Recently Active Algebra Questions

1) Find the remainder when (103+93)752 is divided by (12)3. ...

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\hspace{-16}$ The number of triples of integers $\bf{(x, y, z)}$ satisfying\\\\ $\bf{x^2 + y^2 + z^2-yz-zx-xy = x^3 + y^3 + z^3}$ is... ...

\hspace{-16}$Determine all values ​​of $\bf{x}$ such that for all $\bf{x}$ at least one of $\bf{f(x) = x^2 +2012 x + b}$\\\\ or $\bf{g(x) = x^2 + b-2012x}$ positive. ...

I am in 11th class and looking for a good book from which I can solve quality sums , I have study material from my coaching center but that's bot enough I think. ...

\hspace{-16}$If $\bf{a,b,c\geq 0}$ and $\bf{a+b+c=1}$. Then minimum value of \\\\\\ $\bf{T=3\sum (ab)^{2}+3\sum ab+2\sqrt{\sum a^{2}}}$ ...

|x|2 - |x| - 2/2|x| - |x|2 - 2 > 2 holds if and only if (A) - 1 < x < -2/3 or 2/3 < x < 1 (B) -1 < x < 1 (C) 2/3 < x < 1 (D) x > 1 or x < -1 or -2/3 < x < 2/3 ...

Find the largest positive integer, m such that 2m-1 divides 33!. ...

Six married couples are sitting together.NUmber of ways of selecting 4 people so that there is exactly one married couple among the four is: I thought the answer should be C(6,1)*C(10,1)*C(8,1) that is 480. The answer given i ...

\hspace{-16}$If $\bf{x^3-3x+1=0}$ has a $\bf{\mathbb{R}}$oots $\bf{a\;\;,b\;\;,c}$ Respectively.\\\\ Then $\bf{a^8+b^8+c^8=}$ ...

\hspace{-16}$If $\bf{4m.n(m+n-1)=(m^2+1).(n^2+1)}$. Then no. of Ordered pairs \\\\ of Integers $\bf{(m,n)}$ is ...

\hspace{-16}$If $\bf{k\in \mathbb{R}}$ and $\bf{0\leq k\leq 56}$. Then no. of Real Solution of \\\\ $\bf{(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)=k(x^2-7x)+720}$ ...

\hspace{-16}$Find The Greatest positive Integer $\bf{m}$ such that $\bf{2^m}$\\\\ divides $\bf{2011^{(2013^{2016}-1)}-1.}$ ...

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\hspace{-16}$If $\bf{x^4 + 8x^3 + 18x^2 + 8x + a=0}$ has a $\bf{4}$ Diff. $\bf{\mathbb{R}}$oots.\\\\ Then $\bf{\mathbb{R}}$ange of $\bf{a}$ is ...

In a series of games between team A and team B,they decide to play on till a team wins 5 matches .In how many ways can A win the series if no match ends in a draw? Please explain how you solved it! Answer is 126 ...

\hspace{-16}$If $\bf{\begin{Vmatrix} \bold{x^3+2=3y}\\\\ \bold{y^3+2=3z}\\\\ \bold{z^3+2=2w} \\\\ \bold{w^3+2=3x} \end{Vmatrix}}$\\\\\\ Then no. of Real ordered pairs of $\bf{(x,y,z,w)}$ is ...

Let S = \left\{(x,y): |||x|-2|-1|+|||y|-2|-1|=1 \right\} . If a wire is made out of S, then the length of such wire is? Source : FIITJEE PT II (P1) Q.1 (Maths) ...

If A is an Invertible Matrix, Show that det(AT A)>0 ...

The number of quadratic equations, which are unchanged by squaring their roots is ? ...

Find the sum of n terms: 1+2(1-a) +3(1-a)(1-2a)..........k(1-a)(1-2a)...{1-(k-1)a} ...

if the sides of the triangle is determined by throwing a triplet of dice then the number of different triangles with all the distinct sides is?? ...

202 x 20002 x 200000002 x 20000...(13 zeroes)...2x 2... (31 zeroes)...2. Find the sum of the digits of the product thus formed. ...

The number of quadratic equations, which are unchanged by squaring their roots is ? ...

\hspace{-16}$If $\bf{a_{1}+a_{2}.2!+a_{3}.3!+......+a_{n}.n!=695}$. Then $\bf{a_{4}=}$\\\\ If $\bf{0\leq a_{k}\leq k}$ and $\bf{n!=n.(n-1).(n-2)........3.2.1}$ ...

\hspace{-16}$Find Min. value of $\bf{\mid z^2-az+a\mid}$\\\\ Where $\bf{a\in\mathbb{R}}$ and $\bf{\mid z \mid \leq 1}$ and $\bf{z\in \mathbb{C}}$ ...

The 4th power of the common difference of an A.P. with integer entries is added to the product of any 4 consecutive terms of it. Prove that the resulting sum is the square of an integer. ...

Shan parks his car among 6 cars already standing in a row, his car not being parked at an end. On return he finds that exactly 4 of the 7 cars are still there. What is the probability that both the cars parked on two sides of ...

no. of ways to make a 5 letter word out of the word SUCCESS such that no 2 C and no 2 S are together is?? ...

8 prizes are to be distributed by a lottery.The first person takes 5 tickets from a box containing 50 tickets.In how many ways can he extract them so that exactly two tickets are winning?? ...