List of top Mathematics Questions

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

Two sets $A$ and $B$ are as under: $A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $; $B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then

The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, is :

If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $

Letters in the word HULULULU are rearranged. The probability of all three L being together is

The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $

If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is

If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =

If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is

The number of solutions of $\sin \, x + \sin \, 3x + \sin \, 5x = 0$ in the interval $\left[\frac{\pi}{2} , 3 \frac{\pi}{2}\right] $ is

Matrix $A = \begin{bmatrix}1&2&3\\ 1&1&5\\ 2&4&7\end{bmatrix}$then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33 } + A_{33} $ is

If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is

If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

The negation of the statement: "Getting above 95% marks is necessary condition for Hema to get the admission is good college"

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is

Let \(A, B, C\) be the angles of a plane triangle. If
\[ \tan \frac{A}{2} = \frac{1}{3} \quad \text{and} \quad \tan \frac{B}{2} = \frac{2}{3}, \]
then \(\tan \frac{C}{2}\) is equal to:

If the amplitude of \(z - 2 - 3i\) is \(\pi/4\), then the locus of \(z = x + i y\) is:

The coefficient of \(x^3\) in the expansion of
\[ \left(x - \frac{1}{x}\right)^7 \]
is:

If \(x > 0\), then
\[ 1 + \frac{\log x}{1!} + \frac{(\log x)^2}{2!} + \cdots = \]

The locus of the point of intersection of the lines
\[ x = \frac{1 - t^2}{1 + t^2}, \quad y = \frac{2 a t}{1 + t^2} \]
represents:

Eccentricity of ellipse
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] if it passes through points \((9,5)\) and \((12,4)\) is:

The value of
\[ \lim_{n \to \infty} \frac{1 + 2 + 3 + \cdots + n}{n^2 + 100} \]
is equal to: