List of top Mathematics Questions

The points on the curve \(xy^2 = 1\) which are nearest to the origin, are

The value of \(\lim_{n \to \infty} \left[\sqrt[3]{n^2 - n^3} + n\right]\) is

Total number of regions in which 'n' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to

If \(f(x)\) is a non-negative continuous function for all \(x \ge 1\) such that \(f'(x) \le p f(x)\), where \(p > 0\) and \(f(1) = 0\), then \([f(\sqrt{e}) + f(\sqrt{\pi})]\) is equal to

If \(\theta = \sin^{-1}x + \cos^{-1}x - \tan^{-1}x\), \(1 \le x < \infty\), then the smallest interval in which \(\theta\) lies is

If \(X\) follows a binomial distribution with parameters \(n = 8\) and \(p = \frac{1}{2}\), then \(P(|x - 4| \le 2)\) is equal to

The mean deviation from the mean for the set of observations \(-1, 0, 4\) is

If \(aN = \{an : n \in N\}\) and \(bN \cap cN = dN\), where \(a,b,c \in N\) and \(b,c\) are coprime, then

If \(2a + 3b + 6c = 0\), then at least one root of the equation \(ax^2 + bx + c = 0\) lies in the interval

If a and b be two perpendicular unit vectors such that \(\mathbf{x} = \mathbf{b} - (\mathbf{a} \times \mathbf{x})\), then \(|\mathbf{x}|\) is equal to

The length of the chord $x + y = 3$ intercepted by the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ is

The parabola having its focus at $(3, 2)$ and directrix along the $y$-axis has its vertex at

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation, $y(1 + xy) dx = x \,dy$, then $f \left( - \frac{1}{2} \right)$ is equal to :

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x -60} = 1 $ is

If $A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}$ and $A$ adj $A$ = $AA^T$ , then $5a + b$ is equal to :

The system of linear equations $x + \lambda y - z = 0$ $\lambda x -y - z = 0$ $x + y - \lambda z = 0$ has a non-trivial solution for :

If all the words (with or without meaning) having five letters, formed using the letters of the word $SMALL$ and arranged as in a dictionary; then the position of the word $SMALL$ is:

If the number of terms in the expansion of $\left( 1 - \frac{2}{x} + \frac{4}{x^2} \right)^n , x \neq 0$ , is $28$ , then the sum of the coefficients of all the terms in this expansion, is :

If the $2^{nd}, 5^{th}$ and $9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

If the sum of the first ten terms of the series $\left(1 \frac{3}{5}\right)^{2} + \left(2 \frac{2}{5}\right)^{2} + \left(3 \frac{1}{5}\right)^{2} + 4^{2} + \left(4 \frac{4}{5}\right)^{2} + .... , $ is $\frac{16}{5} m , $ then $m$ is equal to :

Let $p = \displaystyle\lim_{x \to 0^+ } ( 1 + \tan^2 \sqrt{x} )^{\frac{1}{2x}}$ then $log \,p$ is equal to

For $ x \epsilon R , f (x) = | \log 2 - \sin x|$ and $g(x) = f(f(x))$, then :

For $x \, \in \, R , x \neq 0, x \neq 1,$ let $f_0(x) = \frac{1}{1-x}$ and $f_{n+1} (x) | = f_0 (f_n(x)), n = 0 , 1 , 2 , ...$ Then the value of $f_{100}(3) + f_1 \left(\frac{2}{3} \right) + f_2 \left( \frac{3}{2} \right)$ is equal to :

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :