IAT (IISER) 2023 | IAT (IISER) Year Wise Previous Years Questions

Suppose the mean and the standard deviation of the data $\left\{x_1, x_2, \cdots, x_9\right\}$ are $\mu$ and $\sigma(\neq 0)$, respectively. After including one more data value $x_{10}$, the mean of the data $\left\{x_1, x_2, \cdots, x_9, x_{10}\right\}$ remains $\mu$. What is the standard deviation of the data $\left\{x_1, x_2, \cdots, x_9, x_{10}\right\}$ ?

$\frac{\sqrt{10}}{3} \sigma$

$\frac{3}{\sqrt{10}} \sigma$

$\frac{10}{9} \sigma$

$\frac{9}{10} \sigma$

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Consider three biased coins. Let the probability of getting head be $\frac{1}{3}$ and the probability of getting tail be $\frac{2}{3}$ in each of the coins. Consider the experiment of tossing the threee coins one by one, and the following events: $E$ :"At least two heads show up" F:"First coin shows tail". What is the conditional probability of $E$ given that $F$ has already occurred?

$1 / 9$

$2 / 9$

$1 / 4$

$4 / 9$

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Which of the following differential equations has $y=e^x$ as one of its particular solutions?

$y \frac{d^2 y}{d x^2}+e^x \frac{d y}{d x}+y^2=e^{2 x}$

$y \frac{d^2 y}{d x^2}-e^x \frac{d y}{d x}+y^2=e^{2 x}$

$y \frac{d^2 y}{d x^2}-e^x \frac{d y}{d x}+y^2=e^x$

$y \frac{d^2 y}{d x^2}+e^x \frac{d y}{d x}+y^2=e^x$