1
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1

What is the time period of revolution of an electron in the fourth Bohr orbit of $\mathrm{He}^{+}$?

[Bohr radius $=52.9$ picometers, mass of an electron $=9.11 \times 10^{-31} \mathrm{~kg}$, Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ ]

A

24 femtoseconds

B

4.8 femtoseconds

C

24 femtoseconds

D

2.4 femtoseconds

2
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1

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

A

I: $\mathrm{BF}_3, \mathbf{I I}: \mathrm{NF}_3, \mathbf{I I I}: \mathrm{NH}_3$

B

I: $\mathrm{BF}_3, \mathbf{I I}: \mathrm{NH}_3, \mathbf{I I I}: \mathrm{NF}_3$

C

I: $\mathrm{ClF}_3, \mathbf{I I}: \mathrm{NF}_3, \mathbf{I I I}: \mathrm{NH}_3$

D

I: $\mathrm{BCl}_3, \mathbf{I I}: \mathrm{NH}_3, \mathbf{I I I}: \mathrm{NF}_3$

3
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1

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

A

$\mathrm{Pb}^{4+}+4 \mathrm{e}^{-} \rightarrow \mathrm{Pb}$

B

$\mathrm{Pb}^{2+} \rightarrow \mathrm{Pb}^{4+}+2 \mathrm{e}^{-}$

C

$\mathrm{Pb} \rightarrow \mathrm{Pb}^{2+}+2 \mathrm{e}^{-}$

D

$2 \mathrm{~Pb}^{2+} \rightarrow \mathrm{Pb}^{4+}+\mathrm{Pb}$

4
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1

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

A

136

B

128

C

144

D

162

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