CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Given that p,q,r,s,t,u are integers and p+q+r+s+t+u=2005, what is the minimum value of (-1)p + (-1)q +(-1)r +(-1)s +(-1)t +(-1)u ?

A
-2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
-3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
none of these
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is C none of these

p + q + r + s + t + u = 2005 of the 6 integers, the number of integers that can be odd is 5,3 or 1. In the expression (-1)p+ (-1)q +(-1)r +(-1)s +(-1)t +(-1)u

1)When one integer is even and the others are odd, then only one among is +1 and others are -1 each. Hence the sum of the terms is -5 + 1 = -4.

2)When three of the integers are even, then three of the terms are +1 each and the remaining three are -1 each. Hence the sum is 0.

3)When five of the integers are even, then five terms will be +1 each and the other term is -1. Hence the sum is 4. The minimum value of the sum is -4.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon