JEE Main 2025 January 24 Shift 2 Memory Based Questions
Q.1 If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2 \alpha)+\ldots \infty$ terms, then $\alpha$ is equal to
1 6
$2 \quad 6 / 7$
3 1/7
$4 \quad 1$
Q.2 A solid sphere and hollow sphere rolls down purely equal distances on same inclined plane (starting from rest) in time $t_1$ and $t_2$ then
$1 \quad t_1>t_2$
$2 \quad t_1<t_2$
$3 \quad t_1=2 t_2$
$4 \quad t_1=t_2$
Q.3
Consider the following reaction
$
\begin{aligned}
& \mathrm{S}(\mathrm{~s})+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+2 \mathrm{x} \mathrm{KJ} \\
& \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+\mathrm{y} \mathrm{KJ}
\end{aligned}
$
Calculate $\Delta \mathrm{H}_{\mathrm{r}}$ for following reaction (K)
$\mathrm{S}(\mathrm{s})+\mathrm{O}_2 \rightarrow \mathrm{SO}_2(\mathrm{~g})$
Q.4 If $A$ and $B$ are binomial coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ term of binomial expansion $(1+x)^{2 n-1}$. $=5 B$, then the value of $n$ is
1)20
2)21
3)14
4)20
Q.5 If a square is divided in $4 \times 4$ squares.
If two squares are chosen randomly then the probability that the squares doesn't share common side is
(A) 3/5
(B) $4 / 5$
(C) $3 / 20$
(D) $7 / 10$
Q.6Arithmetic mean $\mathrm{S}_{12}=57, \mathrm{~S}_{40}=1030$. Find $\mathrm{S}_{30}-\mathrm{S}_{10}=$ ?
Q.7 A solid sphere rolls without slipping on a horizontal plane. What is ratio of translational kinetic energy to the rotational kinetic energy of the sphere.
$1 \quad 4 / 3$
$2 \quad 3 / 4$
$3 \quad 2 / 5$
$4 \quad 5 / 2$
Q.8 The conditions and consequences that favour the $\mathrm{t}_{2 \mathrm{~g}}^3 \mathrm{e}_{\mathrm{g}}^1$ configuration in a metal complex are
1 Strong field ligand; High spin complex
2 Weak field ligand; High spin complex
3 Strong field ligand; Low spin complex
4 Weak field ligand; Low spin complex
Q.9 There is a group $\mathbf{A}$ of 5 boys and 3 girls and another group $\mathbf{B}$ of 5 boys and 6 girls. How many ways can we invite 4 boys and $\mathbf{4}$ girls for party with $\mathbf{5}$ from group A and 3 from group B.
Q.10 The equation of chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ with $(3,1)$ as mid-point is
$1 \quad 48 x+25 y-169=0$
$2 \quad 25 x+5 y-125=0$
$3 \quad65 x+2 y-12=0$
$4 \quad 45 x+4 y-135=0$
Q.11 If the acceleration due to gravity on the surface of carth is $g$, then acceleration due to gravity on a planet whose diameter is $\frac{1}{3}$ of that of earth and same mass as that of earth is $g^{\prime}=n g$, where $n$ is
Q.12 When ethane-1, 2-diammine is progressively added to aqueous solution of Nickel (II) chloride the sequence of colour change observed will be:
1 Pale Blue $\rightarrow$ Blue $\rightarrow$ Green $\rightarrow$ Violet
2 Violet $\rightarrow$ Blue $\rightarrow$ Pale Blue $\rightarrow$ Green
$3 \quad$ Pale Blue $\rightarrow$ Blue $\rightarrow$ Violet $\rightarrow$ Green
$4 \quad$ Green $\rightarrow$ Pale Blue $\rightarrow$ Blue $\rightarrow$ Violet
Q.13 $7=51+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2 \alpha)+\cdots \infty$. Then $\alpha$ is
1)6
2)$\frac{6}{7}$
3)$\frac{1}{7}$
4)1
Q.14 If system of equations
$
\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 4 x+3 y+\mu z=33 \text { has infinite solutions, then } \lambda+\mu \text { is equal to }
\end{aligned}
$
$1 \quad \frac{1334}{5}$
$2 \quad \frac{1269}{5}$
$3 \quad \frac{261}{5}$
$4 \quad \frac{1063}{5}$
Q.15 A solid sphere and hollow sphere rolls down purely equal distances on same inclined plane (starting from rest) in time $t_1$ and $t_2$ then
(A) $t_1>t_2$
(B) $t_1<t_2$
(C) $t_1=2 t_2$
(D) $t_1=t_2$
Q.16 The thin Biconvex lens is divided in to 4 equal parts by plane AB and CD The original power is 4D. The after dividing power of each piece is
Q.17 If $2 \sin x \frac{d y}{d x}=\sin 2 x-2 y \tan x, y\left(\frac{\pi}{3}\right)=0$ find $y \cdot\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)$
Q.18 Statement - 1: First ionization energy Ge is greater than Si
Statement - 2: First ionization energy Pb is greater than Sn
a) Statement - $\mathbf{1}$ is true Statement $\mathbf{- 2}$ is false
b) Statement - 18 Statement - 2 are false
c) Both the Statements are true
d) Statement - 1 is false Statement - 2 is true
Q.19 In YDSE light of $\lambda 600 \mathrm{~nm}$ \& 480 nm are used. What is the minimum order of Bright fringe of 480 nm coincides with bright frig 600 nm ?
Q.20 A satellite is nine times closer to earth compared to moon. Time period of moon is 27 days then period of the satellite is
(A) 1 days
(B) 3 days
(C) 9 day
(D) $3 \sqrt{3}$ days
Q.21 3,4-Diphenyl Hex-1-en-5-yne have how many sp² and sp carbon atom.
Q.22.Find area bounded by $y=e^* \cdot y=e^*-1$ and $y$ axis
Q.23 If $E_{( }(\beta) m$ and $c$ denote the energy, linear momentum, mass and speed of light, then the equation representing the correct relation could be
$1 \quad E^2=p^2 c^2+m^2 c^4$
$2 \quad E^2=p c^2+m^2 c^4$
$3 \quad E=p^2 c^2+m^2 c^2$
$4 \quad E^2=p c^2+m^2 c^2$
Q.24 S-1:- The first ionisation energy of Pb is greater than that of Sn .
S-II:- The first lonisation energy of Ge is greater than that of Si.
1 S-I and S-ll both are correct
2 S-1 is correct and S-II incorrect
3 S-1 is incorrect and S-11 correct
4 S.1 and S-11 both are incorrect
