List of top Mathematics Questions

If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is

Given \(\frac{d^2y}{dx^2}=cot\,x\frac{dy}{dx}+4y\,cosec^2x=0\). Changing the independent variable x to z by the substitution z=log tan \(\frac{x}{2}\), the equation is changed to 

If y=\(\frac{x}{log_e|cx|}\) is the solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}+\phi(\frac{x}{y})\), then \(\phi (\frac{x}{y})\) is given by 

If \(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\), then the value of k is 

The expression \(\frac{\int_{0}^{n}[x]dx}{\int_{0}^{n}\left \{ x\right \}dx}\), where [x] and {x} are respectively integral and fractional part of x and n∈N, is equal to

Let f:[1,3]\(\rightarrow\)R be continuous and be derivable in (1,3) and f'(x)=[f(x)]²+4∀x∈(1,3). Then

Let \(cos^{-1}\frac{y}{b}\)=\(log_e (\frac{x}{n})^n\), then Ay₂+By₁+Cy=0 is possible :  (where y₂=\(\frac{d^2y}{dx^2}\), y₁=\(\frac{dy}{dx}\))

\(\lim_{x\rightarrow \infty}\){\(x-\sqrt[n]{(x-a_1)(x-a_2)......(x-a_n)}\)} where a₁,a₂,.....a_n are positive rational numbers.The limit

Suppose f:R\(\rightarrow\)R be given by f(x)={\(e^{(x^{10}-1)}+(x-1)^2sin\frac{1}{1-x},if\,\,\,x\neq1\)}, then

The angle between a normal to the plane 2x-y+2z-1=0 and the X-axis is 

If y=logⁿx, where logⁿ means log_e log_e log_e .....(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)

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 \(\int^{2}_{0}f(x)dx=\)

\(∫xlog(1+x^2)dx=\)?