectangle $= ($length $\times$ breadth$)$sq$-$units
$= (12 \times x)m^2$
It is given that the area of the rectangle is $126m^2$
$\Rightarrow 12\text{x}=126$
$\Rightarrow \text{x}=\frac{126}{12}$
$=10.5$
So, the breadth of the rectangle is $10.5m.$
View full question & answer→MCQ 71 Mark
Mark $(\checkmark)$ against the correct answer in the following: The cost of fencing a rectangular field at $Rs. 30$ per meter is $Rs. 2400$. If the length of the field is $24m,$ then its breadth is:
AnswerTotal cost of fencing $= Rs. 2400$
Rate $= Rs. 30$ per m
Perimeter of the rectangular field $=\frac{2400}{30}$
$= 80m$
$\therefore$ Length + breadth $=\frac{80}{2}$
$= 40m$
Length of field $= 24m$
$\therefore$ Breadth $= 40 - 24$
$= 16m$
View full question & answer→MCQ 81 Mark
Mark $(\checkmark)$ against the correct answer in the following: The diameter of a circle is $7\ cm$, its circumference is:
- A
$44\ cm$
- ✓
$22\ cm$
- C
$28\ cm$
- D
$14\ cm$
AnswerCorrect option: B. $22\ cm$
Circumference $=\pi \text{d}$
$=\frac{22}{7}\times 7$
$=22\text{cm}$a
View full question & answer→MCQ 91 Mark
Mark $(\checkmark)$ against the correct answer in the following: The sides of a rectangle are in the ratio $7 : 5$ and its perimeter is $96\ cm$. The length of the rectangle is:
- A
$21\ cm$
- ✓
$28\ cm$
- C
$35\ cm$
- D
$14\ cm$
AnswerCorrect option: B. $28\ cm$
Ratio in the sides of a rectangle $= 7 : 5$
and perimeter $= 96\ cm$
$\therefore $ Length + Breadth $=\frac{96}{2}=48\text{cm}$
Let length $= 7x$
Then breadth $= 5x$
$\therefore 7x + 5x = 48$
$\Rightarrow 12x = 48$
$\Rightarrow \text{x}=\frac{48}{12}$
$= 4$
Length of the rectangle $= 7x$
$= 7 \times 4$
$= 28\ cm$
View full question & answer→MCQ 101 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The circumference of a circle is $88 \ cm$. Its diameter is:
- ✓
$28\ cm$
- B
$42\ cm$
- C
$56\ cm$
- D
AnswerCorrect option: A. $28\ cm$
Diameter $=\frac{\text{Circumference}}{\pi}$
$=\frac{88\times7}{22}$
$=28\text{cm}$
View full question & answer→MCQ 111 Mark
Mark $(\checkmark )$ against the correct answer in the following: Perimeter of a square of side $16\ cm$ is:
- A
$256\ cm$
- ✓
$64\ cm$
- C
$32\ cm$
- D
$48\ cm$
AnswerCorrect option: B. $64\ cm$
Side of the square $= 16\ cm$
Perimeter of the square $= (4 \times $ side)
$= (4 \times 16)cm$
$= 64\ cm$
View full question & answer→MCQ 121 Mark
Mark $(\checkmark)$ against the correct answer in the following: The length of a rectangle is three times its width and the length of its diagonal is $6\ cm$. The perimeter of the rectangle is:
- ✓
$48\ cm$
- B
$36\ cm$
- C
$24\ cm$
- D
$24\sqrt{10}\text{cm}$
AnswerCorrect option: A. $48\ cm$
Let width of a rectangle $= x$
Then length $= 3x$
and diagonal $6\sqrt{10}\text{cm}$
$\therefore(3\text{x})^2+(\text{x})^2$
$=(6\sqrt{10})^2$
$9\text{x}^2+\text{x}^2=360$
$\Rightarrow 10\text{x}^2=360$
$\Rightarrow \text{x}^2=\frac{360}{10}$
$=36=(6)^2$
$\therefore$ Perimeter $= 2(l + b)$
$= 2(3x + x)$
$= 2 \times 4x = 8x$
$= 8 \times 6 = 48m$ View full question & answer→MCQ 131 Mark
Mark $(\checkmark)$ against the correct answer in the following: A room is $5m \ 40\ cm$ long and $4m \ 50\ cm$ broad, its area is:
- A
$23.4m^2$
- ✓
$24.3m^2$
- C
$25m^2$
- D
$98.01m^2$
AnswerCorrect option: B. $24.3m^2$
Length of a rectangular room $(l) = 5m 40\ cm = 5.4m$
and breadth $(b) = 4m 50\ cm$
$= 4.5m$
Area $= l \times b$
$= 5.4 \times 4.5m^2$
$= 24.3m^2$
View full question & answer→MCQ 141 Mark
Mark $(\checkmark)$ against the correct answer in the following: How many envelopes can be made out of a sheet of paper $72\ cm$ by $48\ cm$, if each envelope requires a paper of size $18\ cm$ by $12\ cm?$
AnswerLength of a sheet $(l) = 72 \ cm$
and breadth $(b) = 48 \ cm$
Area $= l x b = 72 \times 48 \ cm^2$
Area of paper for one envelope $= 18 \times 12\ cm^2$
No. of envelopes $=\frac{72\times 48}{18\times 12}=16$
View full question & answer→MCQ 151 Mark
Mark $(\checkmark)$ against the correct answer in the following: If the ratio between the length and perimeter of a rectangular plot is $1 : 3,$ then the ratio between the length and breadth of the plot is:
- A
$1 : 2$
- ✓
$2 : 1$
- C
$3 : 2$
- D
$2 : 3$
AnswerCorrect option: B. $2 : 1$
Ratio in length and perimeter of a rectangle $= 1 : 3$
Let length $= x,$
then perimeter $= 3x$
$\therefore$ Breadth $=\frac{3\text{x}}{2}-\text{x}=\frac{\text{x}}{2}$
$\therefore$ Ratio in length and breadth $=\text{x}:\frac{\text{x}}{2}$
$=2:1$
View full question & answer→MCQ 161 Mark
Mark $(\checkmark)$ against the correct answer in the following: The cost of fencing a rectangular field $34m$ long and $18m$ wide at $Rs. 22.50$ per metre is:
- A
$Rs. 2430$
- ✓
$Rs. 2340$
- C
$Rs. 2400$
- D
$Rs. 3340$
AnswerCorrect option: B. $Rs. 2340$
Length of a rectangular field $(l) = 34m$
and breadth $(b) = 18m$
Circumference $= 2(l + b)$
$= 2(34 + 18)m$
$= 2 \times 52= 104m$
Rate of fencing $= Rs. 22.50$ per m
Total cost $= Rs. 22.50 \times 104$
$= Rs. 2340$
View full question & answer→MCQ 171 Mark
Mark $(\checkmark )$ against the correct answer in the following: The area of a rectangle is $240m^2$ and its length is $16m$. Then, its breadth is:
AnswerLet the breadth of the rectangle be $x m.$
Length of the rectangle $= 16m$
Area of rectangle $= ($Length $\times $ Breadth$)$
$= (16 \times x)m^2$
It is given that the area of the rectangle is $240m^2$
$\Rightarrow 16\times\text{x}=240$
$\Rightarrow \text{x}=\frac{240}{16}$
$=15$
So, the breadth of the rectangle is $15m.$
View full question & answer→MCQ 181 Mark
Mark $(\checkmark)$ against the correct answer in the following: The area of a rectangle is $650\ cm^2$ and its breadth is $13\ cm$. The perimeter of the rectangle is:
- A
$63\ cm$
- B
$130\ cm$
- C
$100\ cm$
- ✓
$126\ cm$
AnswerCorrect option: D. $126\ cm$
Area of a rectangle $= 650\ cm^2$
and breadth $(b) = 13\ cm$
$\therefore$ Length (l) $=\frac{\text{Area}}{\text{Breadth}}$
$=\frac{650}{12}=50\text{cm}$
$\therefore$ Perimeter $= 2(l + b)$
$= 2(50 + 13)cm$
$= 2 \times 63$
$= 126\ cm$
View full question & answer→MCQ 191 Mark
Mark $(\checkmark)$ against the correct answer in the following: The cost of putting a fence around a square field at $Rs. 25$ per metre is $Rs. 2000$. The length of each side of the field is:
AnswerTotal cost of fencing around a square field $= Rs. 2000$
and rate $= Rs. 25$ per metre
$\therefore$ Circumference $=\frac{2000}{25}=80\text{m}$
$\therefore$ Length of each side $=\frac{80}{4}=20\text{m}$
View full question & answer→MCQ 201 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The diameter of a wheel of a car is $70\ cm$. How much distance will it cover in making $50$ revolutions?
- A
$350m$
- ✓
$110m$
- C
$165m$
- D
$220m$
AnswerCorrect option: B. $110m$
Circumference $=\pi \text{d}$
$=\frac{22}{7}\times 70$
$=220\text{cm}$
And distance in $50$ revolutions
$=\frac{22\times 50}{100}\text{m}$
$=110\text{m}$
View full question & answer→