24thanks sir [1]
Column 1
1)Domain of log4log5log3(18x-x2-77)
2)Range of x3+3x2+10x+sinx
Column 2
A)(-∞,∞)
B)[-4,3-√21/2]U(1,∞)
C)(-Ï€,-Ï€/2)
D)none
wrong ques..thats why hiding..i got 1) as (7,11) and marked it A,B but ans is D)
i got 2) as (-∞,∞) and marked as A,B,C but ans is A) only...
am i wrong ??????
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20 Answers
1yeah agree with qwerty regarding ques 1 and 2.he's absolutely right.
answers are (8,10) for q 1 and (-∞,∞) for q 2.
66for Q2) the correct answer is (-∞,∞). The other options must not be marked since then we shall miss out certain values.
23i dont think so B and C can be answers,
u cant limit the range ,
well, i think we shud confirm it from an expert
btw no one else interested it seems [2]
23Q2 is also straight and simple ,
i hav given d ans and explanation also ,
23@ eureka , for x belonging to (7 8], function bcomes undefined , try it out ,
it isnt true just bcz FIITJEE says it
1for 1...ans is (8,10)...then how can it b A, B.....obviously its D.....all the elements of the option...must lie in the domain of ur ans.... for 2...even i think its A,B,C....then the ans must b given as a single option n most apt one
24no its fiitjee....and ya i was wrong for Q1....but i am dead sure for 2
1is it frm BMAT??
Even i have the same doubts , ........i think ur marking is right.......atleast for 2.This has happened in a couple of other BT tests too.......
24ya i was going wrong way for 1)
but anyways for that we had to do x2-18x+77<0 and nthing else....
for 2) here is my argument..
we get range as (-∞,∞) and options B,C are subsets of set (-∞,∞) ..so they should also be marked...
23basically eureka , we hav to match the columns for range , not for codomain !!!!
23if range of f(x) is (a,b) , where a and b are finite no,
then u cant mark (- ∞, ∞)
bcz range means the set of all values that f(x) attains , for all x in its domain.
so if u r marking (- ∞, ∞) , dis means the f(x) exceeds b , for some x , which is false .
On the other hand , if
f(x) lies from (- ∞, ∞) , then u cant mark (a,b) ,
bcz when u mark (a,b) , u are claiming that f(x) never exceeds b , wich is false , since f(x) > b for some x
23(Q2)f(x)=x^{3}+3x^{2}+10x+sinx
f(x)=x^{3}+3x^{2}+3x+1+7x+(sinx-1)
f(x)=(x+1)^{3}+7x+(sinx-1)
f'(x)=3(x+1)^{2}+7+cosx
\Rightarrow ,f'(x)>0\;for\;all\;x
\Rightarrow f(x)\;is\;an\;increasing\;function
\Rightarrow f(x) \in(-∞,∞)
hence only A can be the ans ,
marking B,C also limits the range of f(x) to a certain value
23y =log_{4}log_{5}log_{3}(t)
\Rightarrow log_{5}log_{3}(t)>0
\Rightarrow log_{3}(t)>1
\Rightarrow (t)>3
\Rightarrow 18x-x^{2}-77>3
\Rightarrow x^{2}-18x+80<0
\Rightarrow (x-10)(x-8)<0
\Rightarrow x \; \; \in \; (8,10)