Recently Active Mathematics Questions

\hspace{-16}\bf{\sum_{n=1}^{\infty}\;\prod_{r=1}^{n}\cos \left(\frac{r\pi}{n}\right)} ...

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

\hspace{-16}$Let $\bf{L=\lim_{n\rightarrow \infty}\frac{1}{\frac{1}{\sqrt{2}}.\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}}\big).\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}...... ...

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If the equation y=1+x-2√x represents a parabola then coordinates of vertex are? Please explain how you solved it! Answer is (1/4,1/4) ...

\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... ...

How many common points can 3 or more planes have? ...

\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. ...

\hspace{-16}$If $\bf{x_{1},x_{2}\in \mathbb{R}}$ and $\bf{f\big(x_{1},x_{2}\big)=\big(x_{1}-x_{2}\big)^2+\big(3\sqrt{8}+\sqrt{(4-x^2_{1})}-\sqrt{(x^2_{2}-16)}\big)^2}$\\\\ Then $\bf{f\big(x_{1},x_{2}\big)_{Min.}}$ is from ask ...

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 \\\\\\ $\bf{T=3\sum (ab)^{2}+3\sum ab+2\sqrt{\sum a^{2}}}$ ...

Why do distant hills covered with trees appear blue? ...

∫l log x/x1/2 upper limit 1 lower limit 0 form the positive side ...

lim (1+3x)10/x as x→0+ ...

|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!. ...

\hspace{-16}\bf{P=\left(1+\frac{1}{\cos 1^0}\right).\left(1+\frac{1}{\cos 2^0}\right).\left(1+\frac{1}{\cos 4^0}\right)...\left(1+\frac{1}{\cos 1024^0}\right)} ...

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}$Let $\mathbf{A=\sin \sqrt{2}-\sin \sqrt{3}}$ and $\mathbf{B=\cos \sqrt{3}-\cos \sqrt{2}}$\\\\ Then Correct options is,::::\\\\ $\mathbf{(a)\;\; A>0\;\;,B>0}$\\\\ $\mathbf{(b)\;\; A>0\;\;,B<0}$\\\\ $\m ...

\hspace{-16}\bf{\int \big(x-\sqrt{x^2+1}\big)^{2012}dx} ...

can someone geometrically prove... tan (-A) = -tan A ...

\hspace{-16}$If $\bf{\sin x.\cos x\leq \mathbb{C}\big(\sin^6x+\cos ^6x\big)}$. Then $\bf{\mathbb{C}}$ is ...

Write a 2-digit number ab and the number obtained by reversing its digits i.e., ba. Find their sum. Let the sum be a 3-digit number dad.Find the values of a and d. ...

\hspace{-16}$If $\bf{x,y,z\in \mathbb{R}}$ and $\bf{f(x).f(y).f(z) = 12f(xyz) ô€€€ -16xyz}$\\\\ Then No. of function which satisy $\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$ is ...

\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 ...