Recently Active Mathematics Questions

Given a circle with center at ' A ' which touches the X - Axis at ' B ' with radius 1 unit. ' C ' is the origin from which a tangent at ' E ' is drawn to me line through ' AB ' at ' D ' such that angle ' CBD ' = 90°. The per ...

1)Two squares are chosen at random from the 64 squares of a chessboard The probability that they have a side in common is ___ Probability that they have just one vertex in common is ____ 2)If P(AUB)=P(A∩B), (a)P(A)=P(B) (b) ...

a 4 digit number(numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is same as the sum of its last 2 digits.If a four-digit number is picked up at random,the probability that it is a lucky number i ...

P (5,3) . R lies on y=x and Q lies on x axis. what is the co-ordinate of Q so that PR+PQ+QR is minimum? ...

1)Find the number of isosceles triangles with integer sides if no side exceeds 1994. ...

1)In an AP, Sn = n2p,Sk = k2p ; k,n,p are natural numbers and k≠n Sp = ? can we answer p2p just by seeing the pattern? 2) 1/1x2 + 1/2x3 + 1/3x4 +,,,,,,,,, to n terms 3)Sum of 9 AM's between 2 and 24 is _____ 4)If a,b,c be r ...

1,limit (x-:0) is abbreviated as L0 L0f(x) = l , which is real, then a) L0f(x2) = l2 b) L0f( x/l ) = 1 c) L0f(2x) = 2l d) L0f(-x) = l 2,If La f(x) and Lag(x) exist finitely then an incorrect statement among the following a) L ...

\hspace{-16}$Suppose that $\mathbf{\log_{y}x+\log_{x}y=11}$\\\\ Then Evaluate $\mathbf{(\log_{y}x)^k+(\log_{x}y)^k=}$\\\\ For $\mathbf{k=2\;,3\;,4\;,5}$ ...

\hspace{-16}$Calculate Sum of \\\\ $\mathbf{(1)\;\; \cos^{2n}1^{\arc0}+\cos^{2n}2^{\arc0}+\cos^{2n}3^{\arc0}+\cos^{2n}4^{\arc0}+..........+\cos^{2n}89^{\arc0}=}$\\\\ $\mathbf{(2)}$ \;\; Prove that $\mathbf{\cos^{10}1^{\arc0}+ ...

\hspace{-16}$For each Integer $\mathbf{n\geq 2}$.Determine the values of the integrals\\\\ $\mathbf{(1)\;\;I_{n,3}= \int \sin^3x.\sin (nx)dx}$\\\\ $\mathbf{(2)\;\;I_{n,5}= \int \sin^5x.\sin (nx)dx}$\\\\ ...

\hspace{-16}$Let $f(x)=x+x^2+x^4+x^8+x^{16}+x^{32}+...........................$\\\\ Then find Coeff. of $x^{10}$ in $f(f(x))$ ...

Q4 Let f(x) = ln(2x-x2) + sin Î x/2, then a) Graph of f is symmetrical about the line x=1 b) graph of f is symetrical about the line x=2 c) maximum value of f is 1 d) minimum value of f does not exist ...

Q1 If f(x) and g(x) be periodic and non periodic functions respectively, then f(g(x)) is a) always periodic b) never periodic c) periodic when g(x) is a linear function of x d) can't say Answer is c. Please tell why it is not ...

\hspace{-16}\mathbf{\int\frac{\sqrt{1-x^2}-x}{x^3-x^2-x+1-\sqrt{1-x^2}+x\sqrt{1-x^2}}dx} ...

1. Please tell me the difference between subset and a proper-subset. 2. And that between the powerset and proper-power set 3. What does P(A) denote? 4. Prove that, (A U B)' = (A' ∩ B') Thanks in advance !! ...

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\hspace{-16}$If $\mathbf{x,y>0}$ and $\mathbf{f(x,y)=\sin^{-1}\left(\frac{x}{1+x^2}\right)+\sin^{-1}\left(\frac{y^2+y+1}{y^4+1}\right)}$\\\\\\ Then Find $\mathbf{\mathbb{R}}$ange of The Following $\mathbf{\mathbb{E}}$xpres ...

\hspace{-16}(1)\;\; \int\frac{x^3}{(1+x^3)^2}dx\\\\\\ (2)\;\; \int\frac{2012x-1}{e^{2012x}-2011x}dx ...

Show that the locus formed by z in the equation z^3+iz=1 never crosses the coordinate axes in the argand`s plane.Further show that |z|=√((-Im(z))/(2Re(z)Im(z)+1)) ...

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\text{The equation} (1+k)\cdot\frac{\cos x\cdot\cos(2x-\alpha)}{\cos(x-\alpha )} =1+k\cos 2x \; has no repeated root in it's domain of definition, if : a) |k| ≤ |csc α| , k ≠± 1 a) |k| ≤ |csc α| , k ≠- 1 a) |k| ≥ ...

\bg_green \hspace{-16}$Solve System of equations for real $\mathbf{x\;,y\;,z}$\\\\\\ \begin{Bmatrix} \bold{x^2+y^2=2.(\lfloor z^2 \rfloor +1).(\left\{z^2\right\}+1)} & \\\\ \bold{y^2+z^2=2.(\lfloor x^2 \rfloor +1).(\left\{x^2 ...

\hspace{-16}$(1)\;\; Find all Triplet $x,y,z$ such that \\\\ $\lfloor x \rfloor -y=2\lfloor y \rfloor -z=3\lfloor z \rfloor -x=\frac{2004}{2005}$\\\\\\ (2)\;\; Find all Real no. $x$ such that\\\\ $\frac{x}{x+4}=\frac{5\lfloor ...

\hspace{-16}$Find Max. and Min. value of $\mathbf{f(x)=\frac{2\cos x+2}{\sin x+\cos x+2}}$ ...

\hspace{-16}(1)\;\; \int\frac{\sin^{3n-1}.\cos^{n-1}}{\sin^{4n}x+\cos^{4n}x}dx$\\\\\\ Where $n\in\mathbb{N}$ ...

Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a stra ...

domain of √(x12-x9+x4-x+1) is __________ ...

\hspace{-16}\mathbf{\int \sin (101\;x).\sin^{99}\;xdx} ...

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