List of top Mathematics Questions

IF $f\left(z\right) = \frac{7-z}{1-z^{2}} $ , where $z = 1 + 2i$, then $|f(z)|$ is equal to :
Let $S=\{1,2,3, \ldots \ldots, 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$
The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be
The differential equation of all parabolas whose axis is $y-axis$ is
The particular solution of the differential equation $xdy + 2ydx = 0$, when $x = 2, y = 1$ is

Let \(f(x)=x+log_{e}​x−xlog_{e}​x,\text{ }x∈(0,∞)\).

  • Column 1 contains information about zeros of \(f(x)\), \(f'(x)\) and \(f''(x)\).
  • Column 2 contains information about the limiting behavior of \(f(x)\), \(f'(x)\) and \(f''(x)\) at infinity.
  • Column 3 contains information about increasing/decreasing nature of \(f(x)\) and \(f'(x)\).
Two events $A$ and $B$ will be independent if
If $\log_{\sin \frac{\pi}{6}} \left\{\frac{\left|z-2\right| + 3 }{3\left|z - 2\right| - 1 }\right\}>1 $ , then
The value of the integral $\int \frac{dx}{x \sqrt{x^{2} - a^{2}} } $ is equal to:
The maximum value of the function $y = 2 \, \tan \, x - \tan^2 \, x $ over $\left[ 0 , \frac{\pi}{2} \right]$ is :
The $\displaystyle \lim_{x \to \frac{\pi}{2}} \left\{ 2x \tan x - \frac{\pi}{\cos x }\right\} $ is
The point of inflection of the function $y - \int^{x}_{0} \left(t^{2} - 3t + 2 \right) dt $ is
A chord of the parabola $y = x^2 - 2x + 5$ joins the point with the abscissas $x_1 =1, x_2 = 3$ Then the equation of the tangent to the parabola parallel to the chord is :
If a , b , c are three vectors such that $[ a\,b\,c]= 5 $ then the value of $[a \times b , \times c , \,c \times a] $ is :
For what interval of variation of $x$, the identity $arc \, \cos \frac{1 - x^2}{1 + x^2} = - 2 \, arc \, \tan \, x$ is true ?
The points of the curve $y = x^3 + x - 2$ at which its tangents are parallel to the straight line $y = 4x - 1$ are
Let $f(x) = \begin{cases} a (x) \sin \frac{\pi \ x }{2} & \text{for } x \neq 0 \\ -(n+1)/2 & \text{for} x = 0 \end{cases} $ where $\alpha (x) $ is such that $\displaystyle\lim_{x \to 0} |\alpha (x) | = \infty $ Then the function $f(x)$ is continuous at $x = 0$ if $\alpha (x) $ is chosen as
The $\displaystyle\lim_{y \to a} \left\{ \left(\sin \frac{y-a}{2}\right) . \left(\tan \frac{\pi y}{2a}\right)\right\} $ is
Let $l_{n } = \frac{2^{n } + \left(-2\right)^{n} }{2^{n}} $ and $L_{n} = \frac{2^{n} + \left(- 2\right)^{n}}{3^{n}}$ then as $ n \to\infty$
Let $f(x) = \begin{cases} - 2 \sin x & \quad \text{if } x \leq - \frac{\pi}{2}\\ A \ \sin x + B & \quad \text{if } - \frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos & \quad \text{if } x \leq \frac{\pi}{2} \end{cases} $ For what values of A and B, the function $f (x)$ is continuous throughout the real line ?
If the eccentricity of the hyperbola $x^{2}-y^{2} cos ec^{2} \alpha=25 is \sqrt{5}$ times the eccentricity of the ellipse $x^{2} cos ec^{2} \alpha+y^{2}=5, then \alpha$ is equal to :
If $\int \frac{\cos x-1}{\sin x+1} e^{x} d x$ is equal to:
How many different nine digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?
How many $3 \times 3$ matrices $M$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal entries of $M^{T} M$ is $5$ ?
If '' > 0$ for all $