Applications of P&C: JEE Questions & Solutions

The number of strictly increasing functions f from the set 1, 2, 3, 4, 5, 6 to the set 1, 2, 3,, 9 such that f(i) i for 1 i 6, is equal to:

Let S = (m, n): m, n 1, 2, 3,....., 50. If the number of elements (m, n) in S such that 6^m+9^n is a multiple of 5 is p and the number of…

The largest n N, for which 7^n divides 101!, is:

If ( 1^15C0 + 1^15C1) ( 1^15C1 + 1^15C2) ( 1^15C12 + 1^15C13) = ^13^14C0 ^14C1 ^14C12, then 30 is equal to.

Let ABC be a triangle. Consider four points p1, p2, p3, p4 on the side AB, five points p5, p6, p7, p8, p9 on the side BC, and four points…

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPRSTUVP, is:

The number of ways 16 oranges distributed to 4 children, each gets at least one.

Let S denote the set of 4-digit numbers abcd such that a b c d and P denote the set of 5-digit numbers having product of its digits equal…

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,9, if repetition of…

The largest value of n, for which 40^n divides 60!, is

The letters of the word UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary.…

Let S= 1,2,3,4,5,6,7,8,9. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated…

Three persons enter a lift at the ground floor. The lift will go up to the 10th floor. The number of ways in which the three persons can…

Let A = 1, 2, 3, 4 and B = 1, 4, 9, 16. Then the number of many-one functions f: A B such that 1 f(A) is equal to:

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways in which these girls and boys can stand in a queue such…

If r=1^30 r^2 ( 30r)^2 = 2^29, then is equal to.

The number of words that can be formed using all the letters of the word "DAUGHTER" such that all the vowels never come together, is:

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is.

Number of functions f: 1, 2,, 100 0, 1, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of…

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is.

Let P be the set of seven-digit numbers with the sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2,…

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that…

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at…

The largest n N such that 3^n divides 50! is:

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at…

If the number of seven-digit numbers, such that the sum of their digits is even, is m n 10^a; m, n 1, 2, 3,..., 9, then m + n is equal to

Line L1 of slope 2 and line L2 of slope 12 intersect at the origin O. In the first quadrant, P1, P2,, P12 are 12 points on line L1 and Q1,…

Consider the sets A = (x, y) R R: x^2 + y^2 = 25, B = (x, y) R R: x^2 + 9y^2 = 144, C = (x, y) Z Z: x^2 + y^2 4, and D = A B. The total…

Let m and n, m < n be two 2-digit numbers. Then the total number of pairs (m, n) such that (m, n) = 6, is

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4…

For n 2, let Sn denote the set of all subsets of 1, 2, 3,, n with no two consecutive numbers. For example, 1, 3, 5 S6, but 1, 2, 4 S6.…

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides, and q be the number of…

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number…

Let = (4!)!((4!)^3)! and = (5!)!((5!)^4)!. Then:

All the letters of the word “GTWENTY” are written in all possible ways with or without meaning, and these words are arranged as in a…

If (^11C1)(^11C2) + (^11C2)(^11C3) + + (^11C9)(^11C10) = nm with (n, m) = 1, then n + m is equal to:

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

In an examination of Mathematics paper, there are 20 questions of equal marks, and the question paper is divided into three sections: A, B,…

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…

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:

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of…

There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC. Similarly, there are 6 points P6, P7,, P11 on…

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition, is:

The number of square matrices of order 5 with entries from the set 0, 1, such that the sum of all the elements in each row is 1 and the sum…

Number of Non-Empty Subsets with Sum Divisible by 3 Problem: Let S = 1, 2, 3, 5, 7, 10, 11. The number of non-empty subsets of S such that…

Let x and y be distinct integers where 1 x 25 and 1 y 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5,…

k=0^6 ^(51-k)C3: is equal to

If all the six-digit numbers x1x2x3x4x5x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in increasing order, then the sum of the digits…

Five-digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions allowed, and are written in descending order with serial…

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…

The number of 3-digit numbers that are divisible by either 3 or 4 but not divisible by 48 is:

The number of ways of selecting two numbers a and b, a 2, 4, 6,, 100 and b 1, 3, 5, 7,, 99 such that 2 is the remainder when a + b is…

The number of seven-digit odd numbers that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is........

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to:

Let A = [aij], where aij Z [0, 4], 1 i, j 2. The number of matrices A such that the sum of all entries is a prime number p 2, 13 is:

The value of 11!50! + 13!48! + 15!46! + + 149!2! + 151!1! is:

The number of 3-digit numbers that are divisible by either 2 or 3 but not divisible by 7 is:

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…

The total number of six-digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is.

Number of integral solutions to the equation x + y + z = 21, where x 1, y 3, z 4, is.

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is:

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.…

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…

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is:

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:

The largest natural number n such that 3^n divides 66! is:

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple is in a match, is…

The number of permutations of the digits 1, 2, 3,..., 7 without repetition, which neither contain the string 153 nor the string 2467, is:

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most 3 persons,…

The number of triplets (x, y, z), where x, y, z are distinct non-negative integers satisfying x + y + z = 15, is:

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…

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…

The number of five-digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without…

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…

The number of seven digit positive integers formed using the digits 1, 2, 3, and 4 only and the sum of the digits equal to 12 is:

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written in a dictionary with serial…

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:

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…

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…