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CBSE Questions for Class 11 Commerce Applied Mathematics Numerical Applications Quiz 9 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Numerical Applications
Quiz 9
If
6
painters can complete
9
drawing in
5
hours then
How many painters will make
18
drawing in
5
hours?
Report Question
0%
11
0%
12
0%
13
0%
14
Explanation
Let number of painters required for painting 18 drawing is
x
Now since no. of painters is directly proportion to no. of drawing
6
9
=
x
18
⇒
x
=
6
×
18
9
=
12
A single frame of
35
mm film is about three-quarters of an inch long. A film reel holds up to
1000
feet of film. Find the number of reels required for a
2
:
47
:
00
(
2
hr
47
min) film shot at
24
frames per second.
Report Question
0%
13
0%
14
0%
15
0%
16
Explanation
There are
12
inches in one foot, so a reel is
12
×
1
,
000
=
12
,
000
inches long. Set up a proportion to determine how many frames per reel:
=
1
f
r
a
m
e
3
4
=
12000
3
4
x
=
12000
Cross-multiply to get
3
4
x
=
12000
.
Divide both sides by
3
4
to get
x
=
16
,
000
frames per reel. Next, find the number of frames the film requires.
Convert the time to seconds.
There are
60
minutes in an hour, so
2
hours and
47
minutes is equal to
(
2
×
60
)
+
47
=
167
minutes.
There are
60
seconds in a minute, so there are
60
×
167
=
10020
seconds in this film.
If each second consists of
24
frames, then there are
24
×
10020
=
240480
frames in this film.
To determine the number of reels, divide by the number of frames per reel:
=
15.03
reels. Because
15
reels does not hold quite enough frames, the film requires
16
reels, which is (D).
The number of ways four boys can be seated around a round table in four chairs of different colours is:
Report Question
0%
24
0%
12
0%
23
0%
64
Explanation
Since the chair are of different colours, so you can treat it as linear permutation
So number of ways will be
4
!
=
24
A scanner can print at a rate of
5
pages per minute. Calculate the number of hours will it take to print
300
pages?
Report Question
0%
0.5
0%
1
0%
1.5
0%
3
Explanation
Scanner print
5
pages in
1
minute.
∴
number of hours required to print
300
pages would be
=
\dfrac{300}{5}=60
minute
=1
hour.
If
7
pipes fill a tank in
8
hours, then
4
pipes will fill it in ......... hours
Report Question
0%
14
0%
16
0%
18
0%
20
Explanation
No of pipes is inversely proportional to the taken to fill the tank
\therefore 7\times 8 = k = 4\times x \Rightarrow 56 = 4\times x \Rightarrow x = 14
If
4
persons do a work in
8
days then how many days it will take if
8
persons do the same work?
Report Question
0%
4
0%
16
0%
8
0%
32
Explanation
The no of persons (p) is inversely proportional to the no. of days (d). Hence
p\propto \dfrac {1}{d}
\Rightarrow p_{1}d_{1} = p_{2}d_{2}
Here,
p_{1} = 4, d_{1} = 8, p_{2} = 8, d_{2}
is unknown.
\Rightarrow 4\times 8 = 8d_{2}
\Rightarrow d_{2} = 4
.
Find the no. of pipes required to fill the tank in
16
hours.
Report Question
0%
\dfrac {5}{2}
0%
\dfrac {7}{2}
0%
7
0%
\dfrac {9}{2}
Explanation
7\times 8 = x \times 16 \Rightarrow x =\dfrac {7\times 8}{16} = \dfrac {7}{2}
A coastal geologist estimates that a certain countrys beaches are eroding at a rate of
1.5
feet per year.
According to the geologists estimate, how long will it take, in years, for the countrys beaches to erode
by
21
feet?
Report Question
0%
14
years
0%
12
years
0%
8
years
0%
15
years
Explanation
If the beaches are eroding at the rate of 1.5 feet per year, then for eroding by 21 feet, it will take
\frac {21}{1.5} = 14
years
An 11.2 gb image has been taken of the surface of Jupiter by a camera . A tracking station in Earth can receive data from the spacecraft at a data rate of
3
megabits per second for a maximum of
11
hours each day. If
1
gb equals
1,024
mb, find the maximum number of images that the tracking station can receive from the camera each day. (gb:
gigabits, mb: megabits)
Report Question
0%
3
0%
10
0%
56
0%
144
Explanation
Given: A tracking station in earth can received data from the spacecraft at a data rate
3
megabits per second for a maximum of
11
hour each day.
Then total data received per day
=
3\times 11\times 3600
megabits
Then total data received per day
=
\dfrac{118800}{1024}=116.01
gb
Then tricking station received images by camera
=
\dfrac{116.01}{11.02}=10.35
Then camera received image
=10
.
Jennilina's hobby is to paint the rooms at her college. At top speed, she could paint
5
identical rooms during one
6
-hour shift. Find the time it took her to paint each room.
Report Question
0%
50
minutes
0%
1
hour and
10
minutes
0%
1
hour and
12
minutes
0%
1
hour and
15
minutes
0%
1
hour and
20
minutes
Explanation
There are
60
minuet in
1
hour
So in
6
hours there are
=
6\times 60=360
minutes
So Jennilina takes
360
minutes to paint
5
rooms.
So she paint one room in
=
\dfrac{360}{5}=72
minutes.
72
minutes is equal to
1
hour and
12
minutes.
A square pyramid is inscribed in a cube of total surface area of
24
square cm such that the base of the pyramid is the same as the base of the cube. What is the volume of the pyramid?
Report Question
0%
\dfrac 13
0%
\dfrac 83
0%
6
0%
4
0%
8
Explanation
Given that total surface area of cube is
24
and cube has
6
faces. so the area of each face is
\dfrac {24}6 = 4
therefore the length of side of each face and the height of cube is
2
So the volume of pyramid is
\dfrac {lwh}3 = 2 \times 2 \times \dfrac 23 = \dfrac 83
Computer K can perform
x
calculations in
y
seconds and computer L can perform
r
calculations in
s
minutes. Find the number of calculations they can perform in
t
minutes by working together simultaneously.
Report Question
0%
t\left (\dfrac {x}{60y} + \dfrac {r}{s}\right )
0%
t\left (\dfrac {60x}{y} + \dfrac {r}{s}\right )
0%
t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )
0%
t\left (\dfrac {x}{y} + \dfrac {60r}{s}\right )
0%
60t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )
Explanation
Given, computer
K
can perform
x
calculations in
y
seconds and computer
L
can perform
r
calculations in s minutes.
Then computer
K
can do one calculation
=
\dfrac{60x}{y}
minutes
And
computer
L
can do one calculation
=
\dfrac{r}{s}
minutes
Then both computer
calculation
in
t
minutes
=
\left ( \dfrac{60x}{y}+\dfrac{r}{s} \right )t
Vasu can run
4
Km in
48
minutes. If Vikas can run twice as fast as Vasu, how many minutes does it take Vikas to run
6
Km?
Report Question
0%
24
0%
30
0%
36
0%
48
Explanation
Vasu takes
=\dfrac{48}{4}=12
minutes to run
1
km.
Vikas can run twice as fast as Vasu, means Vikas takes
6
min to run
1
km.
Hence, he takes,
= 6\times 6 = 36
min. to run
6
km.
Three men paint a house in 20 days. How many days do 30 men take to do the same?
Report Question
0%
3 days
0%
2 days
0%
60 days
0%
12 days
Explanation
Using
Work=men\times days
we can see that
Work=3\times 20=60
Since the work is same
60=30\times days
days=2
Therefore, Answer is
(B)
If 100! =
\displaystyle { 2 }^{ a }{ 3 }^{ b }{ 5 }^{ c }{ 7 }^{ d }...
, then
Report Question
0%
a=97
0%
\displaystyle b=\frac { 1 }{ 2 } \left( a+1 \right)
0%
\displaystyle c=\frac { 1 }{ 2 } b
0%
\displaystyle d=\frac { 1 }{ 3 } b
Explanation
i) no. of 2's in 100! are
\left [ \dfrac{100}{2} \right ]+\left [ \dfrac{100}{22} \right ]+\left [ \dfrac{100}{23} \right ]+\left [ \dfrac{100}{24} \right ]+\left [ \dfrac{100}{25} \right ]+\left [ \dfrac{100}{26} \right ]
= 50+25+12+6+3+1
= 97
ie
\boxed{a = 97}
ii) no of 3's 100! are
\left [ \dfrac{100}{3} \right ]+\left [ \dfrac{100}{3^{2}} \right ]+\left [ \dfrac{100}{3^{3}} \right ]+\left [ \dfrac{100}{3^{4}} \right ]
= 33+11+3+1 = \boxed{48 = 6}
iii) no of 5's in 100 ! are
\left [ \dfrac{100}{5} \right ]+\left [ \dfrac{100}{5^{2}} \right ] = 20+4 = \boxed{24 = c}
iv) no of 7's in 100 ! are
\left [ \dfrac{100}{7} \right ]+\left [ \dfrac{100}{7^{2}} \right ] = 14+2 = \boxed{16 =d}
\boxed{c = \dfrac{b}{2}}
&
\boxed{d = \dfrac{b}{3}}
If
20
men working together can finish a job in
20
days, find the number of days taken by
25
men of the same capacity to finish the job.
Report Question
0%
25
0%
20
0%
16
0%
12
Explanation
Using
Work=men\times days
we get
Work=20\times 20
Work=400
Now, work is same and number of days are to be calculated
400=25\times days
days=16
Therefore, the answer is
(C)
.
Riya can do
\displaystyle \frac{1}{12}
of a job in an hour, how many days will she take to complete the job?
Report Question
0%
12
0%
\displaystyle \frac{1}{12}
0%
\displaystyle \frac{1}{24}
0%
24
Explanation
Assuming Riya work 1
hour
per
day
and it is given that Riya can do
\dfrac{W}{12}
in an hour
So, she will take
12
hours
to complete the work and
Thus, take
12
days
to complete it as she works 1
hour
per
day
Therefore Answer is
(A)
Three pipes
A, B
and
C
can fill a tank from empty to full in
30
minutes,
20
minutes, and
10
minutes respectively. When the tank is empty, all the three pipes are opened.
A, B
and
C
discharge chemical solutions
P, Q
and
R
respectively. What is the proportion of the solution
R
in the liquid in the tank after
3
minutes?
Report Question
0%
\displaystyle\frac{5}{11}
0%
\displaystyle\frac{6}{11}
0%
\displaystyle\frac{7}{11}
0%
\displaystyle\frac{8}{11}
Explanation
Rate of filling the tank for A:
\dfrac{1}{30}
Rate of filling the tank for B:
\dfrac{1}{20}
Rate of filling the tank for C:
\dfrac{1}{10}
Part filled by
(A+B+C)
in
3
minutes
3\displaystyle\left(\displaystyle\frac{1}{30}+\frac{1}{20}+\frac{1}{10}\right)
=\displaystyle\left( 3\times \frac{11}{60}\right)=\frac{11}{20}
.
Part filled by C in
3
minutes
=\displaystyle\frac{3}{10}
.
\therefore
Required ratio
=\left(\displaystyle\frac{3}{10}\times \frac{20}{11}\right)=\displaystyle \frac{6}{11}
.
What is the average(arithmetic mean) of all the multiples of ten from
10
to
190
inclusive?
Report Question
0%
90
0%
95
0%
100
0%
105
0%
110
A
alone can do a piece of work in
6
days and
B
alone in
8
days.
A
and
B
undertook to do it for Rs.
3200
. With the help of
C
, they completed the work in
3
days. How much is to be paid to
C
?
Report Question
0%
Rs.
375
0%
Rs.
400
0%
Rs.
600
0%
Rs.
800
Explanation
C
's
1
day's work
=\cfrac{1}{3}-\left( \cfrac { 1 }{ 6 } +\cfrac { 1 }{ 8 } \right) =\cfrac { 1 }{ 3 } -\cfrac { 7 }{ 24 } =\cfrac { 1 }{ 24 }
.
A
's Wages:
B
's wages:
C
's wages
=\cfrac{1}{6}:\cfrac{1}{8}:\cfrac{1}{24}=4:3:1
.
\therefore
C
's share (for
3
days)
=
Rs.
\left( 3\times \cfrac { 1 }{ 24 } \times 3200 \right) =
Rs.
400
.
A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
Report Question
0%
Rs.
7.98
0%
Rs.
8
0%
Rs.
8.50
0%
Rs.
9
Explanation
Total quantity of petrol consumed in 3 years =
\begin{pmatrix}\dfrac{400}{7.50}+\dfrac{4000}{8}+\dfrac{4000}{8.50}\end{pmatrix}
litres
=
4000 \begin{pmatrix}\dfrac{2}{15}+\dfrac{1}{8}\dfrac{2}{17}\end{pmatrix}
litres
=
\begin{pmatrix}\dfrac{76700}{51}\end{pmatrix}
litres
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
\therefore
Average cost = Rs.
\begin{pmatrix}\dfrac{12000\times 51}{76700}\end{pmatrix}
= Rs.
\dfrac{6120}{767}
= Rs.
7.98
18
men can reap a field in
35
days. For reaping the same field in
15
days, how many men are required?
Report Question
0%
42
0%
28
0%
32
0%
40
Explanation
18 Men
\rightarrow
35 days.
1 Men
\rightarrow 35\times 18
days.
\therefore
Reaping in 15 days -
No. of men =
\frac{35\times 18}{15}= 42
men.
A, B
and
C
can do a piece of work in
20,30
and
60
respectively. In how many days can
A
do the work if he is assisted by
B
and
C
on every third day?
Report Question
0%
12
days
0%
15
days
0%
16
days
0%
18
days
Explanation
A
's
1
day's work
=\left( \cfrac { 1 }{ 20 } \times 2 \right) =\cfrac { 1 }{ 10 }
(A+B+C)
's
1
day's work
=\left( \cfrac { 1 }{ 20 } +\cfrac { 1 }{ 30 } +\cfrac { 1 }{ 60 } \right) =\cfrac { 6 }{ 60 } =\cfrac { 1 }{ 10 }
Work done in
3
days
=\left( \cfrac { 1 }{ 10 } +\cfrac { 1 }{ 10 } \right) =\cfrac { 1 }{ 5 }
Now,
\cfrac{1}{5}
work is done in
3
days.
\therefore
Whole work will be done in
(3\times 5)=15
days.
The amount of time taken to paint a wall is inversely proportional to the number of painters working on the job. If it takes 3 painters 5 days to complete such a job, how many days longer will it take if there are only 2 painters working?
Report Question
0%
2.5
0%
2
0%
2.4
0%
None
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Report Question
0%
1
0%
\dfrac{1}{40}
0%
40
0%
80
Explanation
Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
\left.\begin{matrix}Cow & 1 : 40 \\ Bags & 40 : 1 \end{matrix}\right\} :: 40 : x
\therefore 1 \times 40 \times x = 40 \times 1 \times 40
\Rightarrow x = 40
A
takes twice as much time as
B
or thrice as much time as
C
to finish a piece of work. Working together, they can finish the work in
2
days.
B
can do the work alone in:
Report Question
0%
4
days
0%
6
days
0%
8
days
0%
12
days
Explanation
Suppose
A,B
and
C
take,
x,\cfrac{x}{2}
and
\cfrac{x}{3}
days respectively finish the work.
Then,
\left( \cfrac { 1 }{ x } +\cfrac { 2 }{ x } +\cfrac { 3 }{ x } \right) =\cfrac { 1 }{ 2 }
\Rightarrow
\cfrac{6}{x}=\cfrac{1}{2}
\Rightarrow
x=12
So,
B
takes
(12/2)=6
days to finish the work.
What is the average of four tenths and five thousandths?
Report Question
0%
25002
0%
2502
0%
0.225
0%
0.2025
0%
0.02025
A can copy
75
pages in
25
hours, A and B together copy
135
pages in
27
hours. In what time can B copy
42
pages?
Report Question
0%
17\ hours
0%
27\ hours
0%
31\ hours
0%
21\ hours
In how many ways
7
men and
7
women can be seated around a round table such that no two women can sit together?
Report Question
0%
(7!)^2
0%
7!\times 6!
0%
(6!)^2
0%
7!
Explanation
Lets first place the men (M). * here indicates the linker of round table *M -M - M - M - M* which is in
(7-1)!
ways =
6!
So we have to place the women in between the men which is on the
5
empty seats So
7
women can sit on
7
seats in
(7)!
ways
So the answer is
7!\times 6!
A can do a piece of work in
6\dfrac {2}{3}
days and B in
5
days. They work together for
2
days and then A leaves B to finish the work alone. How long will B take to finish it?
Report Question
0%
\dfrac {3}{4}
days
0%
1\dfrac {1}{2}days
0%
3\ days
0%
7\ days
Two pipes
A
and
B
can fill a cistern in
37\displaystyle\frac{1}{2}
minutes and
45\ minutes
respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the
B
is turned off after :
Report Question
0%
5\ min
0%
9\ min
0%
10\ min
0%
15\ min
Explanation
Let B be turned off after x minutes. Then,
Part filled by
(A+B)
in x min.
+
Part filled by A in
(30-x)
min.
=1
.
\therefore x\left(\displaystyle\frac{2}{75}+\dfrac{1}{45}\right)+(30-x).\displaystyle\dfrac{2}{75}=1
\Rightarrow \displaystyle\dfrac{11x}{225}+\dfrac{(60-2x)}{75}=1
\Rightarrow 11x+180-6x=225
.
\Rightarrow x=9
.
A pump can fill a tank with water in
2\ hours
. Because of a leak, it took
2\displaystyle\frac{1}{3}\ hours
to fill the tank. The leak can drain all the water of the tank in.
Report Question
0%
\displaystyle 4\frac{1}{3}\ hrs
0%
\displaystyle 7\ hrs
0%
\displaystyle 8\ hrs
0%
\displaystyle 14\ hrs
Explanation
Rate of filling the Tank by Pump :
\dfrac{1}{2}
Rate of leak while water is being pumped in the tank:
\dfrac{3}{7}
Rate of leak in the tank:
1
hour
=\left(\displaystyle\frac{1}{2}-\frac{3}{7}\right)=\displaystyle\frac{1}{14}
.
\therefore
Leak will empty the tank in
14
hrs.
Which of the following is correct?
Report Question
0%
When the positions are numbered, then the circular permutations are treated as a linear arrangement.
0%
In linear arrangements, it does not make difference whether the positions are numbered are not.
0%
Both A and B
0%
None of these.
Explanation
By numbering position we are actually fixing staring point which makes it similar to linear permutation.so option A is correct
Linear permutation already has a staring point so it dose not need seats to be numbered so option B is correct
A cistern has a leak which would empty it in
8
hours. A tap is turned on which admits
6
litres a minute into the cistern and is now emptied in
12
hours. How many litres does the cistern hold?
Report Question
0%
8640
0%
8500
0%
4320
0%
60\ hours
A
is
50\%
as efficient as
B
.
C
does half of the work done by
A
and
B
together. If
C
alone does the work in
40
days, then
A, B
and
C
together can do the work in
Report Question
0%
\displaystyle 15\frac{1}{3}
days
0%
15
days
0%
13
days
0%
\displaystyle 13\frac{1}{3}
days
Explanation
Work Rate=\dfrac{Work} {Days}
Let Work Rate of A be
W_A
and Work rate of B be
W_B
and it is Given That
\Rightarrow W_A=\dfrac{W_B}{2}
\Rightarrow \dfrac{W}{D_A}=\dfrac{W}{2D_B}
\Rightarrow D_B=\dfrac{D_A}{2}
...............................................(1)
Now, Work Done By
A
and
B
Together
\Rightarrow \dfrac{W}{D_A}+\dfrac{W}{D_B}=\dfrac{3W}{2D_B}
Using Given Information,
\Rightarrow \dfrac{W}{D_C}=\dfrac{3W}{4D_B}
\Rightarrow \dfrac{W}{40}=\dfrac{3W}{4D_B}
\Rightarrow D_B=30
From Relation (1)
\Rightarrow D_A=60
Now,When
A,B
and
C
work Together
\Rightarrow \dfrac{W}{30}+\dfrac{W}{60}+\dfrac{W}{40}=\dfrac{W}{\dfrac{120}{9}}
Therefore The Work will be completed in
\dfrac{120}{9}days=13\dfrac{1}{3}days
Therefore Answer is
(D)
In a class of
100
students there are
70
boys whose average marks in a subject are
75
. If the average marks of the complete class is
72
, then what is the average of the girls?
Report Question
0%
73
0%
65
0%
68
0%
74
Explanation
Number of boys
= 70
Average marks of boys
=75
Total marks of boys
=70 \times 75=5250
Total marks of the class
=72 \times 100 =7200
Total marks of girls
=1950
Average of the girls
=\dfrac{1950}{30}=65
The length of the base of a square pyramid is
2\ cm
and the height is
6\ cm
. Calculate the volume.
Report Question
0%
8\ cm^3
0%
6\ cm^3
0%
4\ cm^3
0%
2\ cm^3
Explanation
Volume of square pyramid
=\dfrac { 1 }{ 3 } \times { a }^{ 2 }\times h=\dfrac { 1 }{ 3 } \times 2\times 2\times 6=8{ cm }^{ 3 }
A regular square pyramid is
3
m height and the perimeter of its base is
16
m. Find the volume of the pyramid.
Report Question
0%
12
12
cu. m
0%
14
14
cu. m
0%
16
16
cu. m
0%
18
18
cu. m
Explanation
Given, height of regular square pyramid is
3
m and the perimeter of its base is
16
m
Let the base side of pyramid is
l
m
Then perimeter of base
=4a=16
So,
a=4
Then volume of pyramid
=
\dfrac{1}{3}l^{2}h=\dfrac{1}{3}\times (4)^{2}\times 3=16
cu. m
How many seating arrangements are possible with
8
people around a round table?
Report Question
0%
5040
0%
8!
0%
7!
0%
720
Explanation
To arrange
n
people around a round table
Number of arrangements
=(n-1)!
To arrange them
8
around the round table.
Number of arrangements
=(8-1)!=7!=5040
Twelve friends go out for a dinner to
UTSAV
restaurant. There are two circular tables one with
7
chairs and one with
5
chairs. In how many ways can the group settle down themselves for dinner?
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0%
\dfrac{12!}{7!\times5!}
0%
\dfrac{12!}{35}
0%
12!
0%
12! 5! 7!
Explanation
Number of ways of selecting
7
people for first round table
={}^{12}C_5
Number of ways of selecting remaining
5
people for second round table
={}^{5}C_5
Arranging
7
people on first round table
=(7-1)!=6!
Arranging
5
people on second round table
=(5-1)!=4!
Hence the answer is
={}^{12}C_5\times {}^{5}C_5\times 6! \times 4!
=\dfrac{{12}!\times 5! \times 6! \times 4!}{7! \times 5!\times 5!\times 0!}=\dfrac{12!}{7 \times 5}=\dfrac{12!}{35}
Hence the correct answer is
\dfrac{12!}{35}
.
The Arithmetic mean of integers from
-5
to
5
is
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0%
3
0%
0
0%
25
0%
10
Explanation
All integers from
-5
to
5
are:
-5,\ -4,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5
.
We know that, arithmetic mean
=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}
Hence, sum of all numbers
=(-5)+(-4)+(-3)+(-2)+(-1)+ 0+ 1+2+3+4+5
=0
Total integers
=11
Hence, arithmetic mean
=\dfrac{0}{11}
=0
.
Hence, the arithmetic mean of integers from
-5
to
5
is
0
.
If
n
books can be arranged on an ordinary shelf in
720
ways, then in how many ways an these books be arranged in a circular shelf ?
Report Question
0%
120
0%
720
0%
360
0%
60
Explanation
n
books can be arranged in
N!
ways
Given:
n!=720=6!
Therefore,
n=6
The number of ways books can be arranged in circular shelf
=(n-1)!=5! =5\times 4\times 3\times 2\times 1=120
Hence the correct answer is
120
.
The Arithmetic mean of all the factors of
24
is
Report Question
0%
8.5
0%
5.67
0%
7
0%
7.5
Explanation
\Rightarrow
Factors of
24
are
1,\,2,\,3,\,4,\,6,\,8,\,12,\,24
So, the observations are
1,2,3,4,6,8,12,24
\therefore
Number of observations
=8
Arithmetic mean
=\dfrac{\text{Sum of observations}}{\text{Number of observations}}
\therefore
Arithmetic mean
=\dfrac{1+2+3+4+6+8+12+24}{8}
\therefore
Arithmetic mean
=\dfrac{60}{8}
\therefore
Arithmetic mean
=7.5
The mean of first
5
whole numbers is
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0%
2
0%
2.5
0%
3
0%
0
Two workers
A
and
B
are engaged to do a piece of work. Working alone,
A
takes
8
hours more to complete the work than if both worked together. On the other hand, working alone,
B
would need
4\displaystyle\frac{1}{2}
hours more to complete the work than if both worked together. How much time would they take to complete the job working together?
Report Question
0%
4
hours
0%
5
hours
0%
6
hours
0%
7
hours
Explanation
Let the number of hours taken by A and B both to complete the work be
x
.
As per the given information, A takes
x + 8
hours to complete when he works alone.
Similarly, B takes
x + 4.5
hours to complete the work, working alone.
\therefore \cfrac{1}{x + 4.5} + \cfrac{1}{x + 8} = \cfrac{1}{x}
\Rightarrow (x + 8 + x + 4.5)x = (x + 4.5)(x + 8)
\Rightarrow 2x^2 + 12.5x = x^2 + 12.5x + 36
\Rightarrow x^2 = 36
or
x = 6
hours
If on the 15th September 2008 was a Friday. Then which day will be on 15th September 2009
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0%
Sunday
0%
Friday
0%
Thursday
0%
Saturday
There are exactly twelve Sundays in the period from January
1
to March
31
in a certain year. Then the day corresponding to February
15
in that year is?
Report Question
0%
Tuesday
0%
Wednesday
0%
Thursday
0%
Not possible to determine from the given data
Explanation
Total number of days from
1
jan to
31
feb
=31+28+31=90
Dividing number of days with
7
, we get
\Rightarrow \dfrac{90}{7}=12\dfrac{6}{7}
Total number of sundays are
12
\therefore 1st
jan must be monday.
15
feb is
46th
day of the year,
number of weeks
\Rightarrow\Bigr(\dfrac{46}{7}=6\dfrac{4}{7}\Bigl)
Thus, 46th day is thursday (or
4
th day of the week).
If 15th August 2011 was Tuesday, then what day of the week was it on 17th September, 2011?
Report Question
0%
Thursday
0%
Friday
0%
Saturday
0%
Sunday
Explanation
The answer is option
D
Number of days from 15th Aug 2011 and 17th Sep 2011 = 16+17=33
Number of odd days in this =Remainder (33/7)=5
Since number of odd days is 5 and 15th Aug 2011 was Tuesday, counting five days from Tuesday, 17th Sep 2011 will be Sunday
A and B can do a piece of work in
6
days and A alone can do it in
9
days. The time take by B alone to do the work is _________.
Report Question
0%
18
days
0%
15
days
0%
12
days
0%
\displaystyle 7\frac{1}{2}
days
Explanation
A and B can do a piece of work in
6
days, so work done by A and B in one day will be
\dfrac{1}{6}
A alone can do the same work in
9
days, so work done by A in one day is
\dfrac{1}{9}
work done by B in one day will be
=\dfrac{1}{6}-\dfrac{1}{9}
=\dfrac{1}{18}
so, we can say that B will take
18
days to complete the same work.
In how many ways a garland can be made from exactly
10
flowers
Report Question
0%
10!
0%
9!
0%
2(9!)
0%
\dfrac{9!}{2}
Explanation
Since
10
things can be permuted along a circle in
9!
ways.
But in a garland anticlockwise and clockwise directions are the same, so we have
\dfrac{9!}{2}
.
Hence, option D is correct.
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers
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