List of top Mathematics Questions

A normal to the curve $ 2x^{2 }- y^{2} = 14 $ at the point $ (x_{1}, y_{1}) $ is parallel to the straight line $ x + 3y = 4 $ . Then the point $ (x_{1}, y_{1}) $ is

When $ y = vx $ , $ y $ and $ x $ are variables, the differential equation $ \frac{dy}{dx}=\frac{2xy}{x^{2}-y^{2}} $ reduces to

Let the function $ f(x) $ be continuous in the interval $ [a, b] $ and differentiable in $ (a, b) $ . Then there is at least one point $ c $ in $ (a, b) $ at which the tangent to the curve $ y = f (x) $ is parallel to

The value of integral \(\int{e^x}(\frac{cosx+sinx}{cos^2x})dx\)

Let $ P\left(x\right)=^{10}C_{x} \left(\frac{1}{2}\right)^{10} , x=0, 1, 2, \ldots,10 $ be the probability mass function of a binomial distribution $ X $ . Then the mean of $ X $ is

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

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 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