List of top Mathematics Questions on Statistics asked in COMEDK UGET

Consider the first 10 natural numbers. If we multiply each number by \( -1 \) and add 1 to each number, the variance of the numbers so obtained is
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
$ y =\tan^{-1} \left( \frac{1}{1+x+x^{2}} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+3x+3} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+5x+7} \right) + ......+ $ upto $n$ terms, then $ \frac{dy}{dx} $ at $x = 0$ and $n = 1$ is equal to
If $y = \sin^{2} \left(\tan^{-1} \sqrt{\frac{1-x^{2}}{1+x^{2}}}\right), $ then $\frac{dy}{dx}$ =
If $\sqrt{\frac{x}{y}} + \sqrt{ \frac{y}{x}} = \sqrt{a}$ , then $ \frac{dy}{dx} = $
Let [ ?] denote the greatest integer function and $f (x) = [\tan^2 x]$. Then
Let $y' = e^{-2x} $ and $ y = 0$ when $x =e$. Then the value of $x$ when $ y =\frac{1}{2}$ is
$\displaystyle\lim_{x \to 0} \frac{6^{x} -3^{x} -2^{ x}+1}{x^{2}} = $
If $f\left(x\right)= \cos^{-1} \left(\frac{1-\left(\log _{e} x\right)^{2}}{1+\left(\log _{e} x\right)^{2}}\right)$ , then $ f'\left(\frac{1}{e}\right) =$
If $y =\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y}}}} +.....$ then $ \frac{dy}{dx} $
The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is
Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}$ then the? values of a and b so that $f(x)$ is continuous are
The number of points at which $f(x) = 3 + 2\, \, \, \sin x$ has maximum in the interval $\left( - \frac{11 \pi}{2} , 100 \pi \right)$ is
A point on the curve $2y^3 + x^2 = 12y$ at which the tangent to the curve is vertical is
If $g$ is the inverse function of $f$ and $f'(x) = \frac{1}{ 1+x^n} $ , then the value of $g'(x)$ is
$\displaystyle\lim_{x \to \infty} \left( \frac{x+6}{x+1}\right)^{x+4} =$
If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $
If $ f(x) = x^m$, where $m$ is a positive integer then the value of $m$ for which $f'(\alpha + \beta) = f'(\alpha ) + f'(\beta)$ for all $ \alpha , \beta > 0$ is
The points of discontinuities of $f(x) = \left(\frac{\pi x}{x+1} \right)$ other than $x = -1$ are
$f(x) = \begin{cases} x , \text{if } x \text{ is rational}\\ 0, \text{if } x \text{ is rational} \end{cases}$ then $f$ is
The shortest distance from the point $(3, 0)$ to the parabola $y = x^2$ is.
Of all open tanks in the form of a rectangular parallelopiped with a square.base having a fixed volume, the one that has the least inner surface area has the property that its
If the greatest angle of a cyclic quadrilateral is 3 times the least angle, then the radian measure of the least angle is
If $x$ and $y$ are related by the relation$x^2 - ax+ y^2 = 0$, then $d^2y/dx^2$ is equal to
The maximum area of a rectangle which can be inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is