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Q1. L1 ≡ ax+by+c and L2 ≡ lx+my+n , where a,b,c,l,m,n are real.
L1+λL2=0 represent all lines passing through intersection of L1=0 and L2=0
(True/False)?
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Q2. Lim(x→0)(sin(1/x))/(sin(1/x)) = ?
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Q.3 x = (2y±(2y-1-y2)1/2 )/2 is a second degree general curve here it represents ?
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Q.4 The solution of f(x)=f-1(x) if exists lie on ?
a) y=x
b) y=-x
c) None(Specify)
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89 Answers
21NO NO..... [2]
not gr8 job
maine tumhara aur sir ka wonderful discussion dekha tha
[2] [17]
33Oh, my teacher asked me this and we were blank so he gave us that example so i never thought of simpler example y=-x
33Easy hai try karo naa.... thode der me khud dikh jaega.... no high concept required...
33Q. 4 is most interesting...
those who have not read the solutions... should try it..
21Q3 mein kya karna hai?
h2-ab and discrimnant apply karna hai kya?
33Q1. L1 ≡ ax+by+c and L2 ≡ lx+my+n , where a,b,c,l,m,n are real.
L1+λL2=0 represent all lines passing through intersection of L1=0 and L2=0
(True/False)?
______________________________________________________
Q2. Lim(x→0)(sin(1/x))/(sin(1/x)) = ?
______________________________________________________
Q.3 x = (2y±(2y-1-y2)1/2 )/2 is a second degree general curve here it represents ?
______________________________________________________
Q.4 The solution of f(x)=f-1(x) if exists lie on ?
a) y=x
b) y=-x
c) None(Specify)
Just for refeernce of question... baar baar 1st page jana padta hai.. :)
33@tapan...
yes there is few pinks... but each post has something....
33Does that linear combination represents the parent line L2 for any value of λ.
More appropriate linear combination would be ...........
62okie.. that 0-pi was a good guess... i mean the line sweeps the whole plane
I though the same thing wud work here as well.. but it does not..
So this correction :)
62yeah i am wrong..
it should have been -1<=λ<=1
sory :)
y? because take an example x=0, y=0
will this give the set of all lines?
no it will give lines only on +ve quadrant!
It will not generate x-y=0!
62hey hang on.. i am getting confused :D
wait give me 5 mins.. i will tell u exactly what :)
33What a gud question i have touched!!! now i need time to think...
may be 4 same reason we need only 0-pi angle 4 line's slope.. well may be..
62In my opinion, this is a slightly better form of ur solution.. *only slightly :)
62well abhishek there u are perfectly correct...
btw ur answers will give a few repetitions...
may be this form? λL1+(1-λ)L2=0 {0≤λ≤1}
33Actually the linear combination is λ1L1+λ2L2=0
and we divide entire eqn by λ1 and write λ1/λ2 = λ assuming λ1 is not equal to 0 thus 1 line is lost in the family.
33Now here comes a complete soln of a question but lets see if others try other questions....
33Read the def of limits...
lim(x→a)f(x)=b means as value of x approaches 'a' (always keeping itself in the domain of the function) f(x) approaches a fixed value 'b'.
1Nishant , isn't the first one true ?
let the point of intersection be ( h , k)
L1 = ah + bk + c = 0
and L2 = lh + mk +n = 0
therefore any linear combination i.e L1 +λ L2 = 0 is true for all λ , as L1 and L2 are separately 0 .