Recently Active Algebra Questions

(i)(x^2+x-2)^4+(2x+1)^4=(x^2+x-1)^4\\\\ (ii)(x^2+3x+2)(x^2+7x+12)+(x^2+5x-6)=0 ...

If S1,S2.....Sn be the sum of first nterms of n G.Ps whose 1st terms of each unity and C.R are 1,2,3.....n respectively prove S1+S2+2S3+3S4+.....(n-1)Sn= 1n+2n+3n+.....+nn. ...

Calculate the value of " L " as depicted below - *Image* Hint : - It is not as big as looks . ...

plzz explain how to do this comprehension( JEE 2010) quesn no. 42 , 43 and 44... http://jee.iitd.ac.in/QP_M1_ANS.pdf ...

$To solve the equation:\\\\ $\mathbf{2^{2x+2}-\frac{1}{2}.2^{x^2}+2x=x^2-3}$\\\\ Ans::\Leftrightarrow$\mathbf{x=3,x=-1}$ ...

if one root of (l-m)x2+lx+1=0 be double of the other and if l be real, show that m≤9/8 ...

Ye kaunse chapter ka question hai?? <<Assertion-Reason type>> STATEMENT-1: ~(p \leftrightarrow ~q) is equivalent to p \leftrightarrow q. STATEMENT-2: ~(p \leftrightarrow ~q) is a tautology. ...

$If $\mathbf{a,b,c\in \mathbb{R^{+}}}$.Then prove that \\\\ $\mathbf{\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq 3.\left(\frac{a^2+b^2+c^2}{ab+bc+ca}\right)^{\frac{2}{3}}}$\\\\ ...

draw the graph of y=ax-(1/(bx)) where x=1/√(ab). ...

Which of these definitions is correct. ML khanna says a square matrix is called nilpotent matrix if Ak=O,where 'k' is a positive integer,smallest value of k is called index of nilpotent matrix SK goyal in Arihant algebra says ...

The following Question is of Assertion and Reason type. Select the correct choice from the following options. Statement 1: The probability for the graph of 16x2 + 8(a+5)x -7 a - 5 in the interval is strictly above the x-axis ...

The probability that two integers chosen at random and their product will have the same last digit is? ...

so i recently bought Arihant Algebra by SK goyal as many people recommended it as best book for algebra. I started doing matrices from it & what i find is,it has lot of mistakes in theory. Havent done any problem yet so cant ...

Q-> 7+2 10 = A + B Find the value of A+B ...

*Image* i believe that answer is not given in options....all options are wrong i mean..or did they mean that "positive real number" rather than "real numbers"? ...

*Image* ...

*Image* *Image* ...

*Image* plz explain how to solve it! ...

if a+b+c>0 is it possible to have (a-b)2+(b-c)2+(c-a)2 =0?if yes when? ...

12+22+32+..........+20032=2003*4007*334 1*2003+2.2002+3*2001+..........+2003*1=2003*334*x what is x? ...

*Image* ...

*Image* ...

for natural number n find Left Hand Derivative of f(x)=1-tannx ...

Evaluate the following expression : - *Image* ...

sir i usually am blank when i see this type of problems(till now i attempted by guessing the possibilites...but now i want some help and to know the method to approach the problems of this type) 1.The number of continuous fun ...

$If $\alpha,\beta$ and $\gamma$ be the Roots of the equation $x^3+x-1=0$.Then Calculate\\\\ value of $\frac{\beta}{\alpha}+\frac{\gamma}{\beta}+\frac{\alpha}{\gamma}=$ ...

plzz just check this quesn How many 6 digit nos. of the type a1a2a3a4a5a6 are possible having the property a1>a2>a3<a4>a5>a6 i initially thot abt this process: 10C6 . 6C3 i.e. i am first selecting 6 nos. from 1 ...

the method i like to study mathematics,first i derive all the formulaes & important results & after clearing all the concepts i jump to excercise but this is possible only if i have a book which has the necessary derivations ...

The sides AB , BC and CA of triangle ABC hav 3 , 4 and 5 interior pts. respectively on them. The no. of triangles that can be constructed using these interior pts. as vertices is?? ...

If " N " be the number of natural numbers <2009 which can be expressed in the form of [x[x]] for some positive Real " x " then the sum of digits of " N " is - { where [.] is GIF } ...