-
question_answer1)
If the best and the worst paper never appear together, then six examination papers can be arranged in how many ways
A)
120 done
clear
B)
480 done
clear
C)
240 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer2)
How many numbers divisible by 5 and lying between 3000 and 4000 can be formed from the digits 1, 2, 3, 4, 5, 6 (repetition is not allowed)
A)
\[\frac{n+r-1}{r}\] done
clear
B)
\[^{5}{{P}_{2}}\] done
clear
C)
\[^{4}{{P}_{2}}\] done
clear
D)
\[^{6}{{P}_{3}}\] done
clear
View Solution play_arrow
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question_answer3)
The number of ways in which 6 rings can be worn on the four fingers of one hand is [AMU 1983]
A)
\[{{4}^{6}}\] done
clear
B)
\[^{6}{{C}_{4}}\] done
clear
C)
\[{{6}^{4}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer4)
How many numbers can be formed from the digits 1, 2, 3, 4 when the repetition is not allowed
A)
\[^{4}{{P}_{4}}\] done
clear
B)
\[^{4}{{P}_{3}}\] done
clear
C)
\[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}\] done
clear
D)
\[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\] done
clear
View Solution play_arrow
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question_answer5)
There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given is
A)
\[{{7}^{3}}\] done
clear
B)
\[{{3}^{7}}\] done
clear
C)
\[^{7}{{C}_{3}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer6)
4 buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are
A)
12 done
clear
B)
16 done
clear
C)
4 done
clear
D)
8 done
clear
View Solution play_arrow
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question_answer7)
If \[{}^{n}{{P}_{5}}=20.\ {}^{n}{{P}_{3}}\], then \[n=\]
A)
4 done
clear
B)
8 done
clear
C)
6 done
clear
D)
7 done
clear
View Solution play_arrow
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question_answer8)
How many words comprising of any three letters of the word UNIVERSAL can be formed
A)
504 done
clear
B)
405 done
clear
C)
540 done
clear
D)
450 done
clear
View Solution play_arrow
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question_answer9)
If \[{}^{n}{{P}_{4}}\ :\ {}^{n}{{P}_{5}}=1:2\], then \[n=\] [MP PET 1987; RPET 1996]
A)
4 done
clear
B)
5 done
clear
C)
6 done
clear
D)
7 done
clear
View Solution play_arrow
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question_answer10)
In how many ways can \[mn\] letters be posted in \[n\] letter-boxes
A)
\[{{(mn)}^{n}}\] done
clear
B)
\[{{m}^{mn}}\] done
clear
C)
\[{{n}^{mn}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
In how many ways can 10 true-false questions be replied
A)
20 done
clear
B)
100 done
clear
C)
512 done
clear
D)
1024 done
clear
View Solution play_arrow
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question_answer12)
How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is not allowed)
A)
224 done
clear
B)
280 done
clear
C)
324 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer13)
If \[^{n}{{P}_{5}}=9{{\times }^{n-1}}{{P}_{4}}\], then the value of \[n\] is
A)
6 done
clear
B)
8 done
clear
C)
5 done
clear
D)
9 done
clear
View Solution play_arrow
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question_answer14)
The value of \[^{n}{{P}_{r}}\] is equal to [IIT 1971; MP PET 1993]
A)
\[^{n-1}{{P}_{r}}+r{{\,}^{n-1}}{{P}_{r-1}}\] done
clear
B)
\[n.{{\ }^{n-1}}{{P}_{r}}{{+}^{n-1}}{{P}_{r-1}}\] done
clear
C)
\[n{{(}^{n-1}}{{P}_{r}}{{+}^{n-1}}{{P}_{r-1}})\] done
clear
D)
\[^{n-1}{{P}_{r-1}}{{+}^{n-1}}{{P}_{r}}\] done
clear
View Solution play_arrow
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question_answer15)
Find the total number of 9 digit numbers which have all the digits different [IIT 1982]
A)
\[9\times 9\ !\] done
clear
B)
\[9\ !\] done
clear
C)
10! done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer16)
Four dice (six faced) are rolled. The number of possible outcomes in which at least one die shows 2 is
A)
1296 done
clear
B)
625 done
clear
C)
671 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer17)
There are 4 parcels and 5 post-offices. In how many different ways the registration of parcel can be made [MP PET 1983]
A)
20 done
clear
B)
\[{{4}^{5}}\] done
clear
C)
\[{{5}^{4}}\] done
clear
D)
\[{{5}^{4}}-{{4}^{5}}\] done
clear
View Solution play_arrow
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question_answer18)
In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes [BIT Ranchi 1990; RPET 1988, 97]
A)
1024 done
clear
B)
625 done
clear
C)
120 done
clear
D)
600 done
clear
View Solution play_arrow
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question_answer19)
In a train five seats are vacant, then how many ways can three passengers sit [RPET 1985; MP PET 2003]
A)
20 done
clear
B)
30 done
clear
C)
10 done
clear
D)
60 done
clear
View Solution play_arrow
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question_answer20)
The product of any \[r\] consecutive natural numbers is always divisible by [IIT 1985]
A)
\[r\ !\] done
clear
B)
\[{{r}^{2}}\] done
clear
C)
\[{{r}^{n}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer21)
The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is [Pb. CET 1990]
A)
18 done
clear
B)
432 done
clear
C)
108 done
clear
D)
144 done
clear
View Solution play_arrow
-
question_answer22)
Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is
A)
20 done
clear
B)
9 done
clear
C)
120 done
clear
D)
40 done
clear
View Solution play_arrow
-
question_answer23)
The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is
A)
72 done
clear
B)
96 done
clear
C)
90 done
clear
D)
98 done
clear
View Solution play_arrow
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question_answer24)
In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls
A)
45 done
clear
B)
75 done
clear
C)
90 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer25)
The sum of all 4 digit numbers that can be formed by using the digits 2, 4, 6, 8 (repetition of digits not allowed) is
A)
133320 done
clear
B)
533280 done
clear
C)
53328 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer26)
There are 5 roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is [MP PET 1996]
A)
25 done
clear
B)
20 done
clear
C)
10 done
clear
D)
\[5\] done
clear
View Solution play_arrow
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question_answer27)
In how many ways can five examination papers be arranged so that physics and chemistry papers never come together
A)
31 done
clear
B)
48 done
clear
C)
60 done
clear
D)
72 done
clear
View Solution play_arrow
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question_answer28)
The number of ways in which first, second and third prizes can be given to 5 competitors is
A)
10 done
clear
B)
60 done
clear
C)
15 done
clear
D)
125 done
clear
View Solution play_arrow
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question_answer29)
The number of 3 digit odd numbers, that can be formed by using the digits 1, 2, 3, 4, 5, 6 when the repetition is allowed, is [Pb. CET 1999]
A)
60 done
clear
B)
108 done
clear
C)
36 done
clear
D)
30 done
clear
View Solution play_arrow
-
question_answer30)
How many numbers of five digits can be formed from the numbers 2, 0, 4, 3, 8 when repetition of digits is not allowed [MP PET 2000; Pb. CET 2001]
A)
96 done
clear
B)
120 done
clear
C)
144 done
clear
D)
14 done
clear
View Solution play_arrow
-
question_answer31)
If \[^{12}{{P}_{r}}=1320\], then r is equal to [Pb. CET 2004]
A)
5 done
clear
B)
4 done
clear
C)
3 done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer32)
Assuming that no two consecutive digits are same, the number of n digit numbers, is [Orissa JEE 2004]
A)
n! done
clear
B)
9! done
clear
C)
\[{{9}^{n}}\] done
clear
D)
\[{{n}^{9}}\] done
clear
View Solution play_arrow
-
question_answer33)
The numbers of arrangements of the letters of the word SALOON, if the two O's do not come together, is
A)
360 done
clear
B)
720 done
clear
C)
240 done
clear
D)
120 done
clear
View Solution play_arrow
-
question_answer34)
The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is
A)
4! done
clear
B)
\[3\,!\,\,\times \,\,4\,!\] done
clear
C)
7 ! done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer35)
In how many ways \[n\] books can be arranged in a row so that two specified books are not together
A)
\[n\,!\,-(n-2)\,!\] done
clear
B)
\[(n-1)\,!\,(n-2)\] done
clear
C)
\[n\,!-2(n-1)\] done
clear
D)
\[(n-2)\,n!\] done
clear
View Solution play_arrow
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question_answer36)
How many numbers lying between 500 and 600 can be formed with the help of the digits 1, 2, 3, 4, 5, 6 when the digits are not to be repeated
A)
20 done
clear
B)
40 done
clear
C)
60 done
clear
D)
80 done
clear
View Solution play_arrow
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question_answer37)
Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed), are [IIT 1976; AIEEE 2002]
A)
350 done
clear
B)
375 done
clear
C)
450 done
clear
D)
576 done
clear
View Solution play_arrow
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question_answer38)
The number of numbers that can be formed with the help of the digits 1, 2, 3, 4, 3, 2, 1 so that odd digits always occupy odd places, is [RPET 1988, 1991, 1992]
A)
24 done
clear
B)
18 done
clear
C)
12 done
clear
D)
30 done
clear
View Solution play_arrow
-
question_answer39)
In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together
A)
\[5\,\,!\,\,\times \,\,3\,\,!\] done
clear
B)
\[^{4}{{P}_{3}}\times 5\,\,!\] done
clear
C)
\[^{6}{{P}_{3}}\times 5\,\,!\] done
clear
D)
\[^{5}{{P}_{3}}\times 3\,!\] done
clear
View Solution play_arrow
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question_answer40)
How many numbers less than 1000 can be made from the digits 1, 2, 3, 4, 5, 6 (repetition is not allowed)
A)
156 done
clear
B)
160 done
clear
C)
150 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer41)
How many words can be formed from the letters of the word COURTESY, whose first letter is C and the last letter is Y
A)
\[6\ !\] done
clear
B)
\[8\ !\] done
clear
C)
\[2(6)\ !\] done
clear
D)
\[2(7)\ !\] done
clear
View Solution play_arrow
-
question_answer42)
How many words can be made from the letters of the word DELHI, if L comes in the middle in every word
A)
12 done
clear
B)
24 done
clear
C)
60 done
clear
D)
6 done
clear
View Solution play_arrow
-
question_answer43)
How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice
A)
30 done
clear
B)
60 done
clear
C)
45 done
clear
D)
90 done
clear
View Solution play_arrow
-
question_answer44)
In how many ways 3 letters can be posted in 4 letter-boxes, if all the letters are not posted in the same letter-box
A)
63 done
clear
B)
60 done
clear
C)
77 done
clear
D)
81 done
clear
View Solution play_arrow
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question_answer45)
The number of 5 digit telephone numbers having at least one of their digits repeated is [Pb. CET 2000]
A)
90,000 done
clear
B)
100,000 done
clear
C)
30,240 done
clear
D)
69,760 done
clear
View Solution play_arrow
-
question_answer46)
How many words can be formed with the letters of the word MATHEMATICS by rearranging them [MP PET 1984; DCE 2001]
A)
\[\frac{11\ !}{2\ !\ 2\ !}\] done
clear
B)
\[\frac{11\ !}{2\ !}\] done
clear
C)
\[\frac{11\ !}{2\ !\ 2\ !\ 2\ !}\] done
clear
D)
\[11\ !\] done
clear
View Solution play_arrow
-
question_answer47)
The number of arrangements of the letters of the word CALCUTTA [MP PET 1984]
A)
2520 done
clear
B)
5040 done
clear
C)
10,080 done
clear
D)
40,320 done
clear
View Solution play_arrow
-
question_answer48)
How many numbers, lying between 99 and 1000 be made from the digits 2, 3, 7, 0, 8, 6 when the digits occur only once in each number [MP PET 1984]
A)
100 done
clear
B)
90 done
clear
C)
120 done
clear
D)
80 done
clear
View Solution play_arrow
-
question_answer49)
In a circus there are ten cages for accommodating ten animals. Out of these four cages are so small that five out of 10 animals cannot enter into them. In how many ways will it be possible to accommodate ten animals in these ten cages [Roorkee 1989]
A)
66400 done
clear
B)
86400 done
clear
C)
96400 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer50)
How many words can be made from the letters of the word COMMITTEE [RPET 1986; MP PET 2002]
A)
\[\frac{9\ !}{{{(2\ !)}^{2}}}\] done
clear
B)
\[\frac{9\ !}{{{(2\ !)}^{3}}}\] done
clear
C)
\[\frac{9\ !}{2\ !}\] done
clear
D)
\[9\ !\] done
clear
View Solution play_arrow
-
question_answer51)
How many numbers can be made with the digits 3, 4, 5, 6, 7, 8 lying between 3000 and 4000 which are divisible by 5 while repetition of any digit is not allowed in any number [RPET 1990]
A)
60 done
clear
B)
12 done
clear
C)
120 done
clear
D)
24 done
clear
View Solution play_arrow
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question_answer52)
The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MODESTY is
A)
5040 done
clear
B)
720 done
clear
C)
1681 done
clear
D)
2520 done
clear
View Solution play_arrow
-
question_answer53)
If \[a\] denotes the number of permutations of \[x+2\] things taken all at a time, \[b\] the number of permutations of \[x\] things taken 11 at a time and \[c\] the number of permutations of \[x-11\] things taken all at a time such that \[a=182\ bc\], then the value of \[x\] is
A)
15 done
clear
B)
12 done
clear
C)
10 done
clear
D)
18 done
clear
View Solution play_arrow
-
question_answer54)
All possible four digit numbers are formed using the digits 0, 1, 2, 3 so that no number has repeated digits. The number of even numbers among them is
A)
9 done
clear
B)
18 done
clear
C)
10 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer55)
The number of ways in which ten candidates \[{{A}_{1}},\ {{A}_{2}},\ .......{{A}_{10}}\] can be ranked such that \[{{A}_{1}}\] is always above \[{{A}_{10}}\] is
A)
\[5\ !\] done
clear
B)
\[2(5\ !)\] done
clear
C)
\[10\ !\] done
clear
D)
\[\frac{1}{2}(10\ !)\] done
clear
View Solution play_arrow
-
question_answer56)
All the letters of the word ?EAMCET? are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is [EAMCET 1987; DEC 2000]
A)
360 done
clear
B)
114 done
clear
C)
72 done
clear
D)
54 done
clear
View Solution play_arrow
-
question_answer57)
In how many ways can 5 boys and 5 girls stand in a row so that no two girls may be together [RPET 1997]
A)
\[{{(5\ !)}^{2}}\] done
clear
B)
\[5\ !\ \times 4\ !\] done
clear
C)
\[5\ !\ \times 6\ !\] done
clear
D)
\[6\times 5\ !\] done
clear
View Solution play_arrow
-
question_answer58)
The total number of permutations of the letters of the word ?BANANA? is [RPET 1997, 2000]
A)
60 done
clear
B)
120 done
clear
C)
720 done
clear
D)
24 done
clear
View Solution play_arrow
-
question_answer59)
The number of words which can be made out of the letters of the word MOBILE when consonants always occupy odd places is [RPET 1999]
A)
20 done
clear
B)
36 done
clear
C)
30 done
clear
D)
720 done
clear
View Solution play_arrow
-
question_answer60)
How many numbers greater than 24000 can be formed by using digits 1, 2, 3, 4, 5 when no digit is repeated [RPET 1999]
A)
36 done
clear
B)
60 done
clear
C)
84 done
clear
D)
120 done
clear
View Solution play_arrow
-
question_answer61)
How many numbers greater than hundred and divisible by 5 can be made from the digits 3, 4, 5, 6, if no digit is repeated [AMU 1999]
A)
6 done
clear
B)
12 done
clear
C)
24 done
clear
D)
30 done
clear
View Solution play_arrow
-
question_answer62)
The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is [Pb. CET 1999]
A)
420 done
clear
B)
840 done
clear
C)
2520 done
clear
D)
5040 done
clear
View Solution play_arrow
-
question_answer63)
The number of 4 digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is [AMU 2001]
A)
1225 done
clear
B)
1252 done
clear
C)
1522 done
clear
D)
480 done
clear
View Solution play_arrow
-
question_answer64)
The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is [Kerala (Engg.) 2001]
A)
120 done
clear
B)
300 done
clear
C)
420 done
clear
D)
20 done
clear
View Solution play_arrow
-
question_answer65)
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are [AIEEE 2002]
A)
216 done
clear
B)
375 done
clear
C)
400 done
clear
D)
720 done
clear
View Solution play_arrow
-
question_answer66)
The number of arrangements of the letters of the word BANANA in which two N?s do not appear adjacently is [IIT Screening 2002]
A)
40 done
clear
B)
60 done
clear
C)
80 done
clear
D)
100 done
clear
View Solution play_arrow
-
question_answer67)
The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl in between two boys [Kerala (Engg.) 2002]
A)
2880 done
clear
B)
1880 done
clear
C)
3800 done
clear
D)
2800 done
clear
View Solution play_arrow
-
question_answer68)
Eleven books consisting of 5 Mathematics, 4 Physics and 2 Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is [AMU 2002]
A)
4! 2! done
clear
B)
11! done
clear
C)
5! 4! 3! 2! done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer69)
The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is [Karnataka CET 2003]
A)
36 done
clear
B)
574 done
clear
C)
144 done
clear
D)
754 done
clear
View Solution play_arrow
-
question_answer70)
The number of ways in which 9 persons can be divided into three equal groups is [Orissa JEE 2003]
A)
1680 done
clear
B)
840 done
clear
C)
560 done
clear
D)
280 done
clear
View Solution play_arrow
-
question_answer71)
If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated is [Pb. CET 2004]
A)
2 done
clear
B)
5 done
clear
C)
20 done
clear
D)
40 done
clear
View Solution play_arrow
-
question_answer72)
If the letters of the word SACHIN arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number [AIEEE 2005]
A)
603 done
clear
B)
602 done
clear
C)
601 done
clear
D)
600 done
clear
View Solution play_arrow
-
question_answer73)
Let the eleven letters \[A,B\].....,K denote an arbitrary permutation of the integers (1, 2,.....11), then \[(A-1)(B-2)(C-3).....(K-11)\] [Orissa JEE 2005]
A)
Necessarily zero done
clear
B)
Always odd done
clear
C)
Always even done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer74)
4 Note of Rs. 100 and 5 note in which first of Rs. 1, second of Rs. 2, Third of Rs. 5, fourth of Rs. 20 and fifth one of Rs. 50 distributed in 3 children such that each child receive at least one note of Rs. 100. The total number of ways of distribution [DCE 2005]
A)
\[3\times {{5}^{3}}\] done
clear
B)
\[5\times {{3}^{5}}\] done
clear
C)
\[{{3}^{6}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer75)
How many numbers lying between 999 and 10000 can be formed with the help of the digit 0,2,3,6,7,8 when the digits are not to be repeated [AMU 2005]
A)
100 done
clear
B)
200 done
clear
C)
300 done
clear
D)
400 done
clear
View Solution play_arrow