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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 6101. |
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 |
| B. | 1880 |
| C. | 3800 |
| D. | 2800 |
| Answer» B. 1880 | |
| 6102. |
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 |
| B. | 60 |
| C. | 80 |
| D. | 100 |
| Answer» B. 60 | |
| 6103. |
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are [AIEEE 2002] |
| A. | 216 |
| B. | 375 |
| C. | 400 |
| D. | 720 |
| Answer» E. | |
| 6104. |
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 |
| B. | 300 |
| C. | 420 |
| D. | 20 |
| Answer» D. 20 | |
| 6105. |
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 |
| B. | 840 |
| C. | 2520 |
| D. | 5040 |
| Answer» B. 840 | |
| 6106. |
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 |
| B. | 12 |
| C. | 24 |
| D. | 30 |
| Answer» C. 24 | |
| 6107. |
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 |
| B. | 16 |
| C. | 4 |
| D. | 8 |
| Answer» B. 16 | |
| 6108. |
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 |
| B. | 36 |
| C. | 30 |
| D. | 720 |
| Answer» C. 30 | |
| 6109. |
The total number of permutations of the letters of the word ?BANANA? is [RPET 1997, 2000] |
| A. | 60 |
| B. | 120 |
| C. | 720 |
| D. | 24 |
| Answer» B. 120 | |
| 6110. |
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. | \[{{(5\ !)}^{2}}\] |
| B. | \[5\ !\ \times 4\ !\] |
| C. | \[5\ !\ \times 6\ !\] |
| D. | \[6\times 5\ !\] |
| Answer» D. \[6\times 5\ !\] | |
| 6111. |
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 |
| B. | 114 |
| C. | 72 |
| D. | 54 |
| Answer» D. 54 | |
| 6112. |
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 |
| B. | 18 |
| C. | 10 |
| D. | None of these |
| Answer» D. None of these | |
| 6113. |
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 |
| B. | 12 |
| C. | 10 |
| D. | 18 |
| Answer» C. 10 | |
| 6114. |
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 |
| B. | 12 |
| C. | 120 |
| D. | 24 |
| Answer» C. 120 | |
| 6115. |
How many words can be made from the letters of the word COMMITTEE [RPET 1986; MP PET 2002] |
| A. | \[\frac{9\ !}{{{(2\ !)}^{2}}}\] |
| B. | \[\frac{9\ !}{{{(2\ !)}^{3}}}\] |
| C. | \[\frac{9\ !}{2\ !}\] |
| D. | \[9\ !\] |
| Answer» C. \[\frac{9\ !}{2\ !}\] | |
| 6116. |
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 |
| B. | 86400 |
| C. | 96400 |
| D. | None of these |
| Answer» C. 96400 | |
| 6117. |
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 |
| B. | 90 |
| C. | 120 |
| D. | 80 |
| Answer» B. 90 | |
| 6118. |
How many words can be formed with the letters of the word MATHEMATICS by rearranging them [MP PET 1984; DCE 2001] |
| A. | \[\frac{11\ !}{2\ !\ 2\ !}\] |
| B. | \[\frac{11\ !}{2\ !}\] |
| C. | \[\frac{11\ !}{2\ !\ 2\ !\ 2\ !}\] |
| D. | \[11\ !\] |
| Answer» D. \[11\ !\] | |
| 6119. |
The number of 5 digit telephone numbers having at least one of their digits repeated is [Pb. CET 2000] |
| A. | 90000 |
| B. | 100000 |
| C. | 30240 |
| D. | 69760 |
| Answer» E. | |
| 6120. |
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 |
| B. | 60 |
| C. | 77 |
| D. | 81 |
| Answer» C. 77 | |
| 6121. |
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 |
| B. | 60 |
| C. | 45 |
| D. | 90 |
| Answer» C. 45 | |
| 6122. |
How many words can be made from the letters of the word DELHI, if L comes in the middle in every word |
| A. | 12 |
| B. | 24 |
| C. | 60 |
| D. | 6 |
| Answer» C. 60 | |
| 6123. |
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. | \[6\ !\] |
| B. | \[8\ !\] |
| C. | \[2(6)\ !\] |
| D. | \[2(7)\ !\] |
| Answer» B. \[8\ !\] | |
| 6124. |
How many numbers less than 1000 can be made from the digits 1, 2, 3, 4, 5, 6 (repetition is not allowed) |
| A. | 156 |
| B. | 160 |
| C. | 150 |
| D. | None of these |
| Answer» B. 160 | |
| 6125. |
How many numbers can be formed from the digits 1, 2, 3, 4 when the repetition is not allowed |
| A. | \[^{4}{{P}_{4}}\] |
| B. | \[^{4}{{P}_{3}}\] |
| C. | \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}\] |
| D. | \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\] |
| Answer» E. | |
| 6126. |
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 |
| B. | 18 |
| C. | 12 |
| D. | 30 |
| Answer» C. 12 | |
| 6127. |
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 |
| B. | 375 |
| C. | 450 |
| D. | 576 |
| Answer» C. 450 | |
| 6128. |
In how many ways \[n\] books can be arranged in a row so that two specified books are not together |
| A. | \[n\,!\,-(n-2)\,!\] |
| B. | \[(n-1)\,!\,(n-2)\] |
| C. | \[n\,!-2(n-1)\] |
| D. | \[(n-2)\,n!\] |
| Answer» C. \[n\,!-2(n-1)\] | |
| 6129. |
The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is |
| A. | 4! |
| B. | \[3\,!\,\,\times \,\,4\,!\] |
| C. | 7 ! |
| D. | None of these |
| Answer» B. \[3\,!\,\,\times \,\,4\,!\] | |
| 6130. |
The numbers of arrangements of the letters of the word SALOON, if the two O's do not come together, is |
| A. | 360 |
| B. | 720 |
| C. | 240 |
| D. | 120 |
| Answer» D. 120 | |
| 6131. |
Assuming that no two consecutive digits are same, the number of n digit numbers, is [Orissa JEE 2004] |
| A. | n! |
| B. | 9! |
| C. | \[{{9}^{n}}\] |
| D. | \[{{n}^{9}}\] |
| Answer» B. 9! | |
| 6132. |
The number of ways in which 6 rings can be worn on the four fingers of one hand is [AMU 1983] |
| A. | \[{{4}^{6}}\] |
| B. | \[^{6}{{C}_{4}}\] |
| C. | \[{{6}^{4}}\] |
| D. | None of these |
| Answer» B. \[^{6}{{C}_{4}}\] | |
| 6133. |
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 |
| B. | 120 |
| C. | 144 |
| D. | 14 |
| Answer» B. 120 | |
| 6134. |
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 |
| B. | 108 |
| C. | 36 |
| D. | 30 |
| Answer» C. 36 | |
| 6135. |
In how many ways can five examination papers be arranged so that physics and chemistry papers never come together |
| A. | 31 |
| B. | 48 |
| C. | 60 |
| D. | 72 |
| Answer» E. | |
| 6136. |
In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls |
| A. | 45 |
| B. | 75 |
| C. | 90 |
| D. | None of these |
| Answer» D. None of these | |
| 6137. |
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 |
| B. | 533280 |
| C. | 53328 |
| D. | None of these |
| Answer» B. 533280 | |
| 6138. |
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 |
| B. | 20 |
| C. | 10 |
| D. | \[5\] |
| Answer» B. 20 | |
| 6139. |
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 |
| B. | 9 |
| C. | 120 |
| D. | 40 |
| Answer» B. 9 | |
| 6140. |
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 |
| B. | 432 |
| C. | 108 |
| D. | 144 |
| Answer» D. 144 | |
| 6141. |
In a train five seats are vacant, then how many ways can three passengers sit [RPET 1985; MP PET 2003] |
| A. | 20 |
| B. | 30 |
| C. | 10 |
| D. | 60 |
| Answer» E. | |
| 6142. |
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 |
| B. | 625 |
| C. | 120 |
| D. | 600 |
| Answer» B. 625 | |
| 6143. |
Four dice (six faced) are rolled. The number of possible outcomes in which at least one die shows 2 is |
| A. | 1296 |
| B. | 625 |
| C. | 671 |
| D. | None of these |
| Answer» D. None of these | |
| 6144. |
Find the total number of 9 digit numbers which have all the digits different [IIT 1982] |
| A. | \[9\times 9\ !\] |
| B. | \[9\ !\] |
| C. | 10! |
| D. | None of these |
| Answer» B. \[9\ !\] | |
| 6145. |
The value of \[^{n}{{P}_{r}}\] is equal to [IIT 1971; MP PET 1993] |
| A. | \[^{n-1}{{P}_{r}}+r{{\,}^{n-1}}{{P}_{r-1}}\] |
| B. | \[n.{{\ }^{n-1}}{{P}_{r}}{{+}^{n-1}}{{P}_{r-1}}\] |
| C. | \[n{{(}^{n-1}}{{P}_{r}}{{+}^{n-1}}{{P}_{r-1}})\] |
| D. | \[^{n-1}{{P}_{r-1}}{{+}^{n-1}}{{P}_{r}}\] |
| Answer» B. \[n.{{\ }^{n-1}}{{P}_{r}}{{+}^{n-1}}{{P}_{r-1}}\] | |
| 6146. |
If \[^{n}{{P}_{5}}=9{{\times }^{n-1}}{{P}_{4}}\], then the value of \[n\] is |
| A. | 6 |
| B. | 8 |
| C. | 5 |
| D. | 9 |
| Answer» E. | |
| 6147. |
In how many ways can 10 true-false questions be replied |
| A. | 20 |
| B. | 100 |
| C. | 512 |
| D. | 1024 |
| Answer» E. | |
| 6148. |
In how many ways can \[mn\] letters be posted in \[n\] letter-boxes |
| A. | \[{{(mn)}^{n}}\] |
| B. | \[{{m}^{mn}}\] |
| C. | \[{{n}^{mn}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6149. |
If the best and the worst paper never appear together, then six examination papers can be arranged in how many ways |
| A. | 120 |
| B. | 480 |
| C. | 240 |
| D. | None of these |
| Answer» C. 240 | |
| 6150. |
If \[2\times {}^{n}{{C}_{5}}=9\,\,\times \,\,{}^{n-2}{{C}_{5}}\], then the value of n will be |
| A. | 7 |
| B. | 10 |
| C. | 9 |
| D. | 5 |
| Answer» C. 9 | |