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05 Jul 2025, 07:36
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a=-15, b=-10 and c=5 verifies that a<b<c, c^4<b^4<a^4 and abc>0
a=-15, b=-10 and c=-5 verifies that a<b<c, c^4<b^4<a^4 and a^3b^5c^7<0
a=-15, b=-10 and c=0 verifies that a<b<c, c^4<b^4<a^4 and a^2b^4c^6=0
All the three could be true.
Answer E
a=-15, b=-10 and c=-5 verifies that a<b<c, c^4<b^4<a^4 and a^3b^5c^7<0
a=-15, b=-10 and c=0 verifies that a<b<c, c^4<b^4<a^4 and a^2b^4c^6=0
All the three could be true.
Answer E
05 Jul 2025, 07:55
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Given required conditions for a,b,c to follow for different scenarios
a < b < c
c^4 < b ^4 < a^4
Now lets go one by one with each option
I. abc > 0
Lets try the case,
a = -4
b = -2
c = 1
This satisfies the a,b,c conditions
a*b*c = -4 * -2 * 1 = 8 > 0
Satisfies abc > 0
II. a^3*b^5*c^7< 0
a = -4
b=-3
c= -2
Satisfies the above required conditions of a,b,c
Now,
a^3*b^5*c^7 = (-4)^3*(-3)^5*(-2)^7
Since the exponential powers are odd for the negative numbers and the addition of the exponents gives an odd number (3+5+7 = 15)
=> a^3*b^5*c^7 <0
It satisfies the option a^3*b^5*c^7< 0
III. a^2*b^4*c^6= 0
a = -4
b = -2
c = 0
Satisifes the required a,b,c conditions
So, a^2*b^4*c^6 = (-4)^2*(-2)^4*(0)^6 = 0
It satisfies the option a^2*b^4*c^6= 0
E. I, II, and III
a < b < c
c^4 < b ^4 < a^4
Now lets go one by one with each option
I. abc > 0
Lets try the case,
a = -4
b = -2
c = 1
This satisfies the a,b,c conditions
a*b*c = -4 * -2 * 1 = 8 > 0
Satisfies abc > 0
II. a^3*b^5*c^7< 0
a = -4
b=-3
c= -2
Satisfies the above required conditions of a,b,c
Now,
a^3*b^5*c^7 = (-4)^3*(-3)^5*(-2)^7
Since the exponential powers are odd for the negative numbers and the addition of the exponents gives an odd number (3+5+7 = 15)
=> a^3*b^5*c^7 <0
It satisfies the option a^3*b^5*c^7< 0
III. a^2*b^4*c^6= 0
a = -4
b = -2
c = 0
Satisifes the required a,b,c conditions
So, a^2*b^4*c^6 = (-4)^2*(-2)^4*(0)^6 = 0
It satisfies the option a^2*b^4*c^6= 0
E. I, II, and III
06 Jul 2025, 05:41
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Given that a<b<c and c^4<b^4<a^4, and which of the following statements COULD BE TRUE
I. abc>0
II. a^3 b^ 5 c^7<0
III. a^2 b^ 4 c^6=0
The possible cases are:
Case 1: a= -2,b=-1,c=2, (a,b negative and C is positive), here statement I could be true
Case 2:a=-2, b=-1, c=0, (a,b negative and C is zero), here statement III could be true
Case 3:a=-3, b=-2, c=-1, (a,b & c negative), here statement II could be true
Therefore, option E, I, II & III could be true.
I. abc>0
II. a^3 b^ 5 c^7<0
III. a^2 b^ 4 c^6=0
The possible cases are:
Case 1: a= -2,b=-1,c=2, (a,b negative and C is positive), here statement I could be true
Case 2:a=-2, b=-1, c=0, (a,b negative and C is zero), here statement III could be true
Case 3:a=-3, b=-2, c=-1, (a,b & c negative), here statement II could be true
Therefore, option E, I, II & III could be true.
