# Maths doubts

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Sorry i m bio studentâ€¦

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No worries! Thanksâ€¦

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bro the first question use standard limits bro if you donâ€™t get it then ill send you the solution

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Thanks yaarâ€¦ @Sanjay_S

Check this outđź‘†

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Perfecto!

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2nd oneâ€¦any idea?

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try kartha hun a bit held up now will try later

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Sureâ€¦anytime! Thanks

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Check the qn pls. I mean r=1 to r=_

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Even I thought the same thingâ€¦maybe itâ€™s just hit and trial after thisđź‘‡

@Ankit_Kumar â€¦ Which option do you think is correctâ€¦?

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Bhai koi bhi option match nhi kar RHA hđź¤”

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Sahi kahaâ€¦maybe something is wrong with questionâ€¦
Thanks for checking @Ankit_Kumar

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For first i assumed x number of fours , y number of sixes and z number of dot balls
X+y+z=20 and 4x+6y=100
Solving we get y=10+2z and i just put random values for z until x,y,z doesnt exceed 20. Any other methods to solve this Q apart this?
For second please provide a short approach too ,
@manan_uppadhyay @LaveshGupta @Rudra_d @Aastik_Guru @Aswin24 @Cooljet123
EDIT: only ellipse one is left. The one thats not blurred. Please try.

@AshWin
For the first question: I didnâ€™t calculate but you may try this method. Since you found two equations you may add them to get one equation.

I took infinite series because there are no restrictions on the number of sixes, fours or dot balls.

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For question 47 , i did this but getting wrong answer , please tell me my mistake

@Cooljet123 @LaveshGupta @Rudra_d
Edit: Doubt Solved.

There is , they have to be less than 20

Ok then restrict the terms. Sorry I didnâ€™t notice.

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Bro! A coincidence ! I was solving the same paper in morning and doing the rest now and correctly you asked these!

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Anyone please tell Q47 first , what mistake did i did there.
I may have done something wrong in area equations.