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let t1 be time of acc,t2 be time of deceleration

v=a(t₁)=2t₁,

also 0-v=-r(t₂)=4t₂

hence ==>2t1=4t2 or t1=2t2

Also t1+t2=3

from these we get t1=2sec,t2=1 sec

fwks_phoenix, tan-cot r positive in 3rd quad..ASTC not ASCT

also,300 and -60 degrees represent the same angle

-60 does not lie btween 0 and 360

This way random errors can be reduced...eg miscalculations.

but errors like instrumental errors will remain the same

It looks like the graph of x-sinx.

BUT IT IS NOT THE INVERSE

can tell u th grph of the inverse..if not the invrse.

graph of x+sin x is shown below.

Graph of inerse can b obtained by taking reflection about line y=x

PS Konichiwa...u forgot 25..so make it 9 solns

Sorry...didnt see konichiwa had already solved 7 mins b4...didnt refresh

roots are -b+-

b²-4ac/2a

For integral roots,

b²-4ac=1+4n is a perfect square

also note...since sq.rt is odd, the -b will make the sum even and on dividing by 2 we get an integer.

values of n for 4n+1 to be a perfect square is

0,2,6,12,20...

or 0,(0+2),(0+2+4),(0+2+4+6)...=z(z+1), z=1,2,3...(since n>0)

hence 2,6,12,20,30,42,56,72,90

or 9 values

1010g! Mass won't disappear anywhere!Apparent lss of weight is just upward force exerted on solid by liquid!

1st one...

(x/1+cos x) +(sinx/1+cosx)

= xsec²x/2+tanx/2

integrate first by parts, second is =2log|secx/2|

Coz the hardness can't be treated by simple physical means like boiling etc (i guess)

To q1

n*mv=MV

n=MV/mv

=40*10/.06*900

=400/54

=7.sumthing...as n is integral,n=8

PS not sure.. tell me if theres any mistake

If we plot the points possible to reach from initial position, we get a tilted square.U can try by taking lesser than 9 first, for eg. 2 or 3.We get a diagram as shown below.The dots represent possible positions after 9 steps, the darkest dot is the starting position.Steps are taken along 1 diagonal

Total points are 2*(1+3+5+...17)+ 19-1

(We subtract 1 as we can't reach startin position in odd no of steps)

=180.

4 points are a distance of 1 step from I.P

therefore probability=4/180=1/45

PS. I am not sure of the solution...if u find any mistakes pl reply and do not hesitate to vote!

I think(not sure of calc) the total no of nos is 7+36+42+180+120=390

The prob=36/390=

6/65

Pl nudge me if htere are any mistakes and rate if useful!

Possible combos are

9998888, 9999887, 9999986, 9999977, 9999995 and their rearrangements

For 9998888, 0 nos. r divisible by 11

9999995 ,0

9999986, there are broken up as (9+9+9+8)-(9+9+6)Hence 3*4=12 possibilities

9999887, (9998),(789) gives required set Hence 6*4=24 possibilities

for 9999977, 0 possibilities.

36 nos satisfy the 11 divisibility