List of top Mathematics Questions

If tan $ y=\frac{sin\,x+cos\,x}{cos\,x-sin\,x} $ , then $ \frac{dy}{dx}= $

If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$

The function $ f (x) = |x-10| $ , $ x $ is real number, is

The equation of the tangent to the curve $y = x^3 - 6x + 5$ at $(2,1)$ is

If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=

The slope of the straight line$\frac{ x}{10 }$-$\frac{y }{4 }$ = 3 is

If $ 25^{th} $ term of an $ A.P. $ is $ 15 $ and if its $ 15^{th} $ term is $ 25 $ , then the $ 40^{th} $ term of the $ A.P. $ is

A pair of unbiased dice is thrown once. Let $ X $ be the random variable denoting the product of numbers that appear on the two dice. Then $ P\left(X \ge21\right)= $

If $\sin^{-1} \, x + \sin^{-1} \,y= \frac{\pi}{2}$ , then $x^2$ is equal to

The equation of the normal to the curve $y(1 + x^2) = 2 - x$ where the tangent crosses $x-axis$ is

The differential equation of the family of circles touching $y$-axis at the origin is

The integrating factor of the differential equation $ \left(1+x^{2}\right)\frac{dy}{dx}+xy=cos\,x $ is equal to

If $PQ$ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ such that $\Delta OPQ$ is equilateral, $O$ being the centre. Then the eccentricity e satisfies

If $A, B$ are two events such that $P\left(A\cup B\right) \ge \frac{3}{4}$ and $\frac{1}{8}\le P\left(A\cap B\right) \le\frac{3}{8}$ then

Standard Deviation of n observations $a_{1}, a_{2}, a_{3} ..... a_{n}$ is $\sigma$. Then the standard deviation of the observations $\lambda a_{1},\lambda a_{2}, .... \lambda a_{n}$ is

Let $R$ be a relation defined on the set $Z$ of all integers and $xRy$ when $x + 2y$ is divisible by $3$. Then

The locus of the midpoints of all chords of the parabola $y^2 = 4ax$ through its vertex is another parabola with directrix

The sum of n terms of the following series; $1^3 + 3^3 + 5^3 + 7^3 + ....$ is

The number of values of $k$ for which the equation $x^2 - 3x + k = 0$ has two distinct roots lying in the interval $(0, 1)$ are

The points of the ellipse $16x^2 + 9y^2 = 400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

In $\Delta ABC \left(a-b\right)^{2} cos^{2} \frac{C}{2} + \left(a+b\right)^{2} sin^{2} \frac{C}{2} = $

The number of points at which the function $f \left(x\right)=max \left\{a-x, a+x, b\right\}, -\infty, 0 < a < b$ cannot be differentiable

$\displaystyle\lim_{x \to 0} \frac{xe^x - \sin \, x}{x}$ is equal to

If $\frac{1}{^{5}C_{r}}+\frac{1}{^{6}C_{r}} =\frac{1}{^{4}C_{r}}$, then the value of $r$ equals to

The simplified form of $\tan^{-1}$ $\left(\frac{x}{y}\right)$ $- \tan^{-1}$ $\left(\frac{x-y}{x+y}\right)$ is equal to