1) The sum of the products of ten numbers +1,-1,+2,-2,+3,-3,+4,-4,+5,-5 taking two at a time is ?
2) If ab=2a+3b,a & b positive then minimum value of ab is?
3) a,b are positive then the minimum value of logba+ logab is ?
4) Maximum value of x/y for (x-2)2=4 & (y-3)2 =25?
5) If a & b are both positive real valuesthen the minimum value of (a+b)(1/a+1/b) is?
6) In the above question what is the maximum value?
7)Maximum value of y=mod(x-5)+mod(x-7)?
8) Minimum value of x/y for (x-2)2=9 and (y-3)2=25 ?
Answer: 1) -55
2)24
3)2
4)1/2
5)4
6)Infinity
7)Infinity
8)5/8
1) The sum of the products of ten numbers +1,-1,+2,-2,+3,-3,+4,-4,+5,-5 taking two at a time is ?
ans is=-55(-1-4-9-16-25=-55)
Little Star
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Qs -2
We can get value of ab in terms of a or b.
if F = ab so from given eq ab=2a+3b
we have
F=2a^2/(a-3) bcz b = 2a/(a-3)
min value of ab is min value of F.
Using fundamental principal find out df/da.
and put df/da=0;
gives a=0,6
for a=6 d^2f/da^2 > 0 hence gives minimum value.
so b =4 now.
Hence min value is 6*4 i.e. 24
Qs 3-
for any +ve number x the min value of x+1/x is 2.
Qs 4-
we have pair of values as x=0,4 & y=8,-2
& we know tht a +ve num > a -ve number or > 0
so by making 4 unique pair of values onle (x,y) i.e. (4,8) gives +ve number
so maximum value of x/y is 4/8 i.e 1/2.
Qs 5-
On simplification
(a+b)(1/a+1/b) yields 2+a/b+b/a
again min value of x+1/x is 2 so min value of a/b+1/(a/b) is 2.
so min value of (a+b)(1/a+1/b) is 2+min of (a/b+b/a) i.e. 2+2
Hence 4
Qs 6-
Is is quite obvious there is no upper limit for x+1/x for +ve x.
so its infinite.
Qs 7-
|x| >= 0 for any x
so |x-5|+|x-7| > 0 for all x.
we can assume any value of x and we get a value higher thn before so maximum
value is infinity.
and min value is 2 for x=5,6,7
Qs 8-
we have pair of values as x=5,-1 & y=8,-2
since no constraint of +ve value is taken so i think min value should be -2/5.
Any comments on above solutions are kindly welcome.
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I think the answer of Q8 should be -1/8...
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