MCQ 511 Mark
Find the diagonal of a rhombus having an area of $270\ cm^2$ and other diagonal a $18\ cm.$
- A
$38\ cm$
- ✓
$30\ cm$
- C
$24\ cm$
- D
$28\ cm$
AnswerCorrect option: B. $30\ cm$
B. $30\ cm$
Solution:
The length of one diagonal is given as $d_1 = 18\ cm$
Let the length of the milling diagonal be $d_1$
We know that area of a rhombus is given by $\frac{1}{2}.\text{d}_1.\text{d}_2=\text{A}$
Putting the values in the above equation,
$\frac{1}{2}.\text{18}.\text{d}_2=\text{270}$
$\Rightarrow\text{d}_2 = \frac{270}{9}$
$\Rightarrow\text{d}_1 = 30\text{cm}$
View full question & answer→MCQ 521 Mark
A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square$?$
- A
$\frac{3}{4}$ of original square.
- ✓
$\frac{1}{2}$ of original square.
- C
$\frac{1}{4}$ of original square.
- D
$\frac{2}{3}$ of original square.
AnswerCorrect option: B. $\frac{1}{2}$ of original square.
Let a be the side of a square sheet.
Then, area of bigger square sheet $a^2...(i)$
Now, we make the circle of maximum possible size from it.
Then, the radius of circle $=\frac{\text{a}}{2} \ ...(\text{ii})$
So, its diameter $(d) =2\times\frac{\text{a}}{2}=\text{a}$
Now any square in a circle of maximum size will have the length of diagonal equal to the diameter of circle.
i.e. diagonal of square made inside the circle $= a$
So, the side of this square $=\frac{\text{a}}{\sqrt{2}}$ [$\because$ diagonal = side $\sqrt{2}$]
$\therefore$ Area of this square $=\frac{\text{a}^2}{2} \ ...(\text{iii})$
From Eqs. $(i)$ and $(iii),$
Area of this square is $\frac{1}{2}$ of original square. View full question & answer→MCQ 531 Mark
Area of the square with side-length $'a'$ is:
- A
$2a$
- B
$4a$
- C
$\frac{\text{a}}{2}$
- ✓
$a^2$
View full question & answer→MCQ 541 Mark
The area of a rhombus whose diagonals are of lengths $10\ cm$ and $8.2\ cm$ is:
- ✓
$41\ cm^2$
- B
$82\ cm^2$
- C
$410\ cm^2$
- D
$820\ cm^2$
AnswerCorrect option: A. $41\ cm^2$
A. $41\ cm^2$
Solution:
Area of rhombus $=\frac{1}{2}\text{d}_1\text{d}_2$
$\text{A}= \frac{1}{2}\times 10\times8.2$
$\text{A}=41\text{cm}^2$
View full question & answer→MCQ 551 Mark
If a cuboidal box has height, length and width as $20\ cm, 15\ cm$ and $10\ cm$ respectively. Then its total surface area is:
- A
$1100\ cm^2$
- B
$1200\ cm^2$
- ✓
$1300\ cm^2$
- D
$1400\ cm^2$
AnswerCorrect option: C. $1300\ cm^2$
C. $1300\ cm^2$
Solution:
Total surface area $= 2(20 \times 15 + 20 \times 10 + 10 \times 15)$
Total surface area $= 2(300 + 200 + 150)$
$= 1300\ cm^2$
View full question & answer→MCQ 561 Mark
What is the curved surface area of a cone of radius $3\ cm\ \&$ height $4\ cm?$
- A
$17\pi\text{cm}^3$
- B
$16\pi\text{cm}^3$
- ✓
$15\pi\text{cm}^3$
- D
$14\pi\text{cm}^3$
AnswerCorrect option: C. $15\pi\text{cm}^3$
$15\pi\text{cm}^3$
View full question & answer→MCQ 571 Mark
The area of a square of side $a$ is:
View full question & answer→MCQ 581 Mark
Which of the following is equal to $1$ kiloliter$?$
- A
$1000$ milliliters
- B
$100$ dm$^3$
- C
$1$ dm$^3$
- ✓
$1000$ dm$^3$
AnswerCorrect option: D. $1000$ dm$^3$
$1$ Kilo Litre = $1000$ Litre $= 1000dm^3$
$1$ Litre $(L)$ $= 1dm^3$
$10$ Litre $(L)$ = $1$ Deca Litre (dal) $= 10dm^3$
$100$ Litre $(L)$ = Hecto Litre (hl) $= 100dm^3$
$1000$ Litre $(L)$ = $1$ Kilo Litre (kl) $= 1000dm^3$
$1000000$ Litre $(L)$ = $1$ Mega Litre (Ml) $= 1000000dm^3 = 1dam$
View full question & answer→MCQ 591 Mark
A trapezium shaped cardboard is having its parallel sides as $20\ cm$ and $24\ cm.$ What will be the area of that cardboard if one of the non-parallel side $18\ cm$ and the perpendicular distance between the parallel sides is 16cm?
- A
$392\ cm^2$
- B
$372\ cm^2$
- ✓
$352\ cm^2$
- D
$300\ cm^2$
AnswerCorrect option: C. $352\ cm^2$
C. $352\ cm^2$
Solution:
We know that, Area of trapezium $(\text{A})=\frac{1}{2}\text{h}(\text{a+b)}$
Hence, we don't need the length of any of the non-parallel side.
Here, $h = 16\ cm$
$a = 20\ cm$
$b = 24\ cm$
$(\text{A})=\frac{1}{2}\times16\times({20+24)}$
$(\text{A})=8\times44$
$(\text{A})=352\text{cm}^2$
View full question & answer→MCQ 601 Mark
Two boxes are need to be constructed. If the dimensions of the first box is $70cm \times 50cm \times 60cm$ and the dimensions of the second box is $60cm \times 60cm \times 60cm.$ Find out which box requires more amount of material to be made?
- ✓
- B
- C
Both will be using same amount of material.
- D
Less information is given.
AnswerThe box having more surface area will require more amount of material to be made.
Total surface area of a cuboid is given by $2(1 h+ bh + lb )$
For the first box,
$1=70 cm $
$b =50 cm $
$h =60 cm$
Total surface area $=2(70 \times 60+50 \times 60+70 \times 50)$
$=2(4200+3000+3500) $
$=21400 cm^2$
The second box is actually a cube as all the side are equal.
Total surface area of a cube is given by $6(\text { side })^2$
$=6 \times 60^2 $
$=21600 cm^2$
The second box, i.e, the cube will require more amount of material to be made.
View full question & answer→MCQ 611 Mark
Tick the correct answer in the following: In the given figure, $AB\ || \ DC$ and $\text{AB}\perp\text{DC}$ If $DC = 7\ cm, BC = 10\ cm, AB = 13\ cm$ and $\text{CL}\perp\text{AB},$ the area of trap. $ABCD$ is:
- A
$84\ cm^2$
- B
$72\ cm^2$
- ✓
$80\ cm^2$
- D
$91\ cm^2$
AnswerCorrect option: C. $80\ cm^2$
C. $80\ cm^2$
Solution:
$D C=7 cm, B C=10 cm, A B=13 cm$
$CL \perp AB$
$A D=D C=7 cm$
and LB - $13-7=6 cm$
In right $\triangle BCE$,
$B C^2=C E^2+E B^2 \Rightarrow(10)^2=C E^2+(6)^2 $
$\Rightarrow 100=C E^2+36 $
$\Rightarrow C E^2=100-36=64=(8)^2 $
$\therefore C F=8 cm$
Now area of trap. $ABCD \frac{1}{2}( AB + CD ) \times CE$
$=\frac{1}{2}(13+7) \times 8 cm^2 $
$=\frac{1}{2} \times 20 \times 8=80 cm^2$ View full question & answer→MCQ 621 Mark
The sides of a triangle are $11\ cm, 15\ cm$ and $16\ cm.$ The altitude to largest side is:
AnswerCorrect option: B. $\frac{15\sqrt{7}}{4}\text{cm}$
$\frac{15\sqrt{7}}{4}\text{cm}$
View full question & answer→MCQ 631 Mark
What is the volume of a cuboid whose dimensions are $5cm \times 3cm \times 2cm?$
- A
$24cm^3$
- B
$20cm^3$
- ✓
$30cm^3$
- D
$17cm^3$
AnswerCorrect option: C. $30cm^3$
C. $30cm^3$
View full question & answer→MCQ 641 Mark
The dimensions of a godown are $40m, 25m$ and $10m.$ If it is filled with cuboidal boxes each of dimensions $2m \times 1.25m \times 1m,$ then the number of boxes will be:
- A
$1800$
- B
$2000$
- ✓
$4000$
- D
$8000$
AnswerCorrect option: C. $4000$
C. $4000$
Solution:
Given, dimensions of a godown are $40m, 25m$ and $10m.$
Volume of godown $= 40 \times 25 \times 10$
$= 10000m^3$
Now, volume of each cuboidal box $= 2 \times 1.25 \times 1$
$= 2.5m^3$
$\therefore$ The number of boxes, that can be filed in the godown $=\frac{\text{Volume of godown}}{\text{Volume of each cuboidal box}}$
$=\frac{10000}{2.5}=4000$
View full question & answer→MCQ 651 Mark
The surface area of a cuboid of length $l,$ breadth $b$ and height $h$ is:
- A
$lbh$
- B
$lb + bh + hl$
- ✓
$2(lb + bh + hl)$
- D
$2(l + b)h$
AnswerCorrect option: C. $2(lb + bh + hl)$
$2(lb + bh + hl)$
View full question & answer→MCQ 661 Mark
What is the total surface area of a cuboid of dimensions $4cm, 5cm$ & $6cm?$
- A
$142cm^2$
- B
$144cm^2$
- C
$146cm^2$
- ✓
$148cm^2$
AnswerCorrect option: D. $148cm^2$
D. $148cm^2$
View full question & answer→MCQ 671 Mark
A rectangular field has its length and breadth in the ratio $5 : 3$. Its area is $3.75$ hectares. The cost of fencing it at $Rs. 5$ per meter is:
- ✓
$Rs. 4000$
- B
$Rs. 500$
- C
$Rs. 400$
- D
$Rs. 1000$
AnswerCorrect option: A. $Rs. 4000$
$Rs.4000$
View full question & answer→MCQ 681 Mark
Area of a circle with radius $'r\ ’$ is:
AnswerCorrect option: B. $\pi\text{r}^2$
$\pi\text{r}^2$
View full question & answer→MCQ 691 Mark
The volume of a room is $80m^3.$ The area of the floor is $20m^2.$ The height of the room is:
AnswerD. $4m$
Solution:
$\text{Height} = \frac{80}{20} = 4\text{m}$
View full question & answer→MCQ 701 Mark
If each edge of a cube is doubled, its surface are will increase.
MCQ 711 Mark
The length of diagonal of a square whose area is $16900m^2$ is:
- A
$144m$
- B
$169m$
- C
- ✓
$130\sqrt{2}\text{m}$
AnswerCorrect option: D. $130\sqrt{2}\text{m}$
D. $130\sqrt{2}\text{m}$
View full question & answer→MCQ 721 Mark
The volume of a cuboid of length $l,$ breadth $b$ and height $h$ is:
- ✓
$lbh$
- B
$lb + bh + hl$
- C
$2(lb + bh + hl)$
- D
$2(l + b)h$
View full question & answer→MCQ 731 Mark
$1L =$
- A
$10cm^3$
- B
$100cm^3$
- ✓
$1000cm^3$
- D
$10000cm^3$
AnswerCorrect option: C. $1000cm^3$
C. $1000cm^3$
View full question & answer→MCQ 741 Mark
If $R$ is the radius of the base of the hat, then the total outer surface area of the hat is:
AnswerCorrect option: C. $2\pi\text{rh}+\pi\text{R}^2$
Given, a cylindrical hat with base radius $R$ and ris radius of the top surface.
Now, total surface area of hat $=$ Curved surface area $+$ Top surface area $+$ Base surface area
$=2\pi\text{rh}+\pi\text{r}^2+\pi(\text{R}^2-\text{r}^2)$
$=2\pi\text{rh}+\pi\text{r}^2+\pi\text{R}^2-\pi\text{r}^2$
$=2\pi\text{rt}+\pi\text{R}^2$
View full question & answer→MCQ 751 Mark
The total surface area of a cylinder of base radius $r$ and height $h$ is:
AnswerCorrect option: A. $2\pi\text{r}(\text{r + h})$
$2\pi\text{r}(\text{r + h})$
View full question & answer→MCQ 761 Mark
$1mm^3 =$
- ✓
$0.001cm^3$
- B
$0.01cm^3$
- C
$0.1cm^3$
- D
$1000cm^3$
AnswerCorrect option: A. $0.001cm^3$
A. $0.001cm^3$
View full question & answer→MCQ 771 Mark
What is the lateral surface area of a cube of side $5cm?$
- A
$150cm^2$
- ✓
$100cm^2$
- C
$140cm^2$
- D
$130cm^2$
AnswerCorrect option: B. $100cm^2$
B. $100cm^2$
View full question & answer→MCQ 781 Mark
What is the area of a rhombus whose diagonals are of lengths $10cm$ & $8.2cm?$
- A
$24cm^2$
- ✓
$41cm^2$
- C
$42cm^2$
- D
$25cm^2$
AnswerCorrect option: B. $41cm^2$
B. $41cm^2$
View full question & answer→MCQ 791 Mark
A cylindrical box has $...........$ curved surface and $............$ circular faces, which are identical.
AnswerA cylindrical box having circular bases have identical top. One curved surface and two circular faces which are identical.
View full question & answer→MCQ 801 Mark
Volume of a cuboid of length $(l),$ width $ (w)$ and height $(h)$ is:
- ✓
$lbh$
- B
$lb + bh + hl$
- C
$2(lb + bh + hl)$
- D
$2(l + b)h$
View full question & answer→MCQ 811 Mark
The perimeter of a trapezium is $52cm$ and its nonparallel sides are each equal to $10cm$ and its altitude is $8cm.$ Its area is:
- A
$118cm^2$
- B
$112cm^2$
- C
$124cm^2$
- ✓
$128cm^2$
AnswerCorrect option: D. $128cm^2$
D. $128cm^2$
View full question & answer→MCQ 821 Mark
The area of the figure is:
- A
$8cm^2$
- B
$6cm^2$
- ✓
$12cm^2$
- D
$16cm^2$
AnswerCorrect option: C. $12cm^2$
C. $12cm^2$
Solution:
Area $= 6^2 = 12cm^2$
View full question & answer→MCQ 831 Mark
The volume of a cube whose edge is $3x$ is:
- ✓
$27x^3$
- B
$9x^3$
- C
$6x^3$
- D
$3x^3$
AnswerCorrect option: A. $27x^3$
A. $27x^3$
Solution:
We know that, the volume of a cube $=$ (Side)$^3$
$= a^3$
$= (3x)^3$[$\because$ a $= 3x,$ given]
$= 27x^2$
View full question & answer→MCQ 841 Mark
The area of a trapezium is $28cm^2$ and one of its parallel sides $6cm.$ If its altitude is $4cm$ then its other parallel side is:
View full question & answer→MCQ 851 Mark
The height of a cuboid whose volume is $275cm^3$ and base area is $25cm^2$ is:
- A
$10cm$
- B
$12cm$
- C
$13cm$$
- ✓
$11cm$
AnswerCorrect option: D. $11cm$
D. $11cm$
Solution:
Volume of a cuboid $=$ Base area $\times$ Height
$\text{Height} =\frac{{\text{Volume}}}{{\text{Base area}}}$
$\text{H} =\frac{275}{25}$
$= 11\text{cm}$
View full question & answer→MCQ 861 Mark
The floor of a room is a square of side $6m.$ Its height is $4m.$ The volume of the room is:
- A
$140m^3$
- B
$142m^3$
- ✓
$144m^3$
- D
$145m^3$
AnswerCorrect option: C. $144m^3$
C. $144m^3$
Solution:
Volume $= 6 \times 6 \times 4 = 144m^3.$
View full question & answer→MCQ 871 Mark
The area of a parallelogram with length $(l)$ and breadth $(b)$ is:
- ✓
$lb$
- B
$\frac{1}{2}\text{lb}$
- C
$2lb$
- D
$(lb)^2$
View full question & answer→MCQ 881 Mark
What is the area of the largest triangle that can be fitted into a rectangle of length $l$ units and width $w$ units$?$
- ✓
$\frac{\text{lw}}{2}$
- B
$\frac{\text{lw}}{3}$
- C
$\frac{\text{lw}}{6}$
- D
$\frac{\text{lw}}{4}$
AnswerCorrect option: A. $\frac{\text{lw}}{2}$
Let $ABCD$ be the rectangle of length $l$ and width $w.$
Now, we construct a triangle of maximum area inside it in all possible ways.
$\because$ We know that,
Area of triangle $=\frac{1}{2}$ $×$ Base $×$ Height
So, for maximum area, base and height of maxmum, length is nooded.
Hero, maximum base length $= l$
and maximum height $= w$
$\therefore$ Area (maximum) of triangle $=\frac{1}{2}\times\text{l}\times\text{w}=\frac{\text{l}\times\text{w}}{2}$ sq units. View full question & answer→MCQ 891 Mark
The diagram has the shape of a:
MCQ 901 Mark
The area of a rhombus is $240cm^2$ and one of the diagonals is $16cm.$ Find the other diagonal.
- A
$16cm$
- ✓
$30cm$
- C
$20cm$
- D
$36cm$
AnswerCorrect option: B. $30cm$
B. $30cm$
Solution:
Area $= 240cm^2$
$d_1 = 16cm$
Area of rhombus $= \frac{1}{2}\text{d}_1\times\text{d}_2$
$240 = \frac{1}{2}\times16\times\text{d}_2$
$\text{d}_2 = \frac{480}{16}$
$= 30\text{cm}$
View full question & answer→MCQ 911 Mark
The height of a cuboid whose volume is $275cm^3$ and base area is $25cm^2$ is:
- A
$10cm$
- ✓
$11cm$
- C
$12cm$
- D
$13cm$
AnswerCorrect option: B. $11cm$
B. $11cm$
Solution:
Volume of a cuboid = Base area $\times$ Height
$\text{Height}=\frac{\text{Volume}}{\text{Base area}}$
$\text{H}= \frac{275}{25}$
$\text{H}=11\text{cm}$
View full question & answer→MCQ 921 Mark
A square plot of side $50cm$ consist of a garden and house of dimension $45m \times 30m.$ Calculate the total cost of the garden at the rate of $Rs. 60$ per $m^2.$
- A
$Rs. 69,000$
- ✓
$Rs. 55,500$
- C
$Rs. 70,000$
- D
$Rs. 65,500$
AnswerCorrect option: B. $Rs. 55,500$
B. $Rs. 55,500$
Solution:
Area of the square plot $= side^2 = 50^2 = 2500m^2$
Area of the house $= l \times w = 45 \times 35 = 1575m^2$
$\therefore$ Area on which garden needs to constructed $= 2500 - 1575 = 925m^2$
The total cost of garden at the rate of $60$ per $m^2 = 925 \times 60$
$= Rs. 55,500$
View full question & answer→MCQ 931 Mark
The area of a rhombus whose diagonals are of lengths $10cm$ and $8.2cm$ is:
- A
$82cm^2$
- B
$410cm^2$
- C
$820cm^2$
- ✓
$41cm^2$
AnswerCorrect option: D. $41cm^2$
D. $41cm^2$
Solution:
Area of rhombus $= \frac{1}{2}\text{d}^1\text{d}^2$
$\text{A}= \frac{1}{2}\times10\times8.2$
$\text{A} = 41\text{cm}^2$
View full question & answer→MCQ 941 Mark
The base area of a right circular cylinder is $16K\ cm^3.$ Its height is $5\ cm.$ Its curved surface area is:
- ✓
$40\pi\text{cm}^2$
- B
$30\pi\text{cm}^2$
- C
$20\pi\text{cm}^2$
- D
$100\pi\text{cm}^2$
AnswerCorrect option: A. $40\pi\text{cm}^2$
$\pi\text{r}^2=16\pi$
$\Rightarrow \text{r}=4\text{cm}$
$\therefore$ Curved surface area,
$=2\times\pi\times4\times5 = 40\pi\text{cm}^2$
View full question & answer→MCQ 951 Mark
Which of the following shape has two dimensions.
MCQ 961 Mark
Volume of a cylinder with base radius $= r$ and height $= h,$ is:
AnswerCorrect option: A. $\pi\text{r}^2\text{h}$
$\pi\text{r}^2\text{h}$
View full question & answer→MCQ 971 Mark
Find the area of the rhombus having the diagonals as $16cm$ and $27cm.$
- A
$210cm^2$
- ✓
$216cm^2$
- C
$208cm^2$
- D
$261cm^2$
AnswerCorrect option: B. $216cm^2$
B. $216cm^2$
Solution:
The length of one diagonal is given as $d_1 = 16cm$
The length of the other diagonal be $d_2 = 27cm$
We know that area of a rhombus is given by $\frac{1}{2}\text{d}_1.\text{d}_2=\text{A}$
Putting the values in the above equation,
$\text{A}=\frac{1}{2}\times{16}\times{27}$
$\text{A} = 8 \times 27$
$\text{A = 216cm}^2$
View full question & answer→MCQ 981 Mark
The perimeter of the figure is:
- A
$7\ cm$
- ✓
$14\ cm$
- C
$12\ cm$
- D
$24\ cm$
AnswerCorrect option: B. $14\ cm$
Perimeter $= 2(4 + 3) = 14\ cm.$
View full question & answer→MCQ 991 Mark
The area of a parallelogram of base $b$ and altitube $h$ is:
- A
$\frac{1}{2}\text{bh}$
- ✓
$\text{bh}$
- C
$\frac{1}{3}\text{bh}$
- D
$\frac{1}{4}\text{bh}$
AnswerCorrect option: B. $\text{bh}$
$\text{bh}$
View full question & answer→MCQ 1001 Mark
What is the area of a trapezium whose two parallel sides are $10cm$ & $12cm$ & height $4cm?$
- A
$42cm^2$
- B
$46cm^2$
- C
$48cm^2$
- ✓
$44cm^2$
AnswerCorrect option: D. $44cm^2$
D. $44cm^2$
View full question & answer→