Please wait...

7. Permutations and Combinations
Pause
Play
176:59 MIN
  • Question 1/177
    4 / -1
    Mark Review

    [27-Jan-2024 Shift 2]

    [27-Jan-2024 Shift 2]

  • Question 2/177
    4 / -1
    Mark Review

    All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS

    [29-Jan-2024 Shift 1]

    All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS

    [29-Jan-2024 Shift 1]

  • Question 3/177
    4 / -1
    Mark Review

    Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

    [29-Jan-2024 Shift 2]

    Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

    [29-Jan-2024 Shift 2]

  • Question 4/177
    4 / -1
    Mark Review

    In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A,B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is_____

    [30-Jan-2024 Shift 2]

    In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A,B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is_____

    [30-Jan-2024 Shift 2]

  • Question 5/177
    4 / -1
    Mark Review

    The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to_____

    [31-Jan-2024 Shift 1]

    The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to_____

    [31-Jan-2024 Shift 1]

  • Question 6/177
    4 / -1
    Mark Review

    The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

    [31-Jan-2024 Shift 2]

    The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

    [31-Jan-2024 Shift 2]

  • Question 7/177
    4 / -1
    Mark Review

    If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

    [1-Feb-2024 Shift 1]

    If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

    [1-Feb-2024 Shift 1]

  • Question 8/177
    4 / -1
    Mark Review

    The lines L1, L2,...,I20 are distinct. For n = 1, 2, 3,...,10 all the lines L2n−1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set {L1, L2,...,L20} is equal to :

    [1-Feb-2024 Shift 2]

    The lines L1, L2,...,I20 are distinct. For n = 1, 2, 3,...,10 all the lines L2n−1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set {L1, L2,...,L20} is equal to :

    [1-Feb-2024 Shift 2]

  • Question 9/177
    4 / -1
    Mark Review
    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 Shift 1]
    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 Shift 1]
  • Question 10/177
    4 / -1
    Mark Review
    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 Shift 1]
    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 Shift 1]
  • Question 11/177
    4 / -1
    Mark Review
    The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition, is
    [24-Jan-2023 Shift 2]
    The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition, is
    [24-Jan-2023 Shift 2]
  • Question 12/177
    4 / -1
    Mark Review
    Let S={1,2,3,5,7,10,11}. The number of nonempty subsets of S that have the sum of all elements a multiple of 3 , is _______.
    [25-Jan-2023 Shift 1]
    Let S={1,2,3,5,7,10,11}. The number of nonempty subsets of S that have the sum of all elements a multiple of 3 , is _______.
    [25-Jan-2023 Shift 1]
  • Question 13/177
    4 / -1
    Mark Review
    The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is
    [25-Jan-2023 Shift 2]
    The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is
    [25-Jan-2023 Shift 2]
  • Question 14/177
    4 / -1
    Mark Review
    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 Shift 2]
    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 Shift 2]
  • Question 15/177
    4 / -1
    Mark Review
    If all the six digit numbers x1x2x3x4x5x6 with 0<x1<x2<x3<x4<x5<x6 are arranged in the increasing order, then the sum of the digits in the 72‌th ‌ number is _______.
    [29-Jan-2023 Shift 1]
    If all the six digit numbers x1x2x3x4x5x6 with 0<x1<x2<x3<x4<x5<x6 are arranged in the increasing order, then the sum of the digits in the 72‌th ‌ number is _______.
    [29-Jan-2023 Shift 1]
  • Question 16/177
    4 / -1
    Mark Review
    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 _______.
    [29-Jan-2023 Shift 1]
    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 _______.
    [29-Jan-2023 Shift 1]
  • Question 17/177
    4 / -1
    Mark Review
    The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is
    [29-Jan-2023 Shift 2]
    The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is
    [29-Jan-2023 Shift 2]
  • Question 18/177
    4 / -1
    Mark Review
    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 Shift 2]
    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 Shift 2]
  • Question 19/177
    4 / -1
    Mark Review
    The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ______.
    [29-Jan-2023 Shift 2]
    The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ______.
    [29-Jan-2023 Shift 2]
  • Question 20/177
    4 / -1
    Mark Review
    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 Shift 1]
    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 Shift 1]
  • Question 21/177
    4 / -1
    Mark Review
    The number of ways of selecting two numbers a and b, a∈{2,4,6,....,100}‌‌ and ‌‌b∈{1,3,5,....,99} such that 2 is the remainder when a+b is divided by 23 is
    [30-Jan-2023 Shift 2]
    The number of ways of selecting two numbers a and b, a∈{2,4,6,....,100}‌‌ and ‌‌b∈{1,3,5,....,99} such that 2 is the remainder when a+b is divided by 23 is
    [30-Jan-2023 Shift 2]
  • Question 22/177
    4 / -1
    Mark Review
    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 Shift 2]
    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 Shift 2]
  • Question 23/177
    4 / -1
    Mark Review
    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 Shift 1]
    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 Shift 1]
  • Question 24/177
    4 / -1
    Mark Review
    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 Shift 1]
    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 Shift 1]
  • Question 25/177
    4 / -1
    Mark Review
    If ‌2n+1Pn−1:‌2n−1Pn=11:21, then n2+n+15 is equal to:
    [31-Jan-2023 Shift 2]
    If ‌2n+1Pn−1:‌2n−1Pn=11:21, then n2+n+15 is equal to:
    [31-Jan-2023 Shift 2]
  • Question 26/177
    4 / -1
    Mark Review
    The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ________.
    [1-Feb-2023 Shift 1]
    The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ________.
    [1-Feb-2023 Shift 1]
  • Question 27/177
    4 / -1
    Mark Review
    Number of integral solutions to the equation x+y+z=21, where x≥1,y≥3,z≥4, is equal to _______.
    [1-Feb-2023 Shift 2]
    Number of integral solutions to the equation x+y+z=21, where x≥1,y≥3,z≥4, is equal to _______.
    [1-Feb-2023 Shift 2]
  • Question 28/177
    4 / -1
    Mark Review
    The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is ______.
    [1-Feb-2023 Shift 2]
    The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is ______.
    [1-Feb-2023 Shift 2]
  • Question 29/177
    4 / -1
    Mark Review
    The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _______.
    [6-Apr-2023 shift 1]
    The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _______.
    [6-Apr-2023 shift 1]
  • Question 30/177
    4 / -1
    Mark Review
    All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :
    [6-Apr-2023 shift 2]
    All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :
    [6-Apr-2023 shift 2]
  • Question 31/177
    4 / -1
    Mark Review
    The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is _______ :
    [6-Apr-2023 shift 2]
    The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is _______ :
    [6-Apr-2023 shift 2]
  • Question 32/177
    4 / -1
    Mark Review
    The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is.
    [8-Apr-2023 shift 1]
    The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is.
    [8-Apr-2023 shift 1]
  • Question 33/177
    4 / -1
    Mark Review
    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
    [8-Apr-2023 shift 1]
    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
    [8-Apr-2023 shift 1]
  • Question 34/177
    4 / -1
    Mark Review
    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
    [8-Apr-2023 shift 2]
    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
    [8-Apr-2023 shift 2]
  • Question 35/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 1]
    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-Apr-2023 shift 1]
  • Question 36/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 1]
    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-Apr-2023 shift 1]
  • Question 37/177
    4 / -1
    Mark Review
    Eight persons are tobe transported from city A to city B in three cars different makes. If each car can accomodate at most three persons, then the number of ways, in which they can be transported, is
    [10-Apr-2023 shift 2]
    Eight persons are tobe transported from city A to city B in three cars different makes. If each car can accomodate at most three persons, then the number of ways, in which they can be transported, is
    [10-Apr-2023 shift 2]
  • Question 38/177
    4 / -1
    Mark Review
    The sum of all the four-digit numbers that can be formed using all the digits 2,1,2,3 is equal to ________.
    [10-Apr-2023 shift 2]
    The sum of all the four-digit numbers that can be formed using all the digits 2,1,2,3 is equal to ________.
    [10-Apr-2023 shift 2]
  • Question 39/177
    4 / -1
    Mark Review
    The number of triplets (x,y,z), where x,y,z are distinct non negative integers satisfying x+y+z=15, is :
    [11-Apr-2023 shift 1]
    The number of triplets (x,y,z), where x,y,z are distinct non negative integers satisfying x+y+z=15, is :
    [11-Apr-2023 shift 1]
  • Question 40/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 1]
    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-Apr-2023 shift 1]
  • Question 41/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 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-Apr-2023 shift 2]
  • Question 42/177
    4 / -1
    Mark Review
    The number of five digit numbers, greater then 40000 and divisible by 5 , which can be formed using the digits 0,1,3,5,7 and 9 without repetition, is equal to
    [12-Apr-2023 shift 1]
    The number of five digit numbers, greater then 40000 and divisible by 5 , which can be formed using the digits 0,1,3,5,7 and 9 without repetition, is equal to
    [12-Apr-2023 shift 1]
  • Question 43/177
    4 / -1
    Mark Review
    Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
    [12-Apr-2023 shift 1]
    Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
    [12-Apr-2023 shift 1]
  • Question 44/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 1]
    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-Apr-2023 shift 1]
  • Question 45/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 2]
    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-Apr-2023 shift 2]
  • Question 46/177
    4 / -1
    Mark Review
    Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is _______.
    [13-Apr-2023 shift 2]
    Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is _______.
    [13-Apr-2023 shift 2]
  • Question 47/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 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-Apr-2023 shift 1]
  • Question 48/177
    4 / -1
    Mark Review
    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-Apr-2023 shift 1]
    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-Apr-2023 shift 1]
  • Question 49/177
    4 / -1
    Mark Review
    The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is
    [25-Jul-2022-Shift-1]
    The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is
    [25-Jul-2022-Shift-1]
  • Question 50/177
    4 / -1
    Mark Review
    The number of 5-digit natural numbers, such that the product of their digits is 36 , is _______.
    [26-Jul-2022-Shift-1]
    The number of 5-digit natural numbers, such that the product of their digits is 36 , is _______.
    [26-Jul-2022-Shift-1]
  • Question 51/177
    4 / -1
    Mark Review
    Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits 1,2,3,4,5 and 6 without repetition of digits. Then the total number of such numbers is _______.
    [26-Jul-2022-Shift-2]
    Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits 1,2,3,4,5 and 6 without repetition of digits. Then the total number of such numbers is _______.
    [26-Jul-2022-Shift-2]
  • Question 52/177
    4 / -1
    Mark Review
    Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is a multiple of 7 but not divisible by 5 , then 9p is equal to
    [27-Jul-2022-Shift-1]
    Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is a multiple of 7 but not divisible by 5 , then 9p is equal to
    [27-Jul-2022-Shift-1]
  • Question 53/177
    4 / -1
    Mark Review
    Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A,B,C,D,E} or a number from {1,2,3,4,5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1,2,3,4,5} is α×56, then α is equal to _______.
    [28-Jul-2022-Shift-1]
    Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A,B,C,D,E} or a number from {1,2,3,4,5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1,2,3,4,5} is α×56, then α is equal to _______.
    [28-Jul-2022-Shift-1]
  • Question 54/177
    4 / -1
    Mark Review
    A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then b+3g is equal to ________.
    [28-Jul-2022-Shift-2]
    A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then b+3g is equal to ________.
    [28-Jul-2022-Shift-2]
  • Question 55/177
    4 / -1
    Mark Review
    Let S={4,6,9} and T={9,10,11,...,1000}. If A={a1+a2+...+ak:k∈N,a1,a2,a3,...,akES}, then the sum of all the elements in the set T−A is equal to _______.
    [29-Jul-2022-Shift-1]
    Let S={4,6,9} and T={9,10,11,...,1000}. If A={a1+a2+...+ak:k∈N,a1,a2,a3,...,akES}, then the sum of all the elements in the set T−A is equal to _______.
    [29-Jul-2022-Shift-1]
  • Question 56/177
    4 / -1
    Mark Review
    The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2,3,4,5,6 (repetition of digits is not allowed) and divisible by 55 is _______.
    [29-Jul-2022-Shift-2]
    The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2,3,4,5,6 (repetition of digits is not allowed) and divisible by 55 is _______.
    [29-Jul-2022-Shift-2]
  • Question 57/177
    4 / -1
    Mark Review
    In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, −2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is___
    [24-Jun-2022-Shift-1]
    In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, −2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is___
    [24-Jun-2022-Shift-1]
  • Question 58/177
    4 / -1
    Mark Review
    The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1,2,3,4, 5,7 and 9 is__
    [24-Jun-2022-Shift-2]
    The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1,2,3,4, 5,7 and 9 is__
    [24-Jun-2022-Shift-2]
  • Question 59/177
    4 / -1
    Mark Review
    The sum of all the elements of the set {α∈{1,2,......,100}:HCF(α,24)=1} is___
    [24-Jun-2022-Shift-2]
    The sum of all the elements of the set {α∈{1,2,......,100}:HCF(α,24)=1} is___
    [24-Jun-2022-Shift-2]
  • Question 60/177
    4 / -1
    Mark Review
    The number of 3-digit odd numbers, whose sum of digits is a multiple of 7 , is____
    [25-Jun-2022-Shift-1]
    The number of 3-digit odd numbers, whose sum of digits is a multiple of 7 , is____
    [25-Jun-2022-Shift-1]
  • Question 61/177
    4 / -1
    Mark Review
    The total number of three-digit numbers, with one digit repeated exactly two times, is___
    [25-Jun-2022-Shift-2]
    The total number of three-digit numbers, with one digit repeated exactly two times, is___
    [25-Jun-2022-Shift-2]
  • Question 62/177
    4 / -1
    Mark Review
    There are ten boys B1,B2,......,B10 and five girls G1,G2,.......,G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is___
    [26-Jun-2022-Shift-1]
    There are ten boys B1,B2,......,B10 and five girls G1,G2,.......,G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is___
    [26-Jun-2022-Shift-1]
  • Question 63/177
    4 / -1
    Mark Review
    The total number of 3-digit numbers, whose greatest common divisor with 36 is 2 , is____
    [26-Jun-2022-Shift-2]
    The total number of 3-digit numbers, whose greatest common divisor with 36 is 2 , is____
    [26-Jun-2022-Shift-2]
  • Question 64/177
    4 / -1
    Mark Review
    The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is
    [27-Jun-2022-Shift-1]
    The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is
    [27-Jun-2022-Shift-1]
  • Question 65/177
    4 / -1
    Mark Review
    The total number of 5-digit numbers, formed by using the digits 1,2,3,5,6, 7 without repetition, which are multiple of 6 , is
    [28-Jun-2022-Shift-1]
    The total number of 5-digit numbers, formed by using the digits 1,2,3,5,6, 7 without repetition, which are multiple of 6 , is
    [28-Jun-2022-Shift-1]
  • Question 66/177
    4 / -1
    Mark Review
    Let A={1,a1,a2.......a18,77} be a set of integers with 1<a1<a2<......<a18<77. Let the set A+A={x+y:x,y∈A} contain exactly 39 elements. Then, the value of a1+a2+......+a18 is equal to___
    [28-Jun-2022-Shift-1]
    Let A={1,a1,a2.......a18,77} be a set of integers with 1<a1<a2<......<a18<77. Let the set A+A={x+y:x,y∈A} contain exactly 39 elements. Then, the value of a1+a2+......+a18 is equal to___
    [28-Jun-2022-Shift-1]
  • Question 67/177
    4 / -1
    Mark Review
    The number of ways to distribute 30 identical candies among four children C1,C2,C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to:
    [28-Jun-2022-Shift-2]
    The number of ways to distribute 30 identical candies among four children C1,C2,C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to:
    [28-Jun-2022-Shift-2]
  • Question 68/177
    4 / -1
    Mark Review
    Let b1b2b3b4 be a 4-element permutation with bi∈{1,2,3,.......,100} for 1≤i≤4 and bi≠bj for i≠j, such that either b1,b2, b3 are consecutive integers or b2,b3,b4 are consecutive integers. Then the number of such permutations b1b2b3b4 is equal to___
    [29-Jun-2022-Shift-1]
    Let b1b2b3b4 be a 4-element permutation with bi∈{1,2,3,.......,100} for 1≤i≤4 and bi≠bj for i≠j, such that either b1,b2, b3 are consecutive integers or b2,b3,b4 are consecutive integers. Then the number of such permutations b1b2b3b4 is equal to___
    [29-Jun-2022-Shift-1]
  • Question 69/177
    4 / -1
    Mark Review
    The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to____
    [29-Jun-2022-Shift-2]
    The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to____
    [29-Jun-2022-Shift-2]
  • Question 70/177
    4 / -1
    Mark Review
    The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
    [2021, 26 Feb. Shift-II]
    The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
    [2021, 26 Feb. Shift-II]
  • Question 71/177
    4 / -1
    Mark Review
    The total number of two digit numbers n′, such that 3n+7n is a multiple of 10 , is
    [2021, 25 Feb. Shift-II]
    The total number of two digit numbers n′, such that 3n+7n is a multiple of 10 , is
    [2021, 25 Feb. Shift-II]
  • Question 72/177
    4 / -1
    Mark Review
    The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 , is ........... .
    [2021, 25 Feb. Shift-I]
    The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 , is ........... .
    [2021, 25 Feb. Shift-I]
  • Question 73/177
    4 / -1
    Mark Review
    A natural number has prime factorisation given by n=2x3y5z, where y and z are such that y+z=5 and y−1+z−1=‌
    5
    6
    ,y>z    .
    Then, the number of odd divisors of n, including 1 , is
    [2021, 26 Feb. Shift-II]
    A natural number has prime factorisation given by n=2x3y5z, where y and z are such that y+z=5 and y−1+z−1=‌
    5
    6
    ,y>z    .
    Then, the number of odd divisors of n, including 1 , is
    [2021, 26 Feb. Shift-II]
  • Question 74/177
    4 / -1
    Mark Review
    The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is ‌‌
    [2021, 26 Feb. Shift-I]
    The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is ‌‌
    [2021, 26 Feb. Shift-I]
  • Question 75/177
    4 / -1
    Mark Review
    The total number of positive integral solutions (x,y,z), such that xyz=24 is
    [2021, 25 Feb. Shift-1]
    The total number of positive integral solutions (x,y,z), such that xyz=24 is
    [2021, 25 Feb. Shift-1]
  • Question 76/177
    4 / -1
    Mark Review
    The students S1,S2,...,S10 are to be divided into 3 groups A,B and C such that each group has at least one student and the group C has at most 3 students. Then, the total number of possibilities of forming such groups is .........
    [2021, 24 Feb. Shift-II]
    The students S1,S2,...,S10 are to be divided into 3 groups A,B and C such that each group has at least one student and the group C has at most 3 students. Then, the total number of possibilities of forming such groups is .........
    [2021, 24 Feb. Shift-II]
  • Question 77/177
    4 / -1
    Mark Review
    A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :
    [24-Feb-2021 Shift 1]
    A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :
    [24-Feb-2021 Shift 1]
  • Question 78/177
    4 / -1
    Mark Review
    The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2,2 and 3 is
    [2021, 18 March Shift-I]
    The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2,2 and 3 is
    [2021, 18 March Shift-I]
  • Question 79/177
    4 / -1
    Mark Review
    The missing value in the following figure is

    [2021, 18 March Shift-I]
    The missing value in the following figure is

    [2021, 18 March Shift-I]
  • Question 80/177
    4 / -1
    Mark Review
    If
    10
    ∑
    r=1
    r!(r3+6r2+2r+5)    =α(11!)    , then the value of α is equal to
    [2021, 18 March Shift-II]
    If
    10
    ∑
    r=1
    r!(r3+6r2+2r+5)    =α(11!)    , then the value of α is equal to
    [2021, 18 March Shift-II]
  • Question 81/177
    4 / -1
    Mark Review
    The number of times the digit 3 will be written when listing the integers from 1 to 1000 is
    [2021, 18 March Shift-1]
    The number of times the digit 3 will be written when listing the integers from 1 to 1000 is
    [2021, 18 March Shift-1]
  • Question 82/177
    4 / -1
    Mark Review
    Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to
    [2021, 17 March Shift-I]
    Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to
    [2021, 17 March Shift-I]
  • Question 83/177
    4 / -1
    Mark Review
    If the sides AB,BC and CA of a triangle △ABC have 3,5 and 6 interior points respectively, then the total number of triangles that
    can be constructed using these points as vertices, is equal to
    [2021, 17 March Shift-II]
    If the sides AB,BC and CA of a triangle △ABC have 3,5 and 6 interior points respectively, then the total number of triangles that
    can be constructed using these points as vertices, is equal to
    [2021, 17 March Shift-II]
  • Question 84/177
    4 / -1
    Mark Review
    Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segments AB,CD,BC,DA, respectively. Let α be the number
    of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then, (β−α) is equal to
    [2021, 16 March Shift-II]
    Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segments AB,CD,BC,DA, respectively. Let α be the number
    of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then, (β−α) is equal to
    [2021, 16 March Shift-II]
  • Question 85/177
    4 / -1
    Mark Review
    Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is
    [2021, 20 July Shift-1]
    Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is
    [2021, 20 July Shift-1]
  • Question 86/177
    4 / -1
    Mark Review
    There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include atleast 4 bowlers, 5 batsman and 1 wicketkeeper, is
    [2021, 20 July Shift-I]
    There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include atleast 4 bowlers, 5 batsman and 1 wicketkeeper, is
    [2021, 20 July Shift-I]
  • Question 87/177
    4 / -1
    Mark Review
    If the digits are not allowed to repeat in any number formed by using the digits 0,2,4,6, 8, then the number of all numbers greater than 10000 is equal to ......... .
    [2021, 22 July Shift-II]
    If the digits are not allowed to repeat in any number formed by using the digits 0,2,4,6, 8, then the number of all numbers greater than 10000 is equal to ......... .
    [2021, 22 July Shift-II]
  • Question 88/177
    4 / -1
    Mark Review
    If ‌nPr=‌nPr+1 and ‌nCr=‌nCr−1′ then the value of r is equal to
    [2021, 25 July Shift-II]
    If ‌nPr=‌nPr+1 and ‌nCr=‌nCr−1′ then the value of r is equal to
    [2021, 25 July Shift-II]
  • Question 89/177
    4 / -1
    Mark Review
    There are 5 students in class 10,6 students in class 11 and 8 students in class 12. If the number of ways in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100k, then k is equal to .........
    [2021, 25 July Shift-I]
    There are 5 students in class 10,6 students in class 11 and 8 students in class 12. If the number of ways in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100k, then k is equal to .........
    [2021, 25 July Shift-I]
  • Question 90/177
    4 / -1
    Mark Review
    Let n∈N and [ x] denote the greatest integer less than or equal to x. If the sum of (n+1) terms ‌nC0,3.‌nC1,5.‌nC2,7.‌nC3....... is equal to 2100.101, then 2[‌
    n−1
    2
    ]     is equal to
    [2021, 25 July Shift-II]
    Let n∈N and [ x] denote the greatest integer less than or equal to x. If the sum of (n+1) terms ‌nC0,3.‌nC1,5.‌nC2,7.‌nC3....... is equal to 2100.101, then 2[‌
    n−1
    2
    ]     is equal to
    [2021, 25 July Shift-II]
  • Question 91/177
    4 / -1
    Mark Review
    Let n be a non-negative integer. Then the number of divisors of the form" 4n+1′′ of the number (10)10⋅(11)11⋅(13)13 is equal to
    [2021, 27 July shift-II]
    Let n be a non-negative integer. Then the number of divisors of the form" 4n+1′′ of the number (10)10⋅(11)11⋅(13)13 is equal to
    [2021, 27 July shift-II]
  • Question 92/177
    4 / -1
    Mark Review
    The sum of all three-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11 , is
    [2021, 26 Aug. Shift-II]
    The sum of all three-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11 , is
    [2021, 26 Aug. Shift-II]
  • Question 93/177
    4 / -1
    Mark Review
    The number of three-digit even numbers, formed by the digits 0,1 , 3,4,6,7, if the repetition of digits is not allowed, is
    [2021, 26 Aug. Shift-I]
    The number of three-digit even numbers, formed by the digits 0,1 , 3,4,6,7, if the repetition of digits is not allowed, is
    [2021, 26 Aug. Shift-I]
  • Question 94/177
    4 / -1
    Mark Review
    A number is called a palindrome if it reads the same backward as well as forward For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is
    [2021, 27 Aug. Shift-I]
    A number is called a palindrome if it reads the same backward as well as forward For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is
    [2021, 27 Aug. Shift-I]
  • Question 95/177
    4 / -1
    Mark Review
    Let S={1,2,3,4,5,6,9}. Then, the number of elements in the set T={A⊂eqS:A≠φ and the sum of all the elements of A is not a multiple of 3 \} is
    [2021, 27 Aug. Shift-II]
    Let S={1,2,3,4,5,6,9}. Then, the number of elements in the set T={A⊂eqS:A≠φ and the sum of all the elements of A is not a multiple of 3 \} is
    [2021, 27 Aug. Shift-II]
  • Question 96/177
    4 / -1
    Mark Review
    The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is
    [2021, 31 Aug. Shift-1]
    The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is
    [2021, 31 Aug. Shift-1]
  • Question 97/177
    4 / -1
    Mark Review
    The number of ordered pairs (r,k) for which 6.35Cr =(k2−3)⋅‌36Cr+1, where k is an integer, is:
    [Jan. 7, 2020 (II)]
    The number of ordered pairs (r,k) for which 6.35Cr =(k2−3)⋅‌36Cr+1, where k is an integer, is:
    [Jan. 7, 2020 (II)]
  • Question 98/177
    4 / -1
    Mark Review
    An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ________.
    [NA Jan. 8, 2020 (I)]
    An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ________.
    [NA Jan. 8, 2020 (I)]
  • Question 99/177
    4 / -1
    Mark Review
    If a,b and c are the greatest values of ‌19Cp,‌20Cq and ‌21Cr respectively, then:
    [Jan. 8, 2020 (I)]
    If a,b and c are the greatest values of ‌19Cp,‌20Cq and ‌21Cr respectively, then:
    [Jan. 8, 2020 (I)]
  • Question 100/177
    4 / -1
    Mark Review
    The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______.
    [NA Jan. 8, 2020 (II)]
    The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______.
    [NA Jan. 8, 2020 (II)]
  • Question 101/177
    4 / -1
    Mark Review
    Lt
    r
    ≡‌25Cr     and C0+5⋅C1+9⋅C2+...+(101)⋅C25=225⋅k, then k is equal to
    [NA Jan. 9, 2020 (II)]
    Lt
    r
    ≡‌25Cr     and C0+5⋅C1+9⋅C2+...+(101)⋅C25=225⋅k, then k is equal to
    [NA Jan. 9, 2020 (II)]
  • Question 102/177
    4 / -1
    Mark Review
    If the number of five digit numbers with distinct digits and 2 at the 10‌th ‌ place is 336k, then k is equal to:
    [Jan. 9, 2020 (I)]
    If the number of five digit numbers with distinct digits and 2 at the 10‌th ‌ place is 336k, then k is equal to:
    [Jan. 9, 2020 (I)]
  • Question 103/177
    4 / -1
    Mark Review
    Total number of 6 -digit numbers in which only and all the five digits 1,3,5,7 and 9 appear, is:
    [Jan. 7, 2020 (I)]
    Total number of 6 -digit numbers in which only and all the five digits 1,3,5,7 and 9 appear, is:
    [Jan. 7, 2020 (I)]
  • Question 104/177
    4 / -1
    Mark Review
    Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
    [Sep. 06, 2020 (I)]
    Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
    [Sep. 06, 2020 (I)]
  • Question 105/177
    4 / -1
    Mark Review
    The value of (2⋅‌1P0−3⋅‌2P1+4⋅‌3P2−... up to 51‌th ‌ term ) +(1!−2!+3!−... up to 51‌th ‌ term ) is equal to :
    [Sep. 03, 2020 (I)]
    The value of (2⋅‌1P0−3⋅‌2P1+4⋅‌3P2−... up to 51‌th ‌ term ) +(1!−2!+3!−... up to 51‌th ‌ term ) is equal to :
    [Sep. 03, 2020 (I)]
  • Question 106/177
    4 / -1
    Mark Review
    If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is _______.
    [NA Sep. 02, 2020 (I)]
    If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is _______.
    [NA Sep. 02, 2020 (I)]
  • Question 107/177
    4 / -1
    Mark Review
    The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is ________.
    [NA Sep. 06, 2020 (II)]
    The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is ________.
    [NA Sep. 06, 2020 (II)]
  • Question 108/177
    4 / -1
    Mark Review
    The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.
    [NA Sep. 05, 2020 (I)]
    The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.
    [NA Sep. 05, 2020 (I)]
  • Question 109/177
    4 / -1
    Mark Review
    There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:
    [Sep. 05, 2020 (II)]
    There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:
    [Sep. 05, 2020 (II)]
  • Question 110/177
    4 / -1
    Mark Review
    A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
    [NA Sep. 04, 2020 (II)]
    A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
    [NA Sep. 04, 2020 (II)]
  • Question 111/177
    4 / -1
    Mark Review
    The total number of 3 -digit numbers, whose sum of digits is 10, is
    [NA Sep. 03, 2020 (II)]
    The total number of 3 -digit numbers, whose sum of digits is 10, is
    [NA Sep. 03, 2020 (II)]
  • Question 112/177
    4 / -1
    Mark Review
    Let n>2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is:
    [Sep. 02, 2020 (II)]
    Let n>2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is:
    [Sep. 02, 2020 (II)]
  • Question 113/177
    4 / -1
    Mark Review
    Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
    [Jan. 9, 2019 (I)]
    Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
    [Jan. 9, 2019 (I)]
  • Question 114/177
    4 / -1
    Mark Review
    The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to:
    [Jan. 09, 2019 (II)]
    The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to:
    [Jan. 09, 2019 (II)]
  • Question 115/177
    4 / -1
    Mark Review
    Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:
    [Jan. 09, 2019 (II)]
    Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:
    [Jan. 09, 2019 (II)]
  • Question 116/177
    4 / -1
    Mark Review
    If
    20
    ∑
    i=1
    (‌
    ‌20Ci−1
    ‌20Ci+‌20Ci−1
    )    3    =‌
    k
    21
    ,     then k equals:
    [Jan. 10, 2019 (I)]
    If
    20
    ∑
    i=1
    (‌
    ‌20Ci−1
    ‌20Ci+‌20Ci−1
    )    3    =‌
    k
    21
    ,     then k equals:
    [Jan. 10, 2019 (I)]
  • Question 117/177
    4 / -1
    Mark Review
    Consider three boxes, each containing 10 balls labelled 1,2,...,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the i‌th ‌ box, (i=1,2,3). Then, the number of ways in which the balls can be chosen such that n1<n2<n3 is :
    [Jan. 12, 2019 (I)]
    Consider three boxes, each containing 10 balls labelled 1,2,...,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the i‌th ‌ box, (i=1,2,3). Then, the number of ways in which the balls can be chosen such that n1<n2<n3 is :
    [Jan. 12, 2019 (I)]
  • Question 118/177
    4 / -1
    Mark Review
    There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is
    [Jan. 12, 2019 (II)]
    There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is
    [Jan. 12, 2019 (II)]
  • Question 119/177
    4 / -1
    Mark Review
    The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is:
    [April 08, 2019 (II)]
    The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is:
    [April 08, 2019 (II)]
  • Question 120/177
    4 / -1
    Mark Review
    A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:
    [April 9, 2019 (I)]
    A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:
    [April 9, 2019 (I)]
  • Question 121/177
    4 / -1
    Mark Review
    All possible numbers are formed using the digits 1,1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:
    [April 8, 2019 (I)]
    All possible numbers are formed using the digits 1,1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:
    [April 8, 2019 (I)]
  • Question 122/177
    4 / -1
    Mark Review
    The number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is:
    [April 10, 2019 (I)]
    The number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is:
    [April 10, 2019 (I)]
  • Question 123/177
    4 / -1
    Mark Review
    Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:
    [April 10, 2019 (II)]
    Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:
    [April 10, 2019 (II)]
  • Question 124/177
    4 / -1
    Mark Review
    The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct is:
    [April 12, 2019 (I)]
    The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct is:
    [April 12, 2019 (I)]
  • Question 125/177
    4 / -1
    Mark Review
    A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750 , then n is equal to :
    [April 12, 2019 (II)]
    A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750 , then n is equal to :
    [April 12, 2019 (II)]
  • Question 126/177
    4 / -1
    Mark Review
    n− digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is
    [Online April 15, 2018]
    n− digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is
    [Online April 15, 2018]
  • Question 127/177
    4 / -1
    Mark Review
    The number of four letter words that can be formed using the letters of the word BARRACK is
    [Online April 15, 2018]
    The number of four letter words that can be formed using the letters of the word BARRACK is
    [Online April 15, 2018]
  • Question 128/177
    4 / -1
    Mark Review
    The number of numbers between 2,000 and 5,000 that can be formed with the digits 0,1,2,3,4, (repetition of digits is not allowed) and are multiple of 3 is?
    [Online April 16, 2018]
    The number of numbers between 2,000 and 5,000 that can be formed with the digits 0,1,2,3,4, (repetition of digits is not allowed) and are multiple of 3 is?
    [Online April 16, 2018]
  • Question 129/177
    4 / -1
    Mark Review
    From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
    [2018]
    From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
    [2018]
  • Question 130/177
    4 / -1
    Mark Review
    If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
    [Online April 8, 2017]
    If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
    [Online April 8, 2017]
  • Question 131/177
    4 / -1
    Mark Review
    The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is:
    [Online April 9, 2017]
    The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is:
    [Online April 9, 2017]
  • Question 132/177
    4 / -1
    Mark Review
    A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
    [2017]
    A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
    [2017]
  • Question 133/177
    4 / -1
    Mark Review
    If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
    [2016]
    If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
    [2016]
  • Question 134/177
    4 / -1
    Mark Review
    If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is :
    [Online April 9, 2016]
    If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is :
    [Online April 9, 2016]
  • Question 135/177
    4 / -1
    Mark Review
    The value of
    15
    ∑
    r=1
    r2(‌
    ‌15Cr
    15Cr−1
    )     is equal to
    [Online April 9, 2016]
    The value of
    15
    ∑
    r=1
    r2(‌
    ‌15Cr
    15Cr−1
    )     is equal to
    [Online April 9, 2016]
  • Question 136/177
    4 / -1
    Mark Review
    If ‌
    ‌n+2C6
    ‌n−2P2
    =11    ,     then n satisfies the equation :
    [Online April 10, 2016]
    If ‌
    ‌n+2C6
    ‌n−2P2
    =11    ,     then n satisfies the equation :
    [Online April 10, 2016]
  • Question 137/177
    4 / -1
    Mark Review
    The sum
    10
    ∑
    r=1
    (r2+1)×(r!)     is equal to
    [Online April 10, 2016]
    The sum
    10
    ∑
    r=1
    (r2+1)×(r!)     is equal to
    [Online April 10, 2016]
  • Question 138/177
    4 / -1
    Mark Review
    The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0,0),(0,41) and (41,0) is :
    [2015]
    The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0,0),(0,41) and (41,0) is :
    [2015]
  • Question 139/177
    4 / -1
    Mark Review
    The number of integers greater than 6,000 that can be formed, using the digits 3,5,6,7 and 8 , without repetition, is:
    [2015]
    The number of integers greater than 6,000 that can be formed, using the digits 3,5,6,7 and 8 , without repetition, is:
    [2015]
  • Question 140/177
    4 / -1
    Mark Review
    The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
    [Online April 10, 2015]
    The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
    [Online April 10, 2015]
  • Question 141/177
    4 / -1
    Mark Review
    Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A×B each having at least three elements is :
    [2015]
    Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A×B each having at least three elements is :
    [2015]
  • Question 142/177
    4 / -1
    Mark Review
    If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is
    [Online April 11, 2015]
    If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is
    [Online April 11, 2015]
  • Question 143/177
    4 / -1
    Mark Review
    The sum of the digits in the unit's place of all the 4 -digit numbers formed by using the numbers 3,4,5 and 6, without repetition, is:
    [Online April 9, 2014]
    The sum of the digits in the unit's place of all the 4 -digit numbers formed by using the numbers 3,4,5 and 6, without repetition, is:
    [Online April 9, 2014]
  • Question 144/177
    4 / -1
    Mark Review
    An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:
    [Online April 11, 2014]
    An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:
    [Online April 11, 2014]
  • Question 145/177
    4 / -1
    Mark Review
    8-digit numbers are formed using the digits 1,1,2,2,2,3,4 4. The number of such numbers in which the odd digits do no occupy odd places, is:
    [Online April 12, 2014]
    8-digit numbers are formed using the digits 1,1,2,2,2,3,4 4. The number of such numbers in which the odd digits do no occupy odd places, is:
    [Online April 12, 2014]
  • Question 146/177
    4 / -1
    Mark Review
    Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:
    [Online April 19, 2014]
    Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:
    [Online April 19, 2014]
  • Question 147/177
    4 / -1
    Mark Review
    A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :
    [Online April 9, 2013]
    A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :
    [Online April 9, 2013]
  • Question 148/177
    4 / -1
    Mark Review
    The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:
    [Online April 22, 2013]
    The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:
    [Online April 22, 2013]
  • Question 149/177
    4 / -1
    Mark Review
    On the sides AB,BC,CA of a ∆ABC,3,4,5 distinct points (excluding vertices A,B,C ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are :
    [Online April 23, 2013]
    On the sides AB,BC,CA of a ∆ABC,3,4,5 distinct points (excluding vertices A,B,C ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are :
    [Online April 23, 2013]
  • Question 150/177
    4 / -1
    Mark Review
    5 - digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p:q is :
    [Online April 25, 2013]
    5 - digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p:q is :
    [Online April 25, 2013]
  • Question 151/177
    4 / -1
    Mark Review
    Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A×B having 3 or more elements is
    [2013]
    Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A×B having 3 or more elements is
    [2013]
  • Question 152/177
    4 / -1
    Mark Review
    Let Tn be the number of all possible triangles formed by joining vertices of an n -sided regular polygon. If Tn+1−Tn=10, then the value of n is :
    [2013]
    Let Tn be the number of all possible triangles formed by joining vertices of an n -sided regular polygon. If Tn+1−Tn=10, then the value of n is :
    [2013]
  • Question 153/177
    4 / -1
    Mark Review
    If the number of 5 -element subsets of the set A={a1,a2,...,a20} of 20 distinct elements is k times the number of 5 -element subsets containing a4, then k is
    [Online May 7, 2012]
    If the number of 5 -element subsets of the set A={a1,a2,...,a20} of 20 distinct elements is k times the number of 5 -element subsets containing a4, then k is
    [Online May 7, 2012]
  • Question 154/177
    4 / -1
    Mark Review
    Statement 1: If A and B be two sets having p and q elements respectively, where q>p. Then the total number of functions from set A to set B is qp
    Statement 2 : The total number of selections of p different objects out of q objects is ‌qCp
    [Online May 12, 2012]
    Statement 1: If A and B be two sets having p and q elements respectively, where q>p. Then the total number of functions from set A to set B is qp
    Statement 2 : The total number of selections of p different objects out of q objects is ‌qCp
    [Online May 12, 2012]
  • Question 155/177
    4 / -1
    Mark Review
    The number of arrangements that can be formed from the letters a,b,c,d,e,f taken 3 at a time without repetition and each arrangement containing at least one vowel, is
    [Online May 19, 2012]
    The number of arrangements that can be formed from the letters a,b,c,d,e,f taken 3 at a time without repetition and each arrangement containing at least one vowel, is
    [Online May 19, 2012]
  • Question 156/177
    4 / -1
    Mark Review
    If n=‌mC2, then the value of ‌nC2 is given by
    [Online May 19, 2012]
    If n=‌mC2, then the value of ‌nC2 is given by
    [Online May 19, 2012]
  • Question 157/177
    4 / -1
    Mark Review
    If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is
    [Online May 26, 2012]
    If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is
    [Online May 26, 2012]
  • Question 158/177
    4 / -1
    Mark Review
    Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
    [2012]
    Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
    [2012]
  • Question 159/177
    4 / -1
    Mark Review
    There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. Then :
    [2011RS]
    There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. Then :
    [2011RS]
  • Question 160/177
    4 / -1
    Mark Review
    Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is9C3
    Statement-2: The number of ways of choosing any 3 places from 9 different places is ‌9C3
    [2011]
    Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is9C3
    Statement-2: The number of ways of choosing any 3 places from 9 different places is ‌9C3
    [2011]
  • Question 161/177
    4 / -1
    Mark Review
    There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
    [2010]
    There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
    [2010]
  • Question 162/177
    4 / -1
    Mark Review
    From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is:
    [2009]
    From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is:
    [2009]
  • Question 163/177
    4 / -1
    Mark Review
    How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
    [2008]
    How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
    [2008]
  • Question 164/177
    4 / -1
    Mark Review
    The set S={1,2,3,......,12} is to be partitioned into three sets A,B,C of equal size.
    Thus A∪B∪C=S,A∩B=B∩C=A∩C=φ. The number of ways to partition S is
    [2007]
    The set S={1,2,3,......,12} is to be partitioned into three sets A,B,C of equal size.
    Thus A∪B∪C=S,A∩B=B∩C=A∩C=φ. The number of ways to partition S is
    [2007]
  • Question 165/177
    4 / -1
    Mark Review
    At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
    [2006]
    At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
    [2006]
  • Question 166/177
    4 / -1
    Mark Review
    If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
    [2005]
    If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
    [2005]
  • Question 167/177
    4 / -1
    Mark Review
    The value of ‌50C4+
    6
    ∑
    r=1
    ‌56−rC3     is
    [2005]
    The value of ‌50C4+
    6
    ∑
    r=1
    ‌56−rC3     is
    [2005]
  • Question 168/177
    4 / -1
    Mark Review
    How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
    [2004]
    How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
    [2004]
  • Question 169/177
    4 / -1
    Mark Review
    The range of the function f(x)=7−xPx−3 is
    [2004]
    The range of the function f(x)=7−xPx−3 is
    [2004]
  • Question 170/177
    4 / -1
    Mark Review
    The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
    [2004]
    The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
    [2004]
  • Question 171/177
    4 / -1
    Mark Review
    The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
    [2003]
    The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
    [2003]
  • Question 172/177
    4 / -1
    Mark Review
    A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
    [2003]
    A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
    [2003]
  • Question 173/177
    4 / -1
    Mark Review
    If ‌nCr denotes the number of combination of n things taken r at a time, then the expression ‌nCr+1+‌nCr−1+2×‌nCr equals
    [2003]
    If ‌nCr denotes the number of combination of n things taken r at a time, then the expression ‌nCr+1+‌nCr−1+2×‌nCr equals
    [2003]
  • Question 174/177
    4 / -1
    Mark Review
    The sum of integers from 1 to 100 that are divisible by 2 or 5 is
    [2002]
    The sum of integers from 1 to 100 that are divisible by 2 or 5 is
    [2002]
  • Question 175/177
    4 / -1
    Mark Review
    Number greater than 1000 but less than 4000 is formed using the digits 0,1,2,3,4 (repetition allowed). Their number is
    [2002]
    Number greater than 1000 but less than 4000 is formed using the digits 0,1,2,3,4 (repetition allowed). Their number is
    [2002]
  • Question 176/177
    4 / -1
    Mark Review
    Total number of four digit odd numbers that can be formed using 0,1,2,3,5,7 (using repetition allowed) are
    [2002]
    Total number of four digit odd numbers that can be formed using 0,1,2,3,5,7 (using repetition allowed) are
    [2002]
  • Question 177/177
    4 / -1
    Mark Review
    Five digit number divisible by 3 is formed using 0,1,2,3,4 6 and 7 without repetition. Total number of such numbers are
    [2002]
    Five digit number divisible by 3 is formed using 0,1,2,3,4 6 and 7 without repetition. Total number of such numbers are
    [2002]
User Profile
-

Not Visited

Un-answered

Answered

Review

Review with Answer

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12
  • 13
  • 14
  • 15
  • 16
  • 17
  • 18
  • 19
  • 20
  • 21
  • 22
  • 23
  • 24
  • 25
  • 26
  • 27
  • 28
  • 29
  • 30
  • 31
  • 32
  • 33
  • 34
  • 35
  • 36
  • 37
  • 38
  • 39
  • 40
  • 41
  • 42
  • 43
  • 44
  • 45
  • 46
  • 47
  • 48
  • 49
  • 50
  • 51
  • 52
  • 53
  • 54
  • 55
  • 56
  • 57
  • 58
  • 59
  • 60
  • 61
  • 62
  • 63
  • 64
  • 65
  • 66
  • 67
  • 68
  • 69
  • 70
  • 71
  • 72
  • 73
  • 74
  • 75
  • 76
  • 77
  • 78
  • 79
  • 80
  • 81
  • 82
  • 83
  • 84
  • 85
  • 86
  • 87
  • 88
  • 89
  • 90
  • 91
  • 92
  • 93
  • 94
  • 95
  • 96
  • 97
  • 98
  • 99
  • 100
  • 101
  • 102
  • 103
  • 104
  • 105
  • 106
  • 107
  • 108
  • 109
  • 110
  • 111
  • 112
  • 113
  • 114
  • 115
  • 116
  • 117
  • 118
  • 119
  • 120
  • 121
  • 122
  • 123
  • 124
  • 125
  • 126
  • 127
  • 128
  • 129
  • 130
  • 131
  • 132
  • 133
  • 134
  • 135
  • 136
  • 137
  • 138
  • 139
  • 140
  • 141
  • 142
  • 143
  • 144
  • 145
  • 146
  • 147
  • 148
  • 149
  • 150
  • 151
  • 152
  • 153
  • 154
  • 155
  • 156
  • 157
  • 158
  • 159
  • 160
  • 161
  • 162
  • 163
  • 164
  • 165
  • 166
  • 167
  • 168
  • 169
  • 170
  • 171
  • 172
  • 173
  • 174
  • 175
  • 176
  • 177
Mark Review Clear Selection
Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Click on Allow to receive notifications
×
Open Now