M4maths Previous Puzzles

27 Sep 2012 Rank

Rank of the word DEHRADUN in the dictionary of words formed by letters of the word DEHRADUN taking all letters at a time?

OPtion

1) 4456
2) 4359
3) 4356
4) 4312
5) 4274
6) 4123
7) 4056
8) 4034
9) 3984
10) none of these

Solution

total no. of words = 8*7*6*5*4*3*2*1/2*1 = 20160
On arranging letters in order we get
a,d,d,e,h,n,r,u
so rank
=[20160/8]*1+[2520*2/7]*2+[720/6]*2+[120/5]*3+[24/4]*0+[6/3]*0+[2/2]*1+1 = 4274

Correct Option: 5 Best Solution (6)

Pallab Roy Chowdhury   12 years AGO

Write the alphabetical order of the letters of the given word 'DEHRADUN' as A,D,D,E,H,N,R,U.
Now strike off the first letter D.
Then count the no.of letters before D, and it is equal to 1(A).
So,number of words starting with A=(7!/2!)[since,there are 2 D's in the remaining 7 letters]
Now strike off the next letter E.
Then count the no.of letters before E, and it is equal to 2(A & D).
So,number of words starting with DA=(6!/1!).
So,number of words starting with DD=(6!/1!).
Now strike off the next letter H.
Then count the no.of letters before H, and it is equal to 2(A & D).
So,number of words starting with DEA=(5!/1!).
So,number of words starting with DED=(5!/1!).
Likewise,number of words starting with DEHA=(4!/1!).
number of words starting with DEHD=(4!/1!).
number of words starting with DEHN=(4!/1!)
number of words starting with DEHRADN=(1!/1!)
Hence,we the requred rank will be=
(1*(7!/2!))+(2*(6!/1!))+(2*(5!/1!))+(3*(4!/1!))+(0*(3!/1!))+(0*(2!/1!))+(1*(1!/1!))+(0*(0!/1!))+1=
2520+1440+240+72+0+0+1+0+1=4274.

Like? Yes (14) | No (2)  

Rthy    12 years AGO

((1*7!)/2!)+((2*6!)/1!)+((2*5!)/1!)+((3*4!)/1!)+(0*3!)+(0*2!)+(1*1!)+(0*0!)+1
= 2520+1440+240+72+0+0+1+0+1
=4274

Like? Yes (1) | No   

Narender Bhardwaj   12 years AGO

Given word is "DEHRADUN"
Now writing the word in the alphabetic order="ADDEHNRU".....(1)

Taking first letter of "DEHRADUN" is D,

D is not the first letter in eq 1 hence no of words formed from it=7!/2!=2520....(2)
Checking second word of eq (1) is D we require it
hence place it in the position,

Taking 2nd letter of "DEHRADUN" is E
Is E is the first letter of “ADEHNRU” no, Hence no of words formed from it=6!=720….(3)
Is E is the 2nd letter of “ADEHNRU” no, Hence no of words formed from it=6!=720….(4)
Since E is the 3rd letter so place it .
Now word is “ADHNRU”
Next word of “DEHRADUN” is H,
Is H is the first letter of “ADHNRU” no, Hence no of words formed=5!=120….(5)
Is H is the 2nd letter of “ADHNRU” no, Hence no of words formed=5!=120….(6)
Since H is next letter so place it.
Now word is “ADNRU”
Is “R” is the first letter of “ADNRU” no, Hence no of words formed=4!=24….(7)
Is “R” is the 2nd letter of “ADHNRU” no, Hence no of words formed=4!=24….(8)
Is “R” is the 3rd letter of “ADHNRU” no, Hence no of words formed=4!=24….(9)
Since R is the next word so place it,
Now word is “ADNU”
Since “A” is the next word so place it,
Now word is “DNU”
Since “D” is the next word so place it,
Now word is “NU”
Since “N” is not the next word, So no of words formed=2!=2……(10)
Hence total no of words are=2520+720+720+120+120+24+24+24+2=4274

Like? Yes (3) | No (6)  

Ashutosh Ranjan   12 years AGO

total letters in "DEHRADUN"=8, D-2
word starting from 'A'- 7!/2!=7*6*5*4*3=2520
word starting from 'DA'-6!=720
word starting from 'DD'-6!=720
word starting from 'DEA'-5!=120
word starting from 'DED'-5!=120
word starting from 'DEHA'-4!=24
word starting from 'DEHD'-4!=24
word starting from 'DEHN'-4!=24
word starting from 'DEHRAD'-2!=2
hence the rank of "DEHRADUN" in dictionary=2520+720+720+120+120+24+24+24+2=4274
so answer is (5)4274

Like? Yes (3) | No (6)  

Balakrishnan M   12 years AGO

Starting with "A" can form the word =(7!/2!)ways
Starting with "DA" can form the word = 6! ways
Starting with "DD" can form the word = 6! ways
Starting with "DEA" can form the word = 5! ways
Starting with "DED" can form the word = 5! ways
Starting with "DEHA" can form the word = 4! ways
Starting with "DEHD" can form the word = 4! ways Starting with "DEHN" can form the word = 4! ways Starting with "DEHRADN" can form the word =1!ways
The word "DEHRADUN" is = 1
The Rank of the word = (7!/2!)+6!+6!+5!+5!+4!+4!+4!+1!+1
= 2520+720+720+120+120+24+24+24+1+1
= 4274

Like? Yes (1) | No (5)  

susmit   12 years AGO

(7!/2)+6!+6!+5!+5!+4!+4!+4!+2=4274

Like? Yes (1) | No (6)  

26 Sep 2012 number

4^125 + 125^4 is

OPtion

1) prime
2) composite even
3) composite odd
4) not possible to decide
5) none of these

Solution

4^125 + 125^4
= (2^125)^2 + (125^2)^2
= (2^125)^2 + (125^2)^2 + 2*2^125*125^2 - 2*2^125*125^2
= (2^125+125^2)^2 - 2^126*125^2
= (2^125+125^2)^2 - (2^63*125)^2
now use a^2-b^2 = (a+b)(a-b) to prove the number composite.

Correct Option: 3 Best Solution (3)

Ajay Kashyap   12 years AGO

while we solved the question
4^125 = always an even no.
125^4 = always an odd no
so Odd + Even No = Composite Odd No.

Like? Yes (14) | No (5)  

susmit   12 years AGO

Last digit of 4^125 is 4 and last digit of 125^4 is 5.
So last digit of the expression is 9.
also the result is not prime . hence the answer is option no.3

Like? Yes (4) | No (4)  

Narender Bhardwaj   12 years AGO

Given 4^125 + 125^4
4^125=even
125^4=odd
Since even+odd=odd
Hence result is always odd number
ans 3

Like? Yes (2) | No (3)  

25 Sep 2012 words

How many words can be formed by letters of the word "MEGAMOTOR" using all at a time.

OPtion

1) 84540
2) 90720
3) 92340
4) 94320
5) 98760
6) 123240
7) 124350
8) 129820
9) 130260
10) none of these

Solution

total letters = 9
repeated letters M = 2
O = 2
so total words = 9*8*7*6*5*4*3*2*1/2*1*2*1 = 90720

Correct Option: 2 Best Solution (15)

Pallab Roy Chowdhury   12 years AGO

Letter Count
M 2
E 1
G 1
A 1
O 2
T 1
R 1

Hence,the required number of words=(9!/(2!*2!))=90720.

Like? Yes (6) | No   

Ajay Kashyap   12 years AGO

(9*8*7*6*5*4*3*2)/ 2*2 = 90720

Like? Yes (7) | No (3)  

sagar arora   12 years AGO

as rthere are 9 letters and M and O are twice so no of possible words=9!/(2!*2!)
=90720

Like? Yes (2) | No (2)  

susmit   12 years AGO

There are nine letters in the word.
so, 9! = 362880
M is repeating twice and O is also repeating twice
Hence 2!*2! = 4
hence the answer is 362880/4 = 90720
Hence option no. 2

Like? Yes (1) | No (1)  

Balakumaran N.A   12 years AGO

9 letters and 2 M 2 O;
so, 9!/ 2!*2! = 362880/4 = 90720

Like? Yes (1) | No (1)  

P M Anoop Sabir   12 years AGO

MMOOTRAGE
9*8*7*6*5*2*3*1*1

Like? Yes (2) | No (2)  

Narender Bhardwaj   12 years AGO

Given word is "MEGAMOTOR"
Total number of words=9
Repeating words=M and O 2 times
Hence words can be formed by letters of the word "MEGAMOTOR" using all at a time=9!/(2!*2!)=90720

Like? Yes (3) | No (3)  

ArunKumar   12 years AGO

total no of words = 9
so = 9! / 2! *2!

= 90720

Like? Yes (1) | No (1)  

Ashutosh Ranjan   12 years AGO

M-2, O-2, E-1,G-1,A-1,T-1 AND R-1
Total no. of letters in word "MEGAMOTOR" is 9.
hence no. of word formed= 9!/(2!*2!)
=9*8*6*5*4*3*2/(2*2)= 90720
Hence answer is option (2)90720
Thanks...

Like? Yes (1) | No (1)  

Nitish Kumar   12 years AGO

total no of letter in "MEGAMOTOR"=9
Reqd. no. =9!/(2!*2!)=90720
because, M & O repeat 2 times, so we divide by 2! & 2! .

Like? Yes (1) | No (1)  

ramkishore   12 years AGO

here megamotor contains 9 letters..
so we can arrange it by 9!
now there bare three verbs..
these we can arrange by 3!
and here m and o are two times..
so the answer is (9!)/(3!*2!*2!)

Like? Yes (1) | No (1)  

vivek kumar   12 years AGO

9 letters can be arranged in 9! ways
there are 2M and 2O
so,no of words can be formed=9!/(2!*2!)=90720

Like? Yes (1) | No (1)  

Rajesh kumar   12 years AGO

we know that we have to find out of permutation of
world "MEGAMOTOR"
n0.of worlds=!9/(!2*!1*!1*!1*!2*!1*!1) =90720=(2)ans
M=2=!2
E=1=!1
G=1=!1
A=1=!1
O=2=!2
T=1=!1
R=1=!1

Like? Yes (1) | No (1)  

sridhar reddy   12 years AGO

MEGAMOTOR has 9 letters
and M & O repeated twice in it
so the number of words
9!/2!*2!
=90720

Like? Yes (1) | No (1)  

ARUNACHALAM   12 years AGO

There are totally 9 letters so we can rearrange it in 9!(i.e)362880 ways.But the letters O and M comes 2 times so we have to divide the answer by 2!*2!.....

Like? Yes (1) | No (1)  

24 Sep 2012 sequence

next number of the sequence
4, 15, 34, 61, 96, ...... will be

OPtion

1) 119
2) 125
3) 133
4) 138
5) 139
6) 145
7) 149
8) 152
9) 159
10) none of these

Solution

4, 15, 34, 61, 96, ......., let next number is x
15-4 = 11
34-15 = 19
61-34 = 27
96-61 = 35
so x-96 = 43
so x = 139

Correct Option: 5 Best Solution (0)

21 Sep 2012 ratio

a:b:c = 6:5:1 and c:d:e = 5:4:3
then ratio a:b:d:e will be

OPtion

1) 30:25:4:3
2) 30:25:5:3
3) 30:25:5:4
4) 30:25:3:4
5) 30:25:3:5
6) 30:25:4:5
7) 25:5:4:3
8) 30:5:4:3
9) 5:4:3:1
10) none of these

Solution

a:b:c = 6:5:1 so a:b:c = 30:25:5 and c:d:e = 5:4:3
so a:b:c:d:e = 30:25:5:4:3
so a:b:d:e = 30:25:4:3

Correct Option: 1 Best Solution (0)

20 Sep 2012 integers

The ratio of two integers is equal to the ratio of a number 9 more than the numerator (of ratio of two integers) and a number 4 times the denominator (of ratio of two integers). That ratio will be

OPtion

1) 1/8
2) 1/10
3) 4/9
4) 4/15
5) 2/17
6) 4/19
7) 5/12
8) no solution
9) infinite solutions
10) none of these

Solution

according to the given condition
x/y = (x+9)/4y
on solving x = 3 and y can take any value

Correct Option: 9 Best Solution (13)

venu chowdary   12 years AGO

let numerator be x
letdenominator be y
then x/y = (x+9)/(4y) ==> x=3 , but y can be any no
so infinite solutions are possible

Like? Yes (7) | No (3)  

sainath   12 years AGO

let x and y be the 2 integers
then x/y=(x+9)/4y
=>4x=x+9
=>x=3
but y can have any integer value...
so the x/y value has infinite solutions...

Like? Yes (8) | No (5)  

SDeep Bhattacharya   12 years AGO

(x/y)=(x+9)/4y....eqn(1)
=>4xy=xy+9y
=>3xy=9y
=>x=3
now putting x=3 in eqn(1)
we get,(3/y)=(3+9)/(4y)
=>(3/y)=12/(4y)
=>3/y=3/y...i.e,it becomes an identity.
So,for any integral value of y not equal to 0,the above will be satisfied.
So,there are infinitely many solutions for the above problem..

Hence OPTION 9) infinite solutions, is correct..

Thanks To All..:-) :-)

Like? Yes (6) | No (3)  

rachana dhekane   12 years AGO

Let the ratio=x:y
according to given conditions,
x:y=x+9:4y
Hence, x=3
For ratio to be equal
y can have any value.
Hence it has infinite solutions.

Like? Yes (5) | No (2)  

Dr.Dipin Singh   12 years AGO

If two integers are x and y , then
as per given condition
x/y = (x+9)/4y
x= (x+9)/4
4x=x+9
x=3

Hence any ratio with numerator 3 will satisfy given condition.

Like? Yes (4) | No (2)  

Ganga Prasad Bhusal   12 years AGO

suppose ratio is x/y
then x/y = (x+9)/4y
on solving it, x=3 and y = any integer
so there will be infinite soln.

Like? Yes (3) | No (1)  

Asloob Sabir   12 years AGO

3/y=12/4y



The second unknown can have any number of values, still we get the required solution,

Like? Yes (3) | No (1)  

Nitish Kumar   12 years AGO

let the ratio will be x/y.
then,
x/y=(x+9)/4Y
=>x=3 when,y!=0
y can take any integer value
so, answer will be infinite solutions

Like? Yes (3) | No (1)  

Narender Bhardwaj   12 years AGO

Let the ratio of two integer=x/y,
according to the question
x/y=9+x/4y......(1)
=>4x=9+x
=>x=3,
Hence by putting x value in (1) we get
3/y=12/4y,
Which is true for any value of y
Hence there are infinite many solutions

Like? Yes (4) | No (2)  

sridhar reddy   12 years AGO

according to the question
let the two integers x & y
x/y=(9+x)/4y
x=3 and y belongs to integer
so the ratio will be infinite solutions

Like? Yes (3) | No (1)  

vivek kumar   12 years AGO

let two integer be x and y
then ratio=x/y
now, x/y=(x+9)/4y
solving this equation we get x=3
then ratio=3/y
and y can be any integer
hence,infinite solution

Like? Yes (2) | No (1)  

Ashutosh Ranjan   12 years AGO

x/y=(x+9)/4*y where y!=0 and y!=n*x[n=1,2,...]
4*x=x+9
x=3
y can be any non-zero integer not multiple of 3.
hence 3/y gives infinite solutions...
thank you!

Like? Yes (2) | No (1)  

VIJAY CHOUDHARY   12 years AGO

let the two integer value are a and b.
now according to the question
a/b=(a+9)/4b
3a=9;
a=3;
for any integer value of b the ratio will be
3/b

Like? Yes (2) | No (2)  

19 Sep 2012 age

Ram said to Meera that his age was double of her age 5 years before, and after 5 years his age will be 1.5 times that of her age. What will be the sum of their ages.

OPtion

1) 20
2) 28
3) 32
4) 34
5) 36
6) 40
7) 45
8) 50
9) 52
10) none of these

Solution

according to the given conditions
r-5 = 2(m-5) or r-2m = -5 (1)
and r+5 = 1.5(m+5) or r-1.5m = 2.5 (2)
(2) - (1) gives
0.5 m = 7.5 or m = 15
and r = 25
so r + m = 25+15 = 40

Correct Option: 6 Best Solution (17)

Ajay Kashyap   12 years AGO

let present age of Ram is R yrs and of Meera is M yrs
so according to question
R-5 = 2(M-5) ----(i)
R+5 = 3/2(M+5)------(ii)
AFTER SOLING BOTH EQUATIONS WE GET
R = 25 , M = 15
SO R+M = 40

Like? Yes (8) | No (3)  

Pallab Roy Chowdhury   12 years AGO

Let current age of Ram & Meera are x & y respectively...
So by question, x-5=2(y-5) and
x+5=1.5(y+5)
Solving above two equations we get x=25 & y=15
Hence, x+y=40...

Like? Yes (4) | No (1)  

Gulshan Kumar   12 years AGO

R-5 = 2(M-5) ----(i)
R+5 = 3/2(M+5)------(ii)
AFTER SOLING BOTH EQUATIONS WE GET
R = 25 , M = 15
SO R+M = 40

Like? Yes (3) | No   

Nitish Kumar   12 years AGO

let ram's age is x, and meera age's is y.
given,
x-5=2(y-5)
=>x-2y=-5 ------(1)
and
x+5=1.5(y+5)
=>x-1.5y=2.5 ------(2)
solving eqn.(1) and (2),
x=25 and y=15
x+y=25+15=40

Like? Yes (3) | No   

Lorna A. Canillo   12 years AGO

let x= age of Ram
y= age of Meera
Ram's age 5 yrs. before is x-5=2(y-5) eq. x-2y=-5
Ram's age 5 yrs. after is x+5=1.5(y+5)
eq. x-1.5y=2.5 => 10x-15y=25 get rid of decimal make real numbers (a,b,c) integral.
find y. -10x+20y=50 =>multiply eq. by -10
add
-10x+20y=50
10x-15y=25
5y=75
y=15
find x: x=2(15)-5
=30-5
x=25
therefore the sum of their ages is 40.

Like? Yes (3) | No   

Narender Bhardwaj   12 years AGO

let Ram current age=x years,
let Meera current age=y years,
Before 5 years Ram age was double of Meera age
Therefore x-5=2(y-5)
=>x-5=2y-10,
=>x-2y=-5.........(1)
Similarly after 5 years Ram age will be 1.5 times that of Meera age
Therefore
x+5=1.5(y+5)
=>x+5=1.5y+7.5
=>x-1.5y=2.5.........(2)

Solving (1) and (2) we get
x=15,y=25,
Hence Sum of Ram's and Meera's age=15+25=40 ans

Like? Yes (4) | No (2)  

Ankit   12 years AGO

Ram Age = R
Meera Age = M

R - 5 = 2 ( M - 5 )
R - 5 = 2M- 10
2M-R = 5
R +5 = 1.5 ( M + 5)
R + 5 = 1.5M +7.5
R- 1.5M = 2.5
2M - 5 - 1.5M = 2.5
.5M = 7.5
M = 15
R = 25
M + R = 40

Like? Yes (3) | No (1)  

shah jignesh   12 years AGO

suppose ram age is x and meera has y
so
x-5=2y-10
x+5=1.5y+7.5 ................
solve them x=25,y=15
sum=40

Like? Yes (2) | No   

subratverma   12 years AGO

let the present age of ram and meera is x and y
then form the question it is clear dat..
(x-5)=2(y-5)..........(1)
(x+5)=1.5(y+5)........(2)

after solving eqution we get x=25,y=15
so the sum of ages will be.
x+y=25+15=40
so option 6 is correct..:)

Like? Yes (2) | No   

Kiran Datti   12 years AGO

ram's present age= r
meera's present age =m
r-5=2(m-5) ------(1)
r+5=3/2(m+5) -----(2)

solving these 2 equations we get m=15 and r=25

then m+r=40

Like? Yes (2) | No   

sridhar reddy   12 years AGO

let the ages of ram and meera are R & M respectively
5 yrs before their ages
R-5=2(M-5)
R=2M-5..........1
after 5 yrs their ages will be
R+5=1.5(M+5)
2R=4M-10...........2
on solving 1 and 2 equations
age of Ram R is 25
age of Meera M is 15
sum of their ages will be 40

Like? Yes (2) | No   

sagar arora   12 years AGO

Let ram's and meera,s present age be R and M
(R-5)=2(M-5)
(R+5)=1.5(M+5)
solving these eqs we get meera.s age 15 and ram,s age 25
so 40 is the ans

Like? Yes (3) | No (2)  

Muhammad Ahmed   12 years AGO

Ram is 25 years old and Meera is 15 years old

Like? Yes (1) | No (1)  

jagannathan   12 years AGO

2x-3.5y=-2.5
x-2y=-5
on solving
x=25
y=15

Like? Yes (1) | No (1)  

Asloob Sabir   12 years AGO

Ram's age is 25, and Meera's is 15.

Like? Yes (1) | No (2)  

P M Anoop Sabir   12 years AGO

2y-10=4x-20
2y+10=3x+15
20=-x+35
x=15
y=25

Like? Yes (1) | No (2)  

swapnil gavtade   12 years AGO

ram age 25 & meera 15 before 5year their ages 20,10 & after 5 year 30,20

Like? Yes (1) | No (2)  

18 Sep 2012 equation

no. of real roots of the equation
x^4 + 3x^3 - 6x^2 + 5x + 4 = 0
will be

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) none of these

Solution

x^4 + 3x^3 - 6x^2 + 5x + 4 = 0
there are 2 times sign conversion
first in + 3x^3 - 6x^2
and second in - 6x^2 + 5x
so 2 real positive roots are there
similarly
take -x in place of x
we will get x^4 - 3x^3 - 6x^2 - 5x + 4 = 0
there are 2 times sign conversion again
first in x^4 - 3x^3
and second in - 5x + 4
so 2 real negative roots are there
total real roots = 4

Correct Option: 5 Best Solution (0)

17 Sep 2012 sequence

next number of the sequence
1362, 1461, 1550, 1629, 1698, ........
will be

OPtion

1) 1725
2) 1729
3) 1735
4) 1739
5) 1740
6) 1749
7) 1750
8) 1757
9) 1762
10) none of these

Solution

1362+99=1461
1461+89=1550
1550+79=1629
1629+69=1698
1698+59=1757

Correct Option: 8 Best Solution (0)

14 Sep 2012 rank

rank of the word INDIA in the dictionary of words formed by the letters of the word INDIA.

OPtion

1) 46
2) 47
3) 48
4) 49
5) 50
6) 51
7) 52
8) 53
9) 54
10) none of these

Solution

INDIA, total no. of words = 5*4*3*2*1/2*1 = 60
arranged letters A D I I N
first letter I, before it there are 2 letters so [60/5]*2
second letter N, before it 3 letters so [12*2/4]*3 (2 is for revision of I)
third letter D, before it 1 letter so [6/3]*1
fourth letter I, before it 1 letter so [2/2]*1
so rank = [60/5]*2 + [12*2/4]*3 + [6/3]*1 + [2/2]*1 + 1 = 24+18+2+1+1 = 46

Correct Option: 1 Best Solution (0)