List of top Statistics Questions asked in CUET (PG)

Which of the following statements are correct?
A. Ogive curves are used to obtain median

B. Histogram are used to obtain mode

C. Boxplots are used to determine mean

D. Pie charts are used to determine quantile

Choose the correct answer from the options given below

Let E, F and G be events such that $P(E|G) = 0.05$ and $P(F|G) = 0.05$ which of the following statement must be true?

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

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

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

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

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

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

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:

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

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

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

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

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

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. $\frac{1}{4}$

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 $x=$

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

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