List of top Mathematics Questions

If y=lognx, where logn means loge loge loge .....(repeated n times), then xlogx log2x log3x....log n-1 xlognx \(\frac{dy}{dx}\) is equal to :
If the lines joining the focii of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)  where a>b and an extremity of its minor axis is inclined at an angle 60°, then the eccentricity of the ellipse is
Let A(2 secθ, 3 tanθ) and B(2 secΦ, 3 tanΦ) where \(\theta+\phi=\frac{\pi}{2}\) be two parts of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{9}=1\). If (α,β) is the point of intersection of normals of the hyperbola at A and B, then β is equal to
If the distance between the plane αx-2y+z=k and the plane containing the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) is \(\sqrt{6}\), then|k| is :
Let O be the vertex, Q be any point on the parabola x2=8y. If point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is 
ABC is an isosceles triangle with an inscribed circle with center O. Let P be the midpoint of BC. If AB=AC=15 and BC=10,then OP equals
If 4a2+9b2-c2+12ab=0, then the family of straight lines ax+by+c=0 is concurrent at 
The straight lines x+2y-9=0, 3x+5y-5=0, and ax+by-1=0 are concurrent if the straight line 35x-22y+1=0 passes through the point:
Consider the trigonometric equation $ \tan(x) - \tan(y) = 0 $, where $x$ and $y$ are not odd multiples of $ \frac{\pi}{2} $. Then the solution of this equation is:
If \( α,β,γ\) are the cube roots of \(-2\) ,then the value of \(xα+yβ+zγ/xβ+yγ+zα\) is (\(x,y,z\) are variables)

Six coins tossed simultaneously then find the probability of getting at least 4 heads.

\(∫\dfrac{1}{cosx(sinx+2cosx)} dx=\)
Let \(f:\R\rightarrow\R\) be defined by
\(f(x) =   \begin{cases} x & \text{if}\ x\leq1 \\  -x+2 & \text{if}\ x\gt1\end{cases}\)
Then \(\int^{2}_{0}f(x)dx=\)
\(∫xlog(1+x^2)dx=\)?
\(\int\frac{2\tan x+3}{\sin^2x+2\cos^2x}dx=\)
\(∫\dfrac{x+5}{x^{2}+1}dx=\)

\(∫sin^2 πx dx =\)?

\(\int\frac{1}{x^2-2x+2}dx=\)
\(\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1\)
If \(y=x^{e^x}+x^{e} for x>0\),the  \( \dfrac{dy}{dx}\) is equal to ?
The equation of the line passing through origin which is parallel to the tangent of the curve \(y=\dfrac{x-2}{x-3}\) at \(x=4\) is 

Let  \(f:R→R\)  be defined by  \(f(x)=\){\(2x+3,x≤5 3x+α,x>5\) .Then the value of \(α\) so that f is continuous on \(R\) is 

 

 

Let \(f(x)=αsin^23x\) .If  \(f ′(\dfrac{π}{12})\) = \(−3\),then the value of \(α \) is
Let \(f:R→R\) be a function defined by
\(f(x) =   \begin{cases}     3e^x       & \quad \text {if}\  {x<0}\\     x^2+3x+3  & \quad \text {if}\  0≤x<1   \\ x^2-3x-3 & \quad \text {if} \ x≥1\end{cases}\)
Let \( f(x)=(1-1/x)2,x>0\). Then