36 - Algebra Questions Answers

Is there a way to do this in terms of area in a coordinate plane. Where difference of larger and smaller can be difference in x coordinate for 1st player and difference in y coordinate for 2nd player
Asked By: LUFFY
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Joshi sir comment

Probability to get following differences  difference     probability 0                   6/36 1                 10/36 2                   8/36 3                   6/36 4                   4/36 5                   2/36 So required probability =1-2636436+236+1036236 now solve problem is based on integral values so area is not very useful

Find Sum to n terms 

 

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

Asked By: LUFFY
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Joshi sir comment

x1-x2=11-x-11-x2 break all terms similarly and solve 

No. of integral roots of the eqn. x8 - 24 x7 - 18x5 + 39 x2 + 1155 = 0 .

Asked By: VAIBHAV GUPTA
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Joshi sir comment

two times sign change so 2 positive roots

 

let a,b,c be three distinct real numbers such that each of expression ax2+bx+c,bx2+cx+a,cx2+ax+b are positive for all x ε R and let

α=bc+ca+ab/a2+b2+c2 then

(A) α<4 (B) α<1 (C) α>1/4 (D) α>1

 

THIS IS MULTIPLE CHOICE QUESTION

Asked By: AKASH
is this question helpfull: 7 0 read solutions ( 1 ) | submit your answer
Joshi sir comment

if ax2+bx+c is positive for real x

then b2< 4ac similarly others

on adding all inequalities we get b2 + c2 + a2< 4(ac+ab+bc)

now get answer 

Maths >> Algebra >> Binomial Theorem Engineering Exam

Find sum of series..1*(n)2  + 2*(n-1)+3*(n-2)2 +...+n .

Asked By: RESHU SINGH
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Joshi sir comment

general term of the series = r(n+1-r)= r(n+1)2 + r3 - 2(n+1)r2

now put sigma then solve                                       

If x+y = 1 ,then ∑ r  nCrxryn-requals nx....How??

Asked By: RESHU SINGH
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Joshi sir comment

  ∑ r nCrxryn-r

∑ r nCrxr(1-x)n-r

∑ r n!/r!(n-r)xr(1-x)n-r

= n (n-1)!/(r-1)!(n-r)! xr(1-x)n-r 

= n (n-1)C(r-1) xr(1-x)n-r

= n (n-1)Cxr+1(1-x)n-r-1             let r = r+1

= nx  (n-1)Cxr(1-x)n-r-1 

now solve 

What is the value of 0⁄0? if its otherthan 1, then how this can be true:      lim      (ex-1)/x = 1

                                                                                                                                x −−>0

Asked By: BONEY HAVELIWALA
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Joshi sir comment

exact 0 and lim tends to 0 are different

what will be the rank of word OPTION in the dictionary of words formed by letters of the word OPTION

Asked By: JIGYASA KUMAR
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Joshi sir comment

OPTION

ordered way INOOPT

total words = 6!/2! = 360

so rank = (360/6)*2+([60*2]/5)*3+(24/4)*3+(6/3)*0+(2/2)*1+1 = 120+72+18+0+1+1 = 212

 

Maths >> Algebra >> Matrices and Determinant Engineering Exam

 

prove using property of determinant

1.  a+b+c      -c                 -b

   -c               a+b+c           -a                   =  2(a+b)( b+c ) (c+a)

  -b              -a                     a+b+c

Asked By: SONAM SHARMA
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Joshi sir comment

first use C1 = C1+C2+C3

then R1 = R1+R2 and R2 = R2+R3

after it solve mathematically

rank of the number 3241?(digits cannot be repeated)

Asked By: HARSHITH
is this question helpfull: 7 2 read solutions ( 1 ) | submit your answer
Joshi sir comment

total numbers = 4*3*2*1 = 24

on arranging these numbers in order we get 1234

so rank = [24/4]*2+[6/3]*1+[2/2]*1+1 = 16

 

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