42 - Algebra Questions Answers

There are 8 distinct boxes and each box can hold any number of balls.A child having 4 identical balls tandomly choosen four boxes.Then another child having four balls,identical to the previous mentioned,again puts one ball in each of the arbitary choosen four boxes.The probability that there are balls in atleast 6 boxes is

 

Sir pls solve

Asked By: KANDUKURI ASHISH
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Between two numbers, whose sum is 13/6, an even number of arithmetic means are inserted, the sum of these means exceed their number by unity. How many means are there?

Asked By: PREM
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Joshi sir comment

If 9a+24b=1, a,b, +, prove that a2+b2 9( 4+93)3.

Asked By: JAMES GHOSH
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Joshi sir comment
The expression ax2 + 2bx + b has same sign as that of b for every real x, then the roots of equation bx2 + (b – c) x + b – c – a = 0 are (A) real and equal (B) real and unequal (C) imaginary (D) None of these
Asked By: PREM
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Joshi sir comment

If a,b and c are positive real numbers, show that

ab+c+bc+a+ca+b32

Asked By: MROY
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How to do it without using cauchy schwartz inequality?
Asked By: LUFFY
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Joshi sir comment
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
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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 

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