JEE Main 2025 January 28 Shift 2 Question Paper with Solutions Available - Download PDF

JEE Main 2025 January 28 Shift 2 Question Paper with Solutions ( Memory based Questions)

JEE Main 2025 Shift 2 Question Paper with Solution will be available on this page after the conduction of the exam. However, these resources are crucial for candidates appearing in subsequent shifts and those preparing for the April session. This will help the students to prepare for the April session as well as the ones who have their exams on the other shifts.

28 Jan shift 2

Q.1 Consider the following oxides,

$\mathrm{V}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4 \text { and } \mathrm{V}_2 \mathrm{O}_5$
Change in oxidation state of vanadium when amphoteric oxide reacts with acids to form $\mathrm{VO}_4{ }^{+}$is

Q.2 Q. Bohr's model is applicable for single electron atom of atomic number Z. Dependency of frequency of rotation of electron in $n^{\text {th }}$ principal quantum number is proportional to
$1 \quad \mathrm{Z} / \mathrm{n}^2$
$2 \quad Z^2 / n^3$
$3 \quad n^3 / Z$
$4 \quad Z / n$

Q.3 Which has maximum oxidising power among the following
$1 . \mathrm{VO}_2{ }^*$
$2 . \mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}$
$3 .\mathrm{MnO}_4^{-}$
$4 .\mathrm{TiO}_2$

Q.4 Let $f(x)=\int \frac{d x}{x^{1 / 4}\left(x^{1 / 4}+1\right)}$. If $f(0)=-6$, then $f(2)$ is
$1 \quad 4\left[\frac{1}{\sqrt{2}}-2^{1 / 4}+\ln \left|1+2^{1 / 4}\right|\right]-6$
$2 \quad 4\left[\frac{1}{\sqrt{2}}-2^{1 / 4}+\ln \left|1+2^{1 / 4}\right|\right]+6$
$3 \quad 4\left[\frac{1}{\sqrt{2}}+2^{1 / 3}+\ln \left|2^{1 / 4}\right|\right]-6$
$4 \quad 4\left[3+2^{1 / 3}-\ln 2^{1 / 4}\right]+6$

Q.5 No. of Paramagnetic species among the following is

$
\mathrm{O}_2, \mathrm{O}_2 \cdot, \mathrm{O}_2^{-}, \mathrm{NO}_2, \mathrm{NO}, \mathrm{CO}
$

Q.6 How many of the following molecules are polar?

$
\mathrm{CH}_4, \mathrm{CCl}_4, \mathrm{CH}_2 \mathrm{Cl}_2, \mathrm{H}_2 \mathrm{O}, \mathrm{NH}_3, \mathrm{H}_2 \mathrm{O}_2, \mathrm{O}_2 \mathrm{~F}_2
$

Q.7 In an electromagnetic wave, the magnetic field is given as $\vec{B}=\left(\frac{\sqrt{3}}{2} \hat{\imath}+\frac{1}{2} \hat{\jmath}\right) 30 \sin (\omega t-k z)$, the corresponding electric field is
$1 \quad\left(\frac{1}{2} \hat{\imath}+\frac{\sqrt{3}}{2} \hat{\jmath}\right) 9 \times 10^9 \sin (\omega t-k z)$
$2\left(\frac{1}{2} \hat{\imath}-\frac{\sqrt{3}}{2} \hat{\jmath}\right) 9 \times 10^9 \sin (\omega t-k z)$
$3\left(\frac{1}{2} \hat{\imath}+\frac{\sqrt{3}}{2} \hat{\jmath}\right) 9 \times 10^9 \cos (\omega t-k z)$
$4 \quad\left(\frac{1}{2} \hat{\imath}-\frac{\sqrt{3}}{2} \hat{\jmath}\right) 9 \times 10^9 \cos (\omega t-k z)$

Q.8 For concave mirror, distance between object and image $=20 \mathrm{~cm}$ and $m=-3$ find focal length

Q.9

Q. Evaluate

$
\sum_{r=1}^{13} \frac{1}{\sin \left[\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right] \sin \left[\frac{\pi}{4}+\frac{r \pi}{6}\right]}
$

$1 \quad2 \sqrt{3}+2$
$2 \quad 2 \sqrt{3}-2$
$3 \quad 3 \sqrt{2}+2$
$4 \quad 3 \sqrt{2}-4$

Q.10 Bags $B_1, B_2, B_3$ contains 4 Blue, 6 white balls, 5 White 5 blue balls and 6 blue 4 white balls respectively. A bag is randomly selected and a ball is drawn. If the drawn ball is white then find the probability that $B_2$ bag was selected.

Q.11 $\begin{gathered}E=\left(\frac{\sqrt{3}}{2} i+\frac{1}{2} j\right) 30 \sin \left(\omega\left(t-\frac{z}{c}\right) j\right) \\ B=?\end{gathered}$

Q.12 If $x-(3-2 i) x-(2 i-2)=0$ has roots $\alpha+i \beta$ and $\gamma+i \delta$ find the value of $\alpha_y+\beta \delta$.

Q.13 Calculate the spin magnetic moment of $\mathrm{Mn}_2 \mathrm{O}_3$

Q.14 Which of the following compound(s) is/are yellow in colour?
(a) CdS, (b) PbS, (c) CuS, (d) ZnS (Cold), (e) $\mathrm{PbCrO}_4$

Choose the correct answer from the options given below:

Q.15 Consider the following oxides, $\mathrm{V}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4$, and $\mathrm{V}_2 \mathrm{O}_5$ Change in oxidation state of vanadium when amphoteric oxide reacts with acids to form $\mathrm{VO}_4$ is

1) 1

2) 2

3) 3

4) 4

Q.16 Find domain of $\sec { }^{\prime}(2[x]+1)$, where [.] denotes GIF.

Q.17 $\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{CH} \xrightarrow[\mathrm{H}_2]{\text { e } \mathrm{Pd} / \mathrm{C}}(\mathrm{A}) \xrightarrow[\text { (ii) } \mathrm{Zn}, \mathrm{H}_2 \mathrm{O}]{\text { (i) } \mathrm{O}_3}(\mathrm{~B})+(\mathrm{C})$

Q.18 212,213,..........., 999
find no. of numbers in the sequence above whose sum of digits is 15 .

Q.19 Q. The correct order of energy of the following subshell
$\quad$ 1s $2 s \quad 3 p \quad 3 d$
$1 \quad 1 s<2 s<3 d<3 p$
$2 \quad 2 s<1 s<3 p<3 d$
$3 \quad 1 s<3 p<2 s<3 d$
$4 \quad 1 s<2 s<3 p<3 d$

Q.20 Q. The magnetic field $\vec{B}$ at the centre $O$ of the given arrangement is
$1 \quad \frac{+\mu_0 I}{8 \pi a}(3 \pi+2) \hat{k}$
$2 \quad \frac{-\mu_0 I}{8 \pi a}(3 \pi+2) \hat{k}$
$3 \quad \frac{+\mu_0 I}{8 \pi a}(3 \pi-2) \hat{k}$
$4 \quad \frac{-\mu_0 I}{8 \pi a}(3 \pi-2) \hat{k}$

Q.21 Find area enclosed by $x\left(y^2+1\right)$ and $y^2=2 x$.

Q.22 If $f(x)=\int \frac{d x}{x^{1 / 4}\left(x^{1 / 4}+1\right)^4 d x \& f(0)=1 \text {. find } f(2)=\text { ? }}$

Q.23 which of the group -15 element forms $\mathrm{d} \pi-\mathrm{d} \pi$ Bond and strongest basic hydride ?
(1) $z=7$
(2) $z=15$
(3) $z=33$
(4) $z=51$

Q.24 Q. Area bounded between the curves $C_1: x\left(1+y^2\right)-1=0$ and $C_2: y^2-2 x=0$ is (in sq. unit)
$1 \quad \frac{\pi}{2}-\frac{1}{3}$
$2 \quad \frac{\pi}{4}-\frac{1}{6}$
$3 \quad 2\left(\frac{\pi}{2}-\frac{1}{6}\right)$
$4 \quad \frac{\pi}{6}+\frac{1}{2}$

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