Test Index

UPSC CDS 2 2021 Math Paper

Directions (Q.Nos. 84 and 85)

C

onsider the following for the next two questions that follow.

Collect all the sequences of five consectutive integers such that their product is equal to one of these integers. Let

X

be the collection of all possible such sequences. Let

P

be the smallest integer and

Q

be the largest integer occuring in these sequences.

Question : 84 of 100

Marks: +1, -0

How many such sequences of five consecutive integers are possible ?

One
Two
Three
Five

Validate

Solution: 👈: Video Solution

Let five consecutive integers be in the form

(x-2),(x-1), x,(x+1)

and

(x+2)

Since, it is given that the product of these five consecutive integers is equal to one of these integers. This is only possible when one of the integer is zero.

Hence, all possible sequences are

(i)

-4,-3,-2,-1,0

(ii)

-3,-2,-1,0,1

(iii)

-2,-1,0,1,2

(iv)

-1,0,1,2,3

and (v)

0,1,2,3,4

Hence, number of required sequences will be five.

Go to Question:

Prev Question

Next Question