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Permutation combination - special cases || Quantitative Aptitude || CAT 2021 || 12 June (App update required to attempt this test)

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Question 1

p, q, r and s are one of the digits 1, 7, 5 or 6, with each digit used only once. How many different values of p × s + r × q can be obtained?

Question 2

A television channel has eight shows – A,B, K,L,M,N,Y,Z − which are available for three prime-time slots on a Wednesday evening. In how many different ways can the shows be shown, if show A can come only after program B provided that maximum of 1 show can run in 1 slot ? (TITA)

Question 3

The number of different solutions (x,y,z) of the equation x + y + z = 10, where x, y and z are positive integers, is

Question 4

All words formed by permutations of the word 'WARE' are arranged in a list according to the dictionary ordering. The position of the word 'WEAR' in this list is at number

Question 5

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Question 6

Ravi has a board, similar to a chessboard, except that it has only 6 × 6 squares. He calculated the number of rectangles (including rectangle whose length and breadth are equal) on the board. How many distinct values can the area of these rectangles assume? (TITA)

Question 7

In how many ways is it possible to choose two black squares on an 8 × 8 chessboard so that they neither lie in the same row nor in the same column?

Question 8

There are 6 boxes numbered 1, 2,..., 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

Question 9

A boy needs to climb a staircase of 10 stairs. At each step he can cover either one stair or two stairs. The number of different ways in which he can climb the staircase is

Question 10

How many elements are present in the domain of 9–xCx+1?
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