# 42 - Algebra Questions Answers

There are 8 distinct boxes and each box can hold any number of balls. A child having 4 identical balls randomly choose four boxes. Then another child having four balls, identical to the previous mentioned, again puts one ball in each of the arbitrary chosen four boxes. The probability that there are balls in at least 6 boxes is

Sir pls solve

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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?

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

$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$

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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
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Find Sum to n terms

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

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

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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

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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)