Recently Active Mathematics Questions

\mathbf{\int_{-1}^{1}\frac{dx}{1+x+x^2+\sqrt{x^4+3x^2+1}}}$\\\\ Ans::\Leftrightarrow $\mathbf{=\frac{\pi}{4}}$ ...

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$Q$:$\Rightarrow$ $Find Min. value of $\int_{0}^{\frac{4\pi}{3}}|sinx-c|dx$, Where $c\geq0.$ ...

what is the L.C.M of 2 and 3 ? ...

Find all continuously differentiable function f ,with the property that f(x) > 0 and f(f(x)) = f'(x) for all x ε R Edits: got this one. couldn't do it yesterday,believe me;) it should be moved to the calculus section. ...

two squares are chosen at random from a chess board. what is the probability that the two squares share a common side?? please help me out. ...

$Q:$\Rightarrow$ Determine The range of the function\\\\ $f(x)=\frac{(x+a)^2}{(a-b).(a-c)}+\frac{(x+b)^2}{(b-c).(b-a)}+\frac{(x+c)^2}{(c-a).(c-b)}$\\\\ Where $a,b$ and $c$ are Different Real no. ...

1. There are n lines drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is ? 2. Number of 6-digit telephone numbers, which ...

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(1) Find value of \left[\frac{2010!}{2009!+2008!+2007!..............3!+2!+1!} \right] where \left[. \right] G.I.F ...

Q. IF x= a sec θ, y = b tan θ, prove that d2y/dx2 = - b4/a2y3. ...

find the largest interval in which x lies satisfying x^{12}-x^{9}+x^{4}-x+1>0 ...

Find\; maximum\; value\; of \frac{\Delta ^3}{abc(a+b-c)(b+c-a)(c+a-b)} ...

two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...

1. If ABCD is cyclic quadrilateral, show that AC . BD = AB . CD + BC . AD 2. In a ΔABC, show that a3 cos (B – C) + b3 cos (C – A) + c3 cos (A – B) = 3 abc ...

1. A man observes, that when he moves up a distance c meters on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30º; and when he moves up further a distance c meters the angl ...

(1) If |z - 25 /z - 5| = 5 then find |z| = ...

1. If p, q, r be in H.P. and p and r be different having same sign, then the root of the equation px2 + 2q + r = 0 will be (A) Real (B) Equal (C) Imaginary (D) None of these 2. If the equation (k – 2) x2- – (k –- 4) x- – ...

Tangents are drawn to curve y=sinx from the origin. Find the locus of points of contact of these tangents. ...

my sir asked me to draw the graph of f((x+1)/3). I used this approach: f(x)→ f(x/3)→f((x+1)/3) a friend of mine used this f(x)→f(x+1) and then he changed the variable to x/3 with believe that this gives graph of f((x+1) ...

In a Class of 300 students, 60 students read all News-paper and a News-paper is read by 5 students. Then find total no. of News -paper. ...

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Q.1 If a, b,c and u ,v ,w are the complex numbers representing the vertices of two triangles such that c= (1- r) a +rb and w =(1-r)u +rv, where r is a complex number, then the two triangles (a) same area (b) are similar (c) a ...

$Calculate $\int_{0}^{\infty}\frac{tan^{-1}(\frac{x}{3})+tan^{-1}(3x)}{1+x^2}dx$ = ...

if, a2 + b2 + c2 = ab + bc + ac then find the relation between a,b and c for real values of a,b and c. sitter question no doubt... ...

Let ABCDEF be a convex hexagon in which the diagonals AD, BE, CF are concurrent at O. Suppose the area of traingle OAF is the geometric mean of those of OAB and OEF; and the area of triangle OBC is the geometric mean of those ...

$\textbf{Find no. of integral values of $\mathbf{a}$ such that\\\\ $\mathbf{\sqrt{9-a^2+2ax-x^2}>\sqrt{16-x^2}$}}$\\\\ $\textbf{for atleast one positive Real value of $\mathbf{x}$}.$ ...

If w ( ≠1) is cube root of unity satisfying 1/a+w + 1/b+w + 1/c+w = 2w2 and ,1/a+w2 + 1/b+w2 + 1/c+w2 = 2w then the value of 1/a+1 + 1/b+1 + 1/c+1 is ? ans 2 ...