Recently Active Mathematics Questions

Q.1) Find the locus of the centre of a circle which touches a fixed line and a fixed circle. Q.2) Find the slope of the directrix of a Parabola which passes through (1,2) and (3,4) and tangents at these points intersect at (6 ...

\mathbf{\int_{0}^{1}\frac{x^2+2}{(x^2+1)^3}dx}$ ...

\hspace{-16}$If $\mathbf{a+b+c=1}$ and $\mathbf{a^2+b^2+c^2=2}\;$\\\\ Then Range of $\mathbf{a^4+b^4+c^4}$ ...

if x+y+z = 1 and 2xy - z^2 = 1 solve for x, y ,z. here x, y, z are real numbers... ...

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Show that (x-2) (x-3) (x-4) (x-5)+2 is always positive ...

Q1. The locus of extremities of the latus rectum of the family of Ellipse b^{2}x^{2}+y^{2} =a^{2}b^{2} . Q2. Total no. of divisors of m=3^{5}5^{7}7^{9} that are of the form (4k+1) is equal to 2.P!. Then P is. Q3. Consider a l ...

i have a doubt in finding Min. value of point MA+MB where M(x,0) and A(3/2,1) and A(3/2,1) my Confusion is that why We can not take MA+MB>=AB and answer given is take Image of A at A(3/2,-1). Then find MA'+MB>=AB and pl ...

\hspace{-16}$Find Complex no. $\mathbf{z}$ which satisfy\\\\ $\mathbf{\mid z \mid+\mid z-25 \mid+\mid z-18-24i \mid+\mid z+7-24i \mid=70}$ Ans:: z=9+12i ...

If a + b + c = 0 then find the value of 7(a2 + b2 + c2)2 (a3 + b3 + c3)/a7 + b7 + c7 ...

\hspace{-16}$Solve for $\mathbf{x}$\\\\ $\mathbf{x+\sqrt{11+\sqrt{x}}=11}$ ...

if the equations x2 + 3x + 5 = 0 and ax2 + bx + c = 0 have a common root and a,b,c E N then find the minimum value of a + b + c. ...

This is not a doubt. Given two circles in plane.They may intersect, may touch or may neither. How will you find their radical axis? a similar thread, http://www.targetiit.com/iit-jee-forum/posts/19-06-2011-parabola-19567.html ...

factorize |x2(y - z) + y2(z - x) + z2(x - y)| Answer : |(x - y)(y - z)(z - x)| ...

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COS-1x/a + COS-1y/b =d , then x2/a2 -2xy/abcos d +y2/b2 = 1.sin2 d 2.cos2d 3. tan2d 4.cot2d ...

1) tan9 - tan27- tan63 + tan81 =4 2) sin4 π/6 + sin4 3π/6 +sin4 5π/6 + sin4 7π/6 = 3/2 3)find the value of : 4cos20 - √3 cot20 4) find the value of : 2√2 sin10 [ sec 5/2 + cos 40/ cos5 - 2sin35] 5)sin212 + sin221 + si ...

In triangle ABC, we are given that 3sin{A}+4cos{B}=6 and 4sin{B}+3cos{A}=1 then find angle C. ...

if x3 + ax3 + 11x + 6 and x3 + bx2 + 14x + 8 have a common factor of the form x2 + px + q, then find (a + b). though i did it in 5 triels ... :P ... but a good prob (fr me atleast) so wanted to share. ...

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Suppose n be a natural number such that |i+2i2 + 3i3+...+nin|=18√2. find n. ...

\hspace{-16}$In a $\mathbf{\triangle ABC},$ Angle $\mathbf{A\;,B}$ and $\mathbf{C}$ satisfy the equation \\\\ $\mathbf{\cos 2A+\sqrt{3}.\cos 2B+\sqrt{3}.\cos 2C+\frac{5}{2}=0}$\\\\ Determine the Type of $\mathbf{\triangle}$ ...

$Prove that the Sum of Given Integral is a Rational no.\\\\ $\mathbf{\int\limits_{-100}^{-10}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2dx+\int\limits_{\frac1{101}}^{\frac1{11}}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2dx+\int\limits_ ...

Find all primes p and q ,and even numbers n > 2 , satisfying the equation pn + pn-1 + · · · + p + 1 = q2 + q + 1. ...

Not exactly Olympiad stuff, infact I don't know if it is. I just needed a section to post it. Others may try and solve it if they please -: Find the sum of terms of the GP : a+ar+ar2.......∞ where a is the value of x for wh ...

Here We have to find Min. of x^2+4 + (x-y)^2+4 + (y-14)^2+1 instead of taking point C(14,5) Why we can not take point C(14,3) explanation for that thing thanks *Image* ...

If any 7 numbers( not necessarily distinct ) are chosen from 2 to 12, prove that among those 7 numbers we can get three which form the sides of a triangle. ...

prove that the tens digit of every power integral power of 3 is an even number. like 3^5 = 243. here it is 4. ...

\hspace{-16}(1)\;\;\mathbf{\int\frac{1}{x^{11}-8x^5}dx}$\\\\\\ $(2)\;\; \mathbf{\int\frac{5x-x^5}{x^8+1}dx}$ ...

find the derivative of x^x with respect to e^x^x. ...