List of top Questions asked in IISER- 2025

Let $A = \left\{ x \in \mathbb{R} \;\middle|\; -31 < \det \begin{bmatrix} 3x - 1 & 2 \\ -2 & 5 \end{bmatrix} \le 29 \right\}$. Which one of the following statements is TRUE?

Let $n = \sum_{r=0}^{10} (-1)^r \binom{10}{r} \left(\frac{2}{3}\right)^{2r} 3^{20}$. Which one of the following statements is TRUE?

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be the function given by $f(x) = \cos(\tan^{-1} x)$. Which one of the following statements is TRUE?

During the charging and discharging of a lead-acid battery (a $\text{Pb}$ anode, a grid of $\text{Pb}$ packed with $\text{PbO}_2$ as cathode, and an aqueous solution of $\text{H}_2\text{SO}_4$ as an electrolyte), which of the following redox reactions does NOT occur?

How many three digit numbers divisible by 5 are there in which no digits are repeated?

What is the major product in the reaction sequence given below?

Compound I undergoes hydroboration-oxidation reaction with $(\text{BH}_3)_2$ followed by treatment with $\text{H}_2\text{O}_2$ and aqueous $\text{NaOH}$ to produce another compound II, which upon oxidation with $\text{CrO}_3$ gives 2,3-dimethyl-cyclohexanone as the product. What is the structure of I?

What is the time period of revolution of an electron in the fourth Bohr orbit of $\text{He}^+$?
(Bohr radius = 52.9 picometers, mass of an electron = $9.11 \times 10^{-31}\text{ kg}$, Planck’s constant = $6.626 \times 10^{-34}\text{ Js}$)}

The work done when one mole of an ideal gas expands at constant temperature $T$ from volume $V$ to $2V$ (in two equal steps of volume in a linear fashion) is $\frac{7}{12}RT$. How much more work would be done by the gas if it expands in three equal steps?
(R is the universal gas constant)}

At a particular temperature, the magnitude of the rate constant of a reaction is $5 \times 10^{-5}$ and the unit of the pre-exponential factor of the Arrhenius equation for this reaction is $\text{mol L}^{-1}\text{ min}^{-1}$. Which of the following plots is correct for this reaction?
[Note: $[\text{R}]_0$ is the initial concentration and $\text{t}_{1/2}$ is the half-life of the reaction]}

The dipole moments of three $\text{AB}_3$-type molecules I, II, and III are measured to be 0.0 D, 0.2 D, and 1.5 D, respectively. Which one of the following options is correct regarding the identity of I, II, and III?

Which of the following reactions do NOT provide an aldehyde as a product?

What are the major products formed in the following reaction sequence?

What are the correct orders of stability for the following compounds?

Consider the following reaction scheme:

Which among the following statements is correct?

How many $\beta$-hydrogen is/are present in 2-methyl-3-phenyl-pentan-1-al?

What is the value of $E^\circ(\text{Fe}^{3+}/\text{Fe}^0)$?
(The standard reduction potential values are $E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+}) = 0.77\text{ V}$, and $E^\circ(\text{Fe}^{2+}/\text{Fe}^0) = -0.44\text{ V}$)}

Which one of the following statements best describes the acidic/basic/amphoteric nature of ZnO and CaO?

The given picture was obtained from an agarose gel electrophoresis of a plasmid after digestion with restriction enzymes either X, Y or both X and Y.

Which one of the following diagrams correctly represents the position of the restriction enzyme sites (X, Y) on the 10,000 bp plasmid?

Honey bee males are haploid and females are diploid. Which one of the following statements is INCORRECT about honey bees?

What are retroviruses?

Which among the following processes is/are associated with increasing bond order but no change in diamagnetic/paramagnetic behaviour?
(i) $\text{N}_2 \rightarrow \text{N}_2^+ + \text{e}^-$
(ii) $\text{O}_2 \rightarrow \text{O}_2^+ + \text{e}^-$
(iii) $\text{O}_2 + \text{e}^- \rightarrow \text{O}_2^-$

Which one of the following statements is FALSE?

Which one of the following autoregulatory mechanisms is employed by the kidney when glomerular filtration rate is reduced?

Which amino acid will be charged on the tRNA with anticodon 5Õ-GUU-3Õ?