List of top Statistics Questions

Consider $x_{1},x_{2},...,x_{n}$ observations such that $\sum_{i=1}^{n}{x_{i}}^{2}=500$ and $\sum_{i=1}^{n}x_{i}=50$. Then a minimum number of observations required is

If $P(E) = \frac{1}{3}$, $P(F) = \frac{2}{5}$ and $P(E \cup F) - P(E \cap F) = \frac{1}{5}$ then $P(E \cup F)$ is equal to

The integrating factor for the differential equation $x~log_{e}x~dy = (2~log_{e}x - y) dx$ is

Let E and F be two events, if $P(E|F)=0.5$, $P(E|\overline{F})=0.6$ and $P(F)=0.6$ then $P(E)$ equals

If A and B are two non-mutually exclusive events such that $P(A|B)=P(B|A)$ then

If $P(E)=\frac{1}{3}$, $P(F)=\frac{1}{5}$ and $P(E\cup F)=\frac{1}{2}$ then $P(E|\overline{F})+P(F|\overline{E})$ is equal to

Which of the following differential equation is satisfied by $y_{1}(x)=e^{x}$, $y_{2}(x)=x~e^{x}$ and $y_{3}=e^{2x}?$

Let $A=\begin{bmatrix}2& 1& -2\\ 1& 1& -1\\ 1& 0& 2\end{bmatrix}$ and if $B=|A|adj(A)$ Then $|B|$ is equal to

If A is an invertible symmetric matrix then
A. $(A^{-1})^{T}=A^{-1}$

B. adj $A=(adj~A)^{T}$

C. $A^{-1}$ is skew-symmetric

D. $|A|=0$

Choose the correct answer from the options given below

If A and B are symmetric matrices of same order then
A. AB is symmetric iff $AB=BA$

B. $AB+BA$ is skew symmetric matrix

C. AB-BA is symmetric matrix

D. $(A+B)^{n}$ is symmetric for all $n \in N$

Choose the correct answer from the options given below

The eigen vectors of the matrix $A=\begin{bmatrix}5 & 4\\ 1& 2\end{bmatrix}$ is

Solution of differential equation $(x^{2}+y^{2})dx-2xy~dy=0,$ where c is constant, is

Let $AX=B$ be a system of n-linear equations in n unknowns then

The value of $\lim_{x\rightarrow1}\frac{\int_{2 \log_{e}x}^{3\log_{e} x} e^{t} \, dt}{x-1}$ equals

The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

The function $f(x)=\int_{e^{x}}^{e^{2x}} t \log_{e}t \, dt$ has an absolute minima at $x=0$ and a local maxima at $x=$

In the Taylor series expansion of function $f(x)=e^{x^{2}-x}$, coefficient of $x^{3}$ is

Match List I with List - II. List - I & List - II
A. $x$ where $f(x)=9x(x-1)^{2}$ attains maximum & I. $e$

B. $x$ where $f(x)=\frac{1}{x}e^{-\frac{1}{2}(\log_{e}x-2)^{2}}$ attains maximum & II. $\frac{2}{3}$

C. $x$ where $f(x)=x^{2}(1-x)^{6}$ attains maximum & III. $\frac{1}{3}$

D. $x$ where $f(x)=x^{2}e^{-3x}$ attains maximum & IV. $\frac{1}{4}$

If $f(1)=1$ and $f^{\prime}(1)=-1$, then the value of $\frac{d}{dx}[\frac{f(x^{3})}{x~f(x^{2})}]$ at $x=1$ is equal to

The function $f(x)=|x^{2}+x-6|$ is not differentiable at $x=a$ and $x=b$ then $(b-a)^{2}$ equals

Value of $\sum_{n=0}^{\infty}\frac{2}{(2n+1)(2n+3)}$ is

The Sum $\sum_{r=1}^{20}(r^{2}+1)\times r!$ is equal to