Recently Active Mathematics Questions

\hspace{-16}\bf{\mathbb{F}}$ind Real values of $\bf{x}$ that satisfy the equation\\\\ $\bf{4^{x.\sin^{-1}(x)}+4^{x.\cos^{-1}(x)}=2^{\frac{2+\pi.x}{2}}}$ ...

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The no. of possible triples (a1,a2,a3) such that a1+a2cos2x+a3sin2x=0 for all x is (a)0 (b)1 (c)2 (d)Infinite ...

\hspace{-16}\bf{\mathbb{F}}$ind all Matrix $\bf{\mathbb{X}}$ that satisfy the Matrix Equation\\\\ $\bf{\begin{pmatrix} \bf{1} & \bf{2}\\ \bf{3} & \bf{5} \end{pmatrix}\mathbb{X}=\begin{pmatrix} \bf{1} & \bf{2}\\ \bf{3} & \bf{5 ...

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\hspace{-16}$Find total no. of matrices for which Inverse of a matrix is exists\\\\ If its element are taken from the set $\bf{\left\{0,1\right\}}$ ...

Find the minimum Value of cot1 x cot2 x cot3 x ...... cot44. ...

\hspace{-16}$If $\bf{x = \prod_{r=0}^{44}\sin \left(\left(2r+1\right)^0)}$\\\\\\ Then $\bf{x}$ is $\bf{\mathbb{R}}$ational or $\bf{\mathbb{I}}$rrational ...

\hspace{-16}$Find all Real values of $\bf{x}$ that satisfy the equation\\\\ $\bf{x^2=4+[x]}$\\\\ Ans = - 2 and x = 6 I have solved it using very Lengthy Method can anyone have a analytical Method without Using Graph ...

Let S={1,2,3,..........n}.If x denotes the set of all subsets of S containing exactly two elements having 1 as least element,then what is the cardinality of X? ...

1. INTEGRATE A)∫dx/x22(x7-6) B)∫dx/(x+3)8/7(x-2)6/7 C) ∫(lnx-1)/((lnx)2-1)dx ...

\hspace{-16}\bf{\mathbb{I}}$f $\bf{a\in \mathbb{Z}}$. Then Find all Integer Roots of the equation \\\\ $\bf{x^3+ax-13x+42=0}$ ...

\hspace{-16}\mathbb{I}$f $\bf{n \; \mathbb{\in \mathbb{N}}}$. Then find value of $\bf{n}$ in \\\\ $\bf{\tan^{-1}\left(\frac{1}{11}\right)+n.\tan^{-1}\left(\frac{1}{7}\right)=\tan^{-1}\left(\frac{1}{n}\right)}$ ...

\hspace{-16}$Find Real values of $\bf{x}$ in \\\\$\bf{2012^{\log_{2010}(x-1)}-2010^{\log_{2012}(x+1)}=2} ...

\hspace{-16}\bf{\tan(1^{0})}$ is $\bf{\mathbb{R}}$ational or $\bf{\mathbb{I}}$rrational ...

\hspace{-16}$The no. of solution of the equation\\\\ $\bf{e^{-\sqrt{\mid \ln\{x\}}\mid}-\{x\}^{\frac{1}{\sqrt{\mid \ln\{x\}}\mid}}=\left[sgn(x)\right]}$\\\\ Where $\bf{\{x\}=}$Fractional part and $\bf{\left[x\right]=}$Integer ...

\hspace{-16}$If $\bf{\mathbb{I}=\int_{0}^{\pi}\frac{\sin(884\;x).\sin(1122\;x)}{\sin (x)}dx}$ and $\bf{\mathbb{J}=\int_{0}^{1}\frac{x^{238}.(x^{1768}-1)}{(x^2-1)}dx}$\\\\\\ Then value of $\bf{\frac{\mathbb{I}}{\mathbb{J}}=}$ ...

Given: f(x) =ax2+bx+c g(x)= px2+qx+r such that f(1)=g(1), f(2)=g(2) and f(3)-g(3) = 2 . Find f(4)-g(4). The q is easy but i want a shorter method... ...

I=∫ 6x3+x2-2x+1/2x-1 . Integrate this function. ...

The men square deviation of a set of n observations x1,x2,x3,.....xn about a point c is defined as \left(1/n \right)\sum_{i=1}^{n}{\left(x_{i}-c \right)^{2}} The mean square deviation about -2 and 2 are 18 and 10 respectively ...

Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...

1) Let f : R -> (0,pi/2] then find the set of val. of a for which f(x) = cot-1 (x2 - 2ax + a + 1) is surjective ..... !! sorry for the irrelevant title....!! ...

x^2 - a*x + b = 0 x^2 - b*x + a = 0 Both these equations have positive,integral and distinct roots. Find a and b. ...

\hspace{-16}\bf{\sum_{n=1}^{\infty}\;\sum_{m=1}^{\infty}\frac{m.n}{(m+n)!}}= ...

every now n then in calculus we encounter this function........moreover surprisingly while solving problems we come across a few properties which r usually not given under standard list given in books.........so i request all ...

\hspace{-16}\bf{\lim_{n\rightarrow \infty}\frac{1}{n}\tan\left\{\sum_{k=1}^{4n+1}\tan^{-1}\left(1+\frac{2}{k.(k+1)}\right)\right\}=} ...

\hspace{-16}\bf{\mathbb{C}}$alculate Integer value of $\bf{n}$ in \\\\\\ $\bf{\frac{1}{i}+\frac{2}{i^2}+\frac{3}{i^3}+.........+\frac{n}{i^n}=405}$ ...

\hspace{-16}$Find Sum of $\bf{4}$ digit no. that can be formed with the digit $\bf{1,2,3,4,5....,9}$\\\\ Repetition not allowed ...

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\hspace{-16}\bf{\mathbb{S}}$olve the inequality\\\\ $\bf{\mid x-1 \mid+3\mid x-3 \mid+5\mid x-5 \mid+.......+2009\mid x-2009\mid}$\\\\\\ $\bf{\geq 2 \mid x-2 \mid+4\mid x-4 \mid+6\mid x-6 \mid+.......+2008\mid x-2008\mid}$ ...