List of top Mathematics Questions

$\int_{a}^{b} (|x-a| + |x-b|) dx = , (0 < a < b)$

If the order and degree of a differential equation $(\frac{d^4y}{dt^4} + \frac{d^2y}{dt^2})^{5/2} = 10 \frac{d^3y}{dt^3}$ are $p$ and $q$, respectively, then $p+q =$

$\int_{0}^{2} \frac{dx}{\sqrt{2+x} + \sqrt{2-x}} =$

If $k \int_{0}^{1} x f(3x) dx = \int_{0}^{3} t f(t) dt$ then $k =$

$\int \frac{1+\cos 4x}{\cot x - \tan x} dx =$

If $I_{n} = \int \frac{t^{n}}{1+t^{2}} dt$ then $I_{6} + I_{4} =$

If $\int \frac{1}{(x+100)\sqrt{x+99}} dx = f(x) + c$ then $f(x) =$

If $\int \frac{2x^{2}+a^{2}}{x^{2}(x^{2}+a^{2})} dx = \frac{k}{x} + \frac{1}{a} \tan^{-1} \frac{x}{a} + c$ then $k =$

$\int (x+1)^{2} e^{x} dx =$

The set of all points of differentiability of the function $f(x)=e^{-|x|}$ is

The value of p such that the line joining (0,3), (5, -2) is a tangent to the curve $y = \frac{p}{x+1}$ is

If there is an error of 3% in the volume of a sphere then the percentage error in its radius is

The interval in which $f(x) = 2x^{2} - \log x$ increases is

The function $y = xe^{x}$ has}

Which of the following functions have finite number of points of discontinuity?

If $(x/a)^n + (y/b)^n = 2$, then $dy/dx$ at $(a,b)$ is

$Lt_{x \to 0}\frac{e^{x^2}-cos x}{sin^2x}=$

The equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola if}

The vertex of the parabola $y=ax^2+bx+c$ is

$Lt_{x \to 0}(\frac{|x|}{x}+x+2)=$

The equation of major axis of the ellipse $\frac{(x-1)^2}{9}+\frac{(y-6)^2}{4}=1$ is

In the complex plane, if the points A and B represent $(1 + i)$ and $(-1 + i)$ then the angle between OA and OB is

If the line $3x-2y+6=0$ meets x-axis and y-axis respectively at A and B, then the equation of the circle with radius AB and centre at A is

The largest distance from (-3, 2) to the circle $x^{2} + y^{2} - 2x + 2y + 1 = 0$

If $z$ is a complex number such that $|z| + z = 3 + i$ where $i = \sqrt{-1}$, then $|z| =$