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5. PERMUTATIONS AND COMBINATION (1.) The total number of three-digit numbers, divisible by 3 , which can be formed using the digits 1,3,5,8 , if repetition of digits is allowed, is [15 APRIL 2023 (MORNING)] (a.) 21 (b.) 18 (c.) 20 (d.) 22 (2.) If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial number, then the serial number of the word THAMS is [11 APRIL 2023 (AFTERNOON)] (a.) 102 (b.) 103 (c.) 101 (d.) 104 (3.) The number of triplets ( x y z , , ) , where x y z , , are distinct non negative integers satisfying x y z + + =15 , is : [11 APRIL 2023 (MORNING)] (a.) 136 (b.) 114 (c.) 80 (d.) 92 (4.) If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k, is equal to [08 APRIL 2023 (EVENING)] (a.) 1890 (b.) 945 (c.) 2835 (d.) 5670 (5.) The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is. [08 APRIL 2023 (MORNING)] (a.) 16800 (b.) 14800 (c.) 18000 (d.) 33600 (6.) The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is [08 APRIL 2023 (MORNING)] (a.) 2 7(720) (b.) 720 (c.) 2 7(360) (d.) 2 126(5!) (7.) All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is [13 APRIL 2023 (EVENING)] (a.) 328 (b.) 327 (c.) 324 (d.) 326 (8.) If 29 1 3 : :10 :1 a C C , then the ratio ( ) ( ) 2 2 n n n n + − + 3 : 3 4 is : [06 APRIL 2023 (MORNING)] (a.) 27:11 (b.) 35:16 (c.) 2:1 (d.) 65:37 (9.) The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :[29 Jan 2023(Evening)] (a.) 89 (b.) 84 (c.) 86 (d.) 79
(10.) The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is [29 Jan 2023(Evening)] (a.) 472 (b.) 432 (c.) 507 (d.) 400
PERMUTATIONS AND COMBINATION-INTEGER TYPE (11.) The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is [24 Jan 2023(Evening)] (12.) A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is [24 Jan 2023(Evening)] (13.) The number of elements in the set n N :10 n 100    and n 3 3 − is a multiple of 7 } is [15 APRIL 2023 (MORNING)] (14.) A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is [15 APRIL 2023 (MORNING)] (15.) The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is [13 APRIL 2023 (MORNING)] (16.) In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is [11 APRIL 2023 (MORNING)] (17.) The number of permutations of the digits 1,2,3, .,7  without repetition, which neither contain the string 153 nor the string 2467 , is [10 APRIL 2023 (MORNING)] (18.) Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple in a match, is 840 , then the total numbers of persons, who participated in the tournament, is [10 APRIL 2023 (MORNING)] (19.) The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is [06 APRIL 2023 (MORNING)] (20.) Let 5 digit numbers be constructed using the digits 0,2,3,4,7,9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is [31 Jan 2023(Morning)] (21.) Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to [31 Jan 2023(Morning)] (22.) The number of seven digits odd numbers, that can be formed using all the seven digits 1,2,2,2,3,3,5 is [30 Jan 2023(Evening)] (23.) If all the six digit numbers 1 2 3 4 5 6 x x x x x x with 1 2 3 4 5 6 0 x x x x x x       are arranged in the increasing order, then the sum of the digits in the th 72 number is
(24.) Five digit numbers are formed using the digits 1,2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1 . Then the serial number of 35337 is (25.) Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is [25 Jan 2023(Evening)] (26.) The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , is [01 Feb 2023(Evening)] (27.) Number of integral solutions to the equation x y z 21 + + = , where x 1, y 3,z 4    , is equal to [01 Feb 2023(Evening)] (28.) Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2,3 and 5 , and are divisible by 15 , is equal to [30 Jan 2023(Morning)] (29.) The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is [29 Jan 2023(Evening)]