Maths Class X Question Bank

Question 1 of 27

1. Question
1 point(s)
Diagonal of a cube of edge a is :
- $\sqrt3\times a $ units
- $\dfrac{\sqrt3}{2}\times a $ units
- $\dfrac{2}{\sqrt3}a $ units
- None of these
Correct

Incorrect

Hint

Diagonal of a cube of edge $a=\sqrt3a$
Question 2 of 27

2. Question
1 point(s)
If each edge of a cube is increased by 50%, the percentage increase in the surface area is :
- 0.25
- 0.5
- 0.75
- 1.25
Correct

Incorrect

Hint

When side is increased by 50%, side become $\dfrac{3}{2}a$
Surface area $=\dfrac{27}{2}a^2$
Percentage $=\dfrac{\dfrac{27}{2}a^2-6a^2}{6a^2}\times100=125\%$
Question 3 of 27

3. Question
1 point(s)
A surahi is the combination of :
- a sphere and a cylinder
- a hemisphere and a cylinder
- two hemispheres
- a cylinder and a cone
Correct

Incorrect

Hint

A surahi is the combination of a sphere and a cylinder.
Question 4 of 27

4. Question
1 point(s)
A funnel is combination of :
- a cone and a cylinder
- frustum of a cone and a cylinder
- a hemisphere and a cylinder
- a hemisphere and a cone
Correct

Incorrect

Hint

funnel is a combination of frustum a cone and a cylinder
Question 5 of 27

5. Question
1 point(s)
The shape of a bucket is usually in the form of:
- a cone
- frustum of a cone
- a cylinder
- a sphere
Correct

Incorrect

Hint

The shape of bucket is in the form of frustum of a cone.
Question 6 of 27

6. Question
1 point(s)
A flask used in the laboratory is the combination of:
- a cylinder and a cone
- a sphere and a cone
- a sphere and a cylinder
- frustum of a cone and a sphere
Correct

Incorrect

Hint

Flask is the combination of cylinder and cone.
Question 7 of 27

7. Question
1 point(s)
Welcome of material of a hollow right circular cylinder of height h and external and internal radii R and r respectively is :
- $\pi h(R^2-r^2) $
- $\pi^2rh\ (R^2-r^2) $
- $\pi r^2h\ (R^2+r^2) $
- $\pi Rh\ (R^2-r^2) $
Correct

Incorrect

Hint

Welcome on $h$ it is volume $\pi (R^2-r^2)h$
Question 8 of 27

8. Question
1 point(s)
The ratio of the volumes of two spheres is 8 : 27. The ratio between their surface areas is :
- 2 : 3
- 4 : 27
- 8 : 9
- 4 : 9
Correct

Incorrect

Hint

$\dfrac{\dfrac{4}{3}\pi r^3_1}{\dfrac{4}{3}\pi r^3_2}=\dfrac{8}{27}\\ \\ \dfrac{r_1}{r_2}=\dfrac{2}{3}\\ \\ \dfrac{4\pi r^2_1}{4\pi r_2^2}=\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}$
Question 9 of 27

9. Question
1 point(s)
On increasing each of the radius of the base and the height of a cone by 20%, its volume will be increased by
- 25%
- 40%
- 50%
- 72.8%
Correct

Incorrect

Hint

New radius $=r+\dfrac{r}{5}=\dfrac{6r}{5}$
New height $=h+\dfrac{h\times20}{100}=\dfrac{6h}{5}$
New volume $=\dfrac{1}{3}\pi\left(\dfrac{6r}{5}\right)^2\times\dfrac{6h}{5}$
Increased $=\dfrac{\dfrac{1}{3}\pi r^2 h\left(\dfrac{216}{125}-1\right)}{\dfrac{1}{3}\pi r^2h}\times100=72.8\%$
Question 10 of 27

10. Question
1 point(s)
The curved surface area of a cylinder is $264\ m^2 $ and its volume is $924\ m^3 $. The height of the pillar is :
- 3m
- 4m
- 6m
- 8m
Correct

Incorrect

Hint

$\dfrac{\pi r^2h}{2\pi rh}=\dfrac{924}{264}\ \Rightarrow \dfrac{r}{2}=\dfrac{7}{2}\Rightarrow r=7\ m\\ \\ 2\pi rh=264\\ \\ \Rightarrow 2\times\dfrac{22}{7}\times7\times h=264\\ \\ \Rightarrow h=6\ m$
Question 11 of 27

11. Question
1 point(s)
A cylindrical vessel of radius 5 cm and height 6 cm is full of water. A marble of radius 2.1 cm is put into the vessel. The volume of water which flows out of the vessel is :
- $471.4\ cm^3 $
- $19.4\ cm^3 $
- $55.4\ cm^3 $
- $38.8\ cm^3 $
Correct

Incorrect

Hint

$\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times\dfrac{22}{7}\times 2.1\times2.1\times 2.1\\ \\ =\dfrac{814.968}{21}=38.8\ cm^3$
Question 12 of 27

12. Question
1 point(s)
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of the new solid is :
- $4\pi r^2 $
- $6\pi r^2 $
- $3\pi r^2 $
- $8\pi r^2 $
Correct

Incorrect

Hint

$2\times2\pi r^2=4\pi r^2$
Question 13 of 27

13. Question
1 point(s)
A right circular cylinder of radius r cm and height h (h > 2r) just encloses a sphere of diameter :
- r cm
- 2r cm
- h cm
- 2h cm
Correct

Incorrect

Hint

Sphere of diameter = diameter of base of cylinder $\therefore d=2r$
Question 14 of 27

14. Question
1 point(s)
Volumes of two spheres are in the ratio 27 : 64. The ratio of their surface areas is :
- 3 : 4
- 4 : 3
- 9 : 16
- 16 : 9
Correct

Incorrect

Hint

$\dfrac{r_1}{r_2}=\sqrt[3]{\dfrac{27}{64}}=\dfrac{3}{4}$
Ratio of surface area $=\left(\dfrac{r_1}{r_2}\right)^2$
$=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}$
Question 15 of 27

15. Question
1 point(s)
In a right circular cone, the cross section made by a plane parallel to the base is a :
- circle
- frustum of a cone
- sphere
- hemisphere
Correct

Incorrect

Hint

A cone is a solid that has a circular base and a single vertex from cone definations, cross function is circle.
Question 16 of 27

16. Question
1 point(s)
The total surface area of a hemisphere of radius 7 cm is :
- $447\pi\ cm^2 $
- $239\pi\ cm^2 $
- $147\pi\ cm^2 $
- $174\pi\ cm^2 $
Correct

Incorrect

Hint

Total surface area $=3\pi\ r^2$
$=3\pi\ (7)^2\\ \\ =3\times49\pi\\ \\ =147\pi\ cm^2$
Question 17 of 27

17. Question
1 point(s)
The height of a conical tent is $14\ m $ and its floor area is $346.5\ m^2 $. The length of $1.1\ m $ wide canvas required to built the tent is :
- 490 m
- 525 m
- 665 m
- 860 m
Correct

Incorrect

Hint

$\pi r^2=346.5\\ \\ \Rightarrow \dfrac{22}{7}\times r^2=346.5\\ \\ \Rightarrow r^2=346.5\times\dfrac{7}{22}=\dfrac{441}{4}\\ \\ \Rightarrow r=\dfrac{21}{2}m\\ \\ l=\sqrt{\left(\dfrac{21}{2}\right)^2+14^2}=\dfrac{35}{4}\ m$
Area of convas $=\pi rl=\dfrac{22}{7}\times\dfrac{21}{2}\times\dfrac{35}{2}=577.5\ m^2$
Length of convas $=\dfrac{577.5}{1.1}=525\ m$
Question 18 of 27

18. Question
1 point(s)
The ratio of the total surface area to the lateral surface area of a cylinder with base diameter 160 cm and height 20 cm is :
- 1 : 2
- 2 : 1
- 3 : 1
- 5 : 1
Correct

Incorrect

Hint

Ratio $=\dfrac{2\pi r\ (r+h)}{2\pi rh}$
$=\dfrac{r+h}{h}=\dfrac{80+20}{20}=\dfrac{100}{20}=5:1$
Question 19 of 27

19. Question
1 point(s)
The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is :
- $30\pi\ cm^2 $
- $65\pi\ cm^2 $
- $80\pi\ cm^2 $
- None of these
Correct

Incorrect

Hint

$CSA=\pi rl\\ \\ l=\sqrt{r^2+h^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=13\\ \\ CSA=\pi \times 13\times5=65\ \pi\ cm^2$
Question 20 of 27

20. Question
1 point(s)
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is :
- $9.7\ cm^3 $
- $58.2\ cm^3 $
- $77.6\ cm^3 $
- $19.4\ cm^3 $
Correct

Incorrect

Hint

Radius $=\dfrac{4.2}{2}=2.1\ cm$
Volume $=\dfrac{1}{3}\times \dfrac{22}{7}\times2.1\times2.1\times4.2=19.404\ cm^3$
Question 21 of 27

21. Question
1 point(s)
A solid piece of iron in the form of a cuboid of dimensions $49\ cm \times 33\ cm \times 24\ cm$ is moulded to form a solid sphere. The radius of the sphere is :
- 21 cm
- 23 cm
- 25 cm
- 19 cm
Correct

Incorrect

Hint

$49\times33\times24=\dfrac{4}{3}\pi r^3\\ \\ \Rightarrow r^3=9261\ \Rightarrow r=21\ cm$
Question 22 of 27

22. Question
1 point(s)
A cubical icecream brick of edge 22 cm is to be distributed among some children by filling the ice cream cones of radius 2 cm and height 7 cm up to its brim. How many children will get the icecream cones ?
- 163
- 263
- 363
- 436
Correct

Incorrect

Hint

$x\times\dfrac{1}{3}\pi r^2h=a^3\\ \\ \Rightarrow x\times\dfrac{1}{3}\times\dfrac{22}{7}\times2\times2\times7=22\times22\times22\\ \\ \Rightarrow x=121\times3=363\ \text{cones}$
Question 23 of 27

23. Question
1 point(s)
The radii of two circular ends of a bucket are 12 cm and 22 cm. If the height of the bucket is 35 cm, the capacity of the bucket is :
- 463.46 litres
- 33.7 litres
- 34.7 litres
- 31.7 litres
Correct

Incorrect

Hint

$\dfrac{1}{3}\pi h\ (R^3+r^3+Rr)\\ \\ =\dfrac{1}{3}\times\dfrac{22}{7}\times35\ [(22)^3+(12)^3+22\times12]\\ \\ =\dfrac{110}{3}\times (10648+1728+264)\\ \\ =\dfrac{110}{3}\times12640\\ \\ =\dfrac{463466.67}{1000}=463.467\ litres$
Question 24 of 27

24. Question
1 point(s)
The height of a cylinder is $14\ cm $ and its curved surface area is $264\ cm^2 $. The volume of the cylinder is :
- $296\ cm^3 $
- $396\ cm^3 $
- $3696\ cm^3 $
- $503\ cm^3 $
Correct

Incorrect

Hint

Volume $\pi r^2h$
$=264\times14=3696\ cm^3$
Question 25 of 27

25. Question
1 point(s)
The ratio between the radius of the base and the height of the cylinder is 2 : 3. If its volume is $1617\ cm^3 $, the total surface area of the cylinder is :
- $208\ cm^2 $
- $77\ cm^2 $
- $707\ cm^2 $
- $770\ cm^2 $
Correct

Incorrect

Hint

$V=\pi r^2h\\ \\ \Rightarrow \dfrac{22}{7}\times(4x^2)\times3x=1617\\ \\ \Rightarrow x^3=42.875\Rightarrow x=3.5\ cm\\ \\ TSA=2\pi rh+2\pi r^2\\ \\ =2\pi r\ (r+h)\\ \\ =2\times\dfrac{22}{7}\times7\ (17.5)=770\ cm^2$
Question 26 of 27

26. Question
1 point(s)
The diameters of the ends of a frustum of a cone of height h are 2 R and 2r. The volume of the frustum of the cone is :
- $\dfrac{\pi h}{3}[R^2+r^2+Rr] $
- $\dfrac{\pi h}{3}[R^2+r^2-Rr] $
- $\dfrac{\pi h}{3}[R^2-r^2+Rr] $
- $\dfrac{\pi h}{3}[R^2-r^2-Rr] $
Correct

Incorrect

Hint

Volume of frustum of cone $=\dfrac{\pi h}{3}[R^2+r^2+Rr]$
Question 27 of 27

27. Question
1 point(s)
12 solid spheres of the same size are made by melting a solid metallic cylinder of base radius 1 cm and height 16 cm. The radius of each sphere is :
- 1 cm
- 3 cm
- 4 cm
- 5 cm
Correct

Incorrect

Hint

$12\times\dfrac{4}{3}\pi r^3=\pi\times 1^2\times16\\ \\ \Rightarrow r^3=1\Rightarrow r=1\ cm$