The perimeter of a rectangle is 42 m. If the area of the square formed on the diagonal
of the rectangle as its side is 1 1/12 % more than the area of the rectangle, find the
longer side of the rectangle.
Correct
Incorrect
Question 2 of 25
2. Question
1 points
At the rate of Rs. 2 per sq m, cost of painting a rectangular floor is Rs 5760. If the length of the floor is 80% more than its breadth, then what is the length of the floor?
Correct
Let the length and the breadth of the floor
be l m and b m respectively.
l = b + 80% of b = l + 0.8 b = 1.8b
Area of the floor = 5760/2 = 2880 sq m
l*b = 2880 i.e., l * l/1.8 = 2880
l = 72
Incorrect
Let the length and the breadth of the floor
be l m and b m respectively.
l = b + 80% of b = l + 0.8 b = 1.8b
Area of the floor = 5760/2 = 2880 sq m
l*b = 2880 i.e., l * l/1.8 = 2880
l = 72
Question 3 of 25
3. Question
1 points
A 7 m wide path is to be made around a circular garden having a diameter of 7 m.
What will be the area of the path in square metre?
Correct
Area of the path = Area of the outer circle –
Area of the inner circle = π{7/2 + 7}2 – π[7/2]2
= 308 sq m
Incorrect
Area of the path = Area of the outer circle –
Area of the inner circle = π{7/2 + 7}2 – π[7/2]2
= 308 sq m
Question 4 of 25
4. Question
1 points
The perimeter of a rectangle of length 62 cm and breadth 50 cm is four times
perimeter of a square. What will be the circumference of a semicircle whose
diameter is equal to the side of the given square?
Correct
Let the side of the square be a cm.
Parameter of the rectangle = 2(62 + 50) =
224 cm Parameter of the square = 56 cm
i.e. 4a = 56
So a = 14
Diameter, d of the semicircle = 14 cm
Circumference of the semicircle = 1/2(π)(r)+ d
= 1/2(22/7)(7) + 14 = 25 cm
Incorrect
Let the side of the square be a cm.
Parameter of the rectangle = 2(62 + 50) =
224 cm Parameter of the square = 56 cm
i.e. 4a = 56
So a = 14
Diameter, d of the semicircle = 14 cm
Circumference of the semicircle = 1/2(π)(r)+ d
= 1/2(22/7)(7) + 14 = 25 cm
Question 5 of 25
5. Question
1 points
A cone with diameter of its base as 30 cm is formed by melting a spherical ball of
diameter 10 cm. What is the approximate height of the cone?
Correct
Radius of cone = 30/2 = 15, radius of ball = 10/2 = 5
Volumes will be equal, so
Incorrect
Radius of cone = 30/2 = 15, radius of ball = 10/2 = 5
Volumes will be equal, so
Question 6 of 25
6. Question
1 points
A cylinder whose base of circumference is 6 m can roll at a rate of 3 rounds per second. How much distance will the cylinder cover in 9 seconds?
Correct
Distance covered in one round = 2 x π x r = 6 m
Distance covered in 1 second = 3 x 6 = 18m
So distance covered in 9 seconds = 18×9= 162 m
Incorrect
Distance covered in one round = 2 x π x r = 6 m
Distance covered in 1 second = 3 x 6 = 18m
So distance covered in 9 seconds = 18×9= 162 m
Question 7 of 25
7. Question
1 points
A container is formed by surmounting a hemisphere on a right circular cylinder of same radius as that of hemisphere. If the volume of the container is
and radius of cylinder is 6 m, then find the height of the container.
Correct
Volume of the container = Volume of the cylinder + Volume of the hemisphere
Volume of the container =
= π 36 (h + 4) = 576π
Solving we get h = 12
So the height of the container = 12 + 6 = 18m
Incorrect
Volume of the container = Volume of the cylinder + Volume of the hemisphere
Volume of the container =
= π 36 (h + 4) = 576π
Solving we get h = 12
So the height of the container = 12 + 6 = 18m
Question 8 of 25
8. Question
1 points
The radii of two cylinders are in the ratio 3: 2 and their curved surface areas are in the
ratio 3 : 5. What is the ratio of their volumes?
Correct
Incorrect
Question 9 of 25
9. Question
1 points
A right circular cone is exactly fitted inside a cube in such a way that the edges of the
base of the cone are touching the edge of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volumes of cube is 216 cm3 , what is the volume of the cone (approximately)?
Correct
radius of cone= a/2
volume(a3)=216 , hence a=6
r= 3 cm; height of the cone= 6cm (as it is
fitted in this cube of side 6 cm, hence its
height will also be 6 cm)
Volume of cone= 1/3 π*r2 * h =56
Incorrect
radius of cone= a/2
volume(a3)=216 , hence a=6
r= 3 cm; height of the cone= 6cm (as it is
fitted in this cube of side 6 cm, hence its
height will also be 6 cm)
Volume of cone= 1/3 π*r2 * h =56
Question 10 of 25
10. Question
1 points
If a square, circle and rectangle has same perimeter then which one of them has the maximum area?
Correct
In such case the area in descending order is: Circle> Square> Rectangle
Incorrect
In such case the area in descending order is: Circle> Square> Rectangle
Question 11 of 25
11. Question
1 points
A cylinder has some water at height 20 cm. If a sphere of radius 6 cm is poured into it
then find the rise in height of water if the radius of cylinder is 4 cm.
Correct
Volume of ball= volume of rising water in
the cylinder
4/3*6*6*6=4*4*h
h=18 cm
Incorrect
Volume of ball= volume of rising water in
the cylinder
4/3*6*6*6=4*4*h
h=18 cm
Question 12 of 25
12. Question
1 points
A sphere of 5 cm radius is melted and small sphere of radius 1 cm is made from it. Find
the number of sphere that can be made from it.
Correct
Incorrect
Question 13 of 25
13. Question
1 points
If radius of cone decrease by 50% and height increase by 20%. Then find the
percentage change in the volume.A) 70% decrease
Correct
Incorrect
Question 14 of 25
14. Question
1 points
The parameter of a square is equal to the perimeter of a rectangle of length 14 cm and
breadth 20 cm. Find the circumference of a semicircle (approx.) whose diameter is equal to the side of the square.
Correct
Parameter of square = 2 * (14+20) = 68cm
So side of square = 68/4 = 17 cm
So diameter of semicircle = 17 cm
So circumference of a semicircle = πr = 22/7 *17/2 = 27 cm
Incorrect
Parameter of square = 2 * (14+20) = 68cm
So side of square = 68/4 = 17 cm
So diameter of semicircle = 17 cm
So circumference of a semicircle = πr = 22/7 *17/2 = 27 cm
Question 15 of 25
15. Question
1 points
There are two circles of different radius such that radius of the smaller circle is three – sevens that of the larger circle. A square whose area equals 3969 sq cm has its side as thrice the radius of the larger circle. What is the circumference of the smaller circle?
Correct
Side of square = √3969 = 63 cm
So radius of larger circle = 1/3 * 63 = 21 cm
So radius of smaller circle = 3/7 * 21 = 9 cm
So circumference of smaller circle = 2 * 22/7 * 9= 56.5 cm
Incorrect
Side of square = √3969 = 63 cm
So radius of larger circle = 1/3 * 63 = 21 cm
So radius of smaller circle = 3/7 * 21 = 9 cm
So circumference of smaller circle = 2 * 22/7 * 9= 56.5 cm
Question 16 of 25
16. Question
1 points
The barrel of a fountain pen is cylindrical in shape which radius of base as 0.7 cm and is 5
cm long. One such barrel in the pen can be used to write 300 words. A barrel full of ink which has a capacity of 14 cu cm can be used to write how many words approximately?
Correct
Volume of the barrel of pen = πr2h = 22/7 *0.7*0.7 * 5 = 7.7 cu cm
A barrel which has capacity 7.7 cu cm can write 300 words
So which has capacity 14 cu cm can write =
300/7.7 * 14 = 545 words
Incorrect
Volume of the barrel of pen = πr2h = 22/7 *0.7*0.7 * 5 = 7.7 cu cm
A barrel which has capacity 7.7 cu cm can write 300 words
So which has capacity 14 cu cm can write =
300/7.7 * 14 = 545 words
Question 17 of 25
17. Question
1 points
A car has wheels of diameter 70 m. How many revolutions can the wheel complete in 20
minutes if the car is travelling at a speed of 110 m/s?
Correct
Radius of wheel = 70/2 = 35 cm
Distance travelled in one revolution = 2πr = 2 *22/7 * 35 = 220 cm
Let the number of revolutions made by wheel is x
So total distance travelled = distance travelled in
one revolution * number of revolutions
So total distance travelled = 220x cm
20 mins = 20*60 seconds
Speed of car = 220x/(20*60)
So 110 = 220x/(20*60)
Solve, x = 600
Incorrect
Radius of wheel = 70/2 = 35 cm
Distance travelled in one revolution = 2πr = 2 *22/7 * 35 = 220 cm
Let the number of revolutions made by wheel is x
So total distance travelled = distance travelled in
one revolution * number of revolutions
So total distance travelled = 220x cm
20 mins = 20*60 seconds
Speed of car = 220x/(20*60)
So 110 = 220x/(20*60)
Solve, x = 600
Question 18 of 25
18. Question
1 points
The diameters of the internal and external surfaces of a hollow spherical shell are 10cm
and 6 cm respectively. If it is melted and recasted into a solid cylinder of length 8/3 cm,
find the diameter of the cylinder.
Correct
Incorrect
Question 19 of 25
19. Question
1 points
The radii of two cylinders are in the ratio 4 : 5 and their curved surface areas are in the ratio 3 : 5. What is the ratio of their volumes?
Correct
Incorrect
Question 20 of 25
20. Question
1 points
The side of a square base of a pyramid increases by 20% and its slant height increases by 10%. Find the per cent change in Curved Surface Area.
Correct
C.S.A=1/2*(perimeter of base)*l20+10+(20*10)/100=32%
Incorrect
C.S.A=1/2*(perimeter of base)*l20+10+(20*10)/100=32%
Question 21 of 25
21. Question
1 points
A man wants to make small sphere of size 1 cm of radius from a large sphere of size
of 6 cm of radius. Find out how many such sphere can be made?
Correct
Volume of sphere1/volume of sphere 2=required number of sphere
=6*6*6/1*1*1=216
Incorrect
Volume of sphere1/volume of sphere 2=required number of sphere
=6*6*6/1*1*1=216
Question 22 of 25
22. Question
1 points
A sphere of radius 9 cm is dip into a cylinder who is filled with water upto 20 cm. If the radius of cylinder is 6 cm find the percentage change in height.
Correct
Volume of sphere= volume of cylinder
from height 20 cm to upwards.
4/3 * π * 9*9*9 = π * 6*6*h
h=9
new height=20+9=29
%change= 9/20*100=45%
Incorrect
Volume of sphere= volume of cylinder
from height 20 cm to upwards.
4/3 * π * 9*9*9 = π * 6*6*h
h=9
new height=20+9=29
%change= 9/20*100=45%
Question 23 of 25
23. Question
1 points
The length of the perpendicular drawn from any point in the interior of an equilateral
triangle to the respective sides are P1, P2 and P3. Find the length of each side of the
triangle.
Correct
Incorrect
Question 24 of 25
24. Question
1 points
Assume that a drop of water is spherical and its diameter is one tenth of a cm. A
conical glass has equal height to its diameter of rim. If 2048000 drops of water
fill the glass completely then find the height of the glass.
Correct
diameter of drop of water=1/10 =>
radius=1/20
volume of 204800 drop of
water=204800*4/3* π*1/20 *1/20*1/20 =
1024 π/3
Volume of cone=1024 π/3 = 1/3 * π *r2 * h
(r=h/2)
h=16
Incorrect
diameter of drop of water=1/10 =>
radius=1/20
volume of 204800 drop of
water=204800*4/3* π*1/20 *1/20*1/20 =
1024 π/3
Volume of cone=1024 π/3 = 1/3 * π *r2 * h
(r=h/2)
h=16
Question 25 of 25
25. Question
1 points
If the radius of a sphere increase by 4 cm then the surface area increase by 704 cm2 .
The radius of the sphere initially was?
