Q1) If IxI - IyI =13, then which of the following cannot be the value of x - y ? a) -18 b) -9 c) -17 d) none of these Q2) The min value of 3x + 3y + z , subjected to the condition xyz = 24,where x,y,z are all positive real no's, is? a) 14 x 31/3 b) 18 c) 216 d) 12 Q3) A group of children walk to a shop & bought pastries for a total for a total of Rs.168 & ice candies for a total for a total of Rs.126. Each child has one pastry & one ice candy. How many children could be there in the group? a)28 b) 21 c) 42 d) 36 Q4) What is the least value of (x-2)(x-4)2(x-6) + 6, for real values of x? a) 6 b) 4/3 c) 4 d) none of these Q5) If a,b,c are all positive, then what is the min value of a/(b+c) + b/(c+a) +c/(a+b) ? a) 1 b) 3 c) 9 d) 27 Q6) The min value of 3x + 4y , subjected to the condition x2y3=6,where x,y are positive is? a) 10 b) 14 c) 13 d) 15 Q7) Consider the following funcns: f(x) = x2 + 3x g(x) = 3x + 4 For what value of 'x' will f[g(x)] have its min value ? a) 0 b) -11/2 c) -11/6 d) none of these Q8) What is the max value of f(x) = max (4x+3 , 3x+6), for x € [-6,10]? a) +infinity b) 4 c) 6 d) none of these Q9) What is the max value of f(x) = min (4-5x , x-3), for x € (0,4)? a) -1 b) 2 c) 4 d) none of these
ANSWERS GIVEN: 1) b 2) b 3) c 4) d 5) c 6) a 7) a 8) c 9) d |
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Q2) The min value of 3x + 3y + z , subjected to the condition xyz = 24,where x,y,z are all positive real no's, is?
a) 14 x 31/3 b) 18 c) 216 d) 12
ANS:
To minimize 3x + 3y + z , we need to minimize all the three terms 3x, 3y and z.
as the coefficient of x and y are same 3, the value 3x + 3y 'll be minimum when x = y
So we get x2 z= 24
=> z = 24/x2
Now we have to minimize the function f(x) = 6x + 24/x2
=> 6 - 24*2*x-3 = 0
=>6 = 48x-3
=>x=2=y
and z=6
So the minimum value = 18
n/a
Q3. Please check it again . . . The question doesn’t make any sense. .
n/a
Q4) What is the least value of (x-2)(x-4)2(x-6) + 6, for real values of x?
a) 6 b) 4/3 c) 4 d) none of these
ANS:
I am getting the minimum value at x = 5/2
and the value as 33/16
n/a
Consider the following funcns:
f(x) = x2 + 3x
g(x) = 3x + 4
For what value of 'x' will f[g(x)] have its min value ?
a) 0 b) -11/2 c) -11/6 d) none of these
Ans:
Here also I m getting the answer as c -11/6
and the minimum value of f[g(x)] at x= -11/6 is -20.25 and at x =0 is 28
Plz confirm the answer
n/a
Q3
HCF of 168 and 126 which is 42 .
n/a
Q5
Given a,b,c are positive. Assume them as 1,2,3 ( since real not specified)
substituting them we get the answer as 1.7 which is way less than 9 which is the given ans.
If we take positive real values the ans would be even less than 1.7 approaching the limit of '1'.
Any body got the correct ans?
n/a
Q6
x2y3=6
y = 61/3/x2/3 substitute in 3x + 4y and differentiate w.r.t 'x' and equate to zero
we get the 'x' value as 4/3.
So y = 3/2
Substitute in equ and we get minimum value of '10'
so ans (a)
n/a
Q7
Yes the equ will be min when x = -11/6
At this value the function becomes '-9/4' ( -2.25) not -20.25.
n/a
Q9
Given x € ( 0,4) i.e x = 1,2,3
x = 1 min ( -1,-4) = -4
x = 2 min ( -6,-1) = -6
x = 3 min ( -11,0) = -11
now max of min of the function is '-4'
so ans (d)
n/a
Q8
max (4x+3 , 3x+6),
max of above will be when x = 10 which is '43'.
but the ans given is '6'
anyone got the ans?
n/a
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