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needle

ouestion repeat:

a plane is ruled with parallel straight lines at equal distances of 2a units. aneedle 2l long(l<a) is thrown on the plane at random.

find the probability that the needle will hit any of the lines

the answer is 2l /

a

but how??????

i could get any idea of getting this

benzoyl chloride on hydrolysis gives benzoic acid bcoz O being more e.n attracts the b.p from C and also Cl is also more E.N so it takes the C-Cl bond pair and leaves of so C gets +ve charge so when it is hydrolysed OH attacks the electron defficientC and forms BENZOIC ACID

paddy ur right

^n-3P_{r -1}/ ^n-1P_r-1

x³-3x²-9x+p=0

let the common root be "a" and the other be "b"

then 2a+b=3 .........(1)

and a²+2ab= -9........(2)

and a²b=-p => b= - p / a²............(3)

(1)=> 2a - p/a² =3 => a³-3a²-p =0 ....(4)

(2)=> a²-2p / a = -9 => a³+9a - 2p = 0...(5)

(4) & (5) must hav real roots and roots of both are same

(5) - (4) => 3a² +9a -p=0must hav real roots

there fore 9²-4(-p)(3) >= 0 => p >= -81/12

plzz check if any thing is wrong

Re:question.........

for the 2nd bit::::::

x+y+z=11

the only possibilities of x,y are even iss::::

(x,y)=(2,2),,,,(2,4),,,(4,2),,(2,6),,,(6,2),,,(2,8),,,,(8,2),,,,(4,4),,(4,6),,,(6,4)

=10 ways

total possibilities ==¹¹⁺²C₂

there fore the answer is

==10x2 / 13x12== 5/39

1st arrange the no of 3's

if one 3 is there then 2 can be put in 7ways
_3_3_3_3_3_3_

and
similarly if there are 2 2's them the total no.of arranged in 15ways

6c2
_3_3_3_3_3_

if there r 3 2's the
_3_3_3_3_
5c3= 10

if there r 4 2's the
_3_3_3_
4c4 = 1

and further will not be possible bcoz 2's will definitely come side by side
so total no,s = 7+15+10+1=33

is the answer 33?

yes the answwer is right but how?

a plane is ruled with parallel straight lines at equal distances of 2a units. aneedle 2l long(l<a) is thrown on the plane at random.

find the probability that the needle will hit any of the lines

it is very nice this gives some enrichment about each topic every month and some questions at the end of the enrichment differently for iit and aieee

with well explained solutions

the two eyes blink together, sleep together,wake together even if they dont see each other that is friend ship