List of top Questions asked in CUET (PG)

If $X_{1}, X_{2}, X_{3}$ are independent and identically distributed standard normal variates and let $U=\frac{\sqrt{2}X_{3}}{\sqrt{X_{1}^{2}+X_{2}^{2}}}$ then $U^{2}$ follows

A fair coin is tossed $2n$ times, then the probability that the outcomes do not result in an equal number of heads and tails is

If $r \cdot v X \sim N(0, 1)$ then $E\left(\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{X} e^{-z^2/2} dz\right)$ equals to

Let $G_x(\cdot)$ be the distribution function of an arbitrary random variable symmetric about $0$ (zero) and $G_x^{\leftarrow}$ is the inverse function of $G_x$ then for $p \in (0, 1)$ value of $G_x^{\leftarrow}(p) + G_x^{\leftarrow}(1-p)$ is

If $X, X_1, X_2$ are independent and identically distributed positive random variables with distribution function $F_X(x)$ then $\int_{0}^{\infty} 2 \cdot x \cdot \overline{F}_X^2(x) dx$ equals

If $G(x)$ be the distribution function of random variable $X$ symmetric about $0$ then $\int_{-a}^{a} G(x)dx$ equals

Let $X$ and $Y$ be independent non negative integer valued random variables with $E(X) < \infty$, $E(Y) < \infty$, then

Let X be a random variable with distribution function $F(x) = \begin{cases} 0 & \text{for } x < 0 \\ \frac{1 + x}{8} & \text{for } 0 \le x < 1 \\ \frac{x + 4}{8} & \text{for } 1 \le x < 2 \\ \frac{x + 16}{24} & \text{for } 2 \le x < 3 \\ 1 & \text{for } x \ge 3 \end{cases}$ then $P(1 \le X < 2)$ is

Let $X_{1}, X_{2}$ be independent random variables each from a discrete probability mass function $P_{X}(x) = \begin{cases} 1/3 & \text{if } x = 0 \\ 2/3 & \text{if } x = 1 \end{cases}, i = 1, 2$. Then the moment generating function of $Y = X_{1} \cdot X_{2}$ is

You are given $P(A \cup B) = 0.6$ and $P(A \cup \overline{B}) = 0.8$ then $P(A)$ is

If G is a geometric mean of observations $x_{1}, x_{2}, \dots, x_{n}$ then the geometric mean of $y_{i} = e^{-\alpha \log_{e} x_{i}}$, $i = 1, 2, \dots, n$ is

In a set of 2n observations the geometric mean of first 'n' observations is 81 and the geometric mean of remaining n-observations is 16 then the geometric mean of all 2n observations is

Let E, F and G be mutually independent events such that $P(E) = 0.4$, $P(F) = 0.6$ and $P(G) = 0.8$ then $P(\overline{E} \cup \overline{F} \cup G)$ 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

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

Three dice have the probabilities of throwing a "five" as p, q and r respectively. One of the dice is chosen at random (each is equally likely to be chosen) and thrown and a "five" appeare
D. What is the probability that the die chosen was the first one?

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?

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

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

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

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

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

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