1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Let $I=\int_{e^{-\pi / 2}}^{e^{\pi / 2}}\left(\sin ^2(\log (x))+\sin \left(\log \left(x^2\right)\right)\right) d x$. What is the value of $I$ ?
2
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Consider the following subset of the $X Y$-plane.
$$ S=\left\{\left(|z-\mathrm{i} z|,|z|^2\right): \quad z \text { is a complex number }\right\} $$
Which one of the following statements is correct?
3
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
A ship sets off on a voyage with three engines, labelled $A, B$, and $C$, which work independently. The ship can complete the voyage only if at least two of these engines keep working. The probability that engine $A$ breaks down is $1 / 4$, that engine $B$ breaks down is $1 / 4$, and that engine $C$ breaks down is $1 / 2$. What is the probability that the ship can complete the voyage?
4
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Consider the differential equation $\cos (y) \frac{d y}{d x}+\frac{1}{x} \sin (y)=x, \quad(x>0)$; given that, $y=\frac{\pi}{2}$ at $x=\sqrt{3}$. Which one of the following is the value of $y$ at $x=\sqrt{\frac{3}{2}}$ ?
Paper analysis
Total Questions
Biology
15
Chemistry
15
Mathematics
15
Physics
15
More papers of IAT (IISER)
IAT (IISER)
Papers
2024
2020