Permutations and Combinations questions
785 published questions with worked solutions.
- Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits...
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word 'MATHS' such that any...
- 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 number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is...
- The largest n ∈ N such that 3^n divides 50! is :
- Line L1 of slope 2 and line L2 of slope 1 2 intersect at the origin O. In the first quadrant, P1, P2 ….P12 are 12 points on line...
- The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers...
- If S is a set with 10 elements and A= (x,y):x,y S, x y , then the number of elements in A is
- Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n(X Y) is equal...
- If A= n: n^3+5n^2+2 n is an integer , n itself is an integer , then the number of elements in the set A is
- If A= p:p= (n+2)(2n^5+3n^4+4n^3+5n^2+6) n^2+2n , n,p Z^+ , then the number of elements in the set A is
- Let X= 1,2,3,4,5 . The number of different ordered pairs (Y,Z) that can be formed such that Y X, Z X and Y Z is empty, is (AIEEE...
- Let S= 1,2,3,4,5,6,9 . Then the number of elements in the set T= A S:A and the sum of all the elements of A is not a multiple of...
- Let n(A)=4 and n(B)=6. The number of one-one functions from A to B is
- Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is
- Let n be a natural number. Then the range of the function f(n)= ^ 8-n P_ n-4 , 4 n 6, is
- If D_ 30 is the set of the divisors of 30, for x,y D_ 30 we define x+y= LCM (x,y), x y= GCD (x,y), x'= 30 x and f(x,y,z)=(x+y)...
- If X= 1,2,3,4 , then one-one onto mappings f:X X such that f(1)=1, f(2) 2, f(4) 4 are given by
- If f:N N is defined by f(n)= the sum of positive divisors of n, then f(2^k 3), where k is a positive integer, is
- The domain of definition of the function f(x)= ^ 7-x P_ x-3 is
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