# 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

**Asked By: KANDUKURI ASHISH**

**submit your answer**

**Joshi sir comment**

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**

**submit your answer**

**Joshi sir comment**

$If\frac{9}{a}+\frac{24}{b}=1,a,b,\in {\mathrm{\mathbb{R}}}^{+},provethat{a}^{2}+{b}^{2}\ge 9{(4+\sqrt[3]{9})}^{3}.$

**Asked By: JAMES GHOSH**

**read solutions ( 1 ) | submit your answer**

**Joshi sir comment**

**Asked By: PREM**

**submit your answer**

**Joshi sir comment**

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

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

**Asked By: MROY**

**read solutions ( 1 ) | submit your answer**

**Joshi sir comment**

**Asked By: LUFFY**

**submit your answer**

**Joshi sir comment**

$Probabilitytogetfollowingdifferences\phantom{\rule{0ex}{0ex}}differenceprobability\phantom{\rule{0ex}{0ex}}06/36\phantom{\rule{0ex}{0ex}}110/36\phantom{\rule{0ex}{0ex}}28/36\phantom{\rule{0ex}{0ex}}36/36\phantom{\rule{0ex}{0ex}}44/36\phantom{\rule{0ex}{0ex}}52/36\phantom{\rule{0ex}{0ex}}Sorequiredprobability=1-2\left[\frac{6}{36}\left(\frac{4}{36}+\frac{2}{36}\right)+\frac{10}{36}\left(\frac{2}{36}\right)\right]\phantom{\rule{0ex}{0ex}}nowsolve\phantom{\rule{0ex}{0ex}}problemisbasedonintegralvaluessoareaisnotveryuseful$

Find Sum to n terms

x/1-x² + x²/1-x⁴ + x⁴/1-x⁸ + ....

**Asked By: LUFFY**

**submit your answer**

**Joshi sir comment**

$\frac{x}{1-{x}^{2}}=\frac{1}{1-x}-\frac{1}{1-{x}^{2}}\phantom{\rule{0ex}{0ex}}breakalltermssimilarlyandsolve\phantom{\rule{0ex}{0ex}}$

No. of integral roots of the eqn. x^{8} - 24 x^{7} - 18x^{5} + 39 x^{2} + 1155 = 0 .

**Asked By: VAIBHAV GUPTA**

**submit your answer**

**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 ax^{2}+bx+c,bx^{2}+cx+a,cx^{2}+ax+b are positive for all x ε R and let

α=bc+ca+ab/a^{2}+b^{2}+c^{2} then

(A) α<4 (B) α<1 (C) α>1/4 (D) α>1

THIS IS MULTIPLE CHOICE QUESTION

**Asked By: AKASH**

**read solutions ( 1 ) | submit your answer**

**Joshi sir comment**

if ax^{2}+bx+c is positive for real x

then b^{2}< 4ac similarly others

on adding all inequalities we get b^{2} + c^{2} + a^{2}< 4(ac+ab+bc)

now get answer