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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

If the mean and the variance of $6,4, a, 8, b, 12,10,13$ are 9 and 9.25 respectively, then $a+b+a b$ is equal to :

If the mean and the variance of $6,4, a, 8, b, 12,10,13$ are 9 and 9.25 respectively, then $a+b+a b$ is equal to :
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^1 f(\mathrm{t}) \mathrm{dt}=5 x f(x)-x^5-9$ for all $x \geqslant 1$, then the value of $f(3)$ is :

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^1 f(\mathrm{t}) \mathrm{dt}=5 x f(x)-x^5-9$ for all $x \geqslant 1$, then the value of $f(3)$ is :
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : JEE Main 2025 (Online) 2nd April Evening Shift Mathematics - Permutations and Combinations Question 6 English
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : JEE Main 2025 (Online) 2nd April Evening Shift Mathematics - Permutations and Combinations Question 6 English
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$, then $m^2+n^2$ is equal to :
Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$, then $m^2+n^2$ is equal to :
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt

If the system of equations

$$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4 x+5 y+\mu z=9 \end{aligned} $$

has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :

If the system of equations

$$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4 x+5 y+\mu z=9 \end{aligned} $$

has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Let $A$ be a $3 \times 3$ real matrix such that $A^2(A-2 I)-4(A-I)=O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5=\alpha A^2+\beta A+\gamma I$, where $\alpha, \beta$, and $\gamma$ are real constants, then $\alpha+\beta+\gamma$ is equal to :
Let $A$ be a $3 \times 3$ real matrix such that $A^2(A-2 I)-4(A-I)=O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5=\alpha A^2+\beta A+\gamma I$, where $\alpha, \beta$, and $\gamma$ are real constants, then $\alpha+\beta+\gamma$ is equal to :
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

$$If\,\mathop {\lim }\limits_{x \to 0} {{\cos (2x) + a\cos (4x) - b} \over {{x^4}}}is\,finite,\,then\,(a + b)\,is\,equal\,to:$$

$$If\,\mathop {\lim }\limits_{x \to 0} {{\cos (2x) + a\cos (4x) - b} \over {{x^4}}}is\,finite,\,then\,(a + b)\,is\,equal\,to:$$
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If the image of the point $\mathrm{P}(1,0,3)$ in the line joining the points $\mathrm{A}(4,7,1)$ and $\mathrm{B}(3,5,3)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to :
If the image of the point $\mathrm{P}(1,0,3)$ in the line joining the points $\mathrm{A}(4,7,1)$ and $\mathrm{B}(3,5,3)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to :
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If $\theta \epsilon\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is equal to :
If $\theta \epsilon\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is equal to :
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
Let $A=\{1,2,3, \ldots ., 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$. Let $\left(a_1\right.$, $\left.a_2\right),\left(a_2, a_3\right),\left(a_3, a_4\right), \ldots .,\left(a_k, a_{k+1}\right)$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :
Let $A=\{1,2,3, \ldots ., 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$. Let $\left(a_1\right.$, $\left.a_2\right),\left(a_2, a_3\right),\left(a_3, a_4\right), \ldots .,\left(a_k, a_{k+1}\right)$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to :
If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to :
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Let the area of the triangle formed by a straight line $\mathrm{L}: x+\mathrm{b} y+\mathrm{c}=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $45^{\circ}$ with the positive $x$-axis, then the value of $\mathrm{b}^2+\mathrm{c}^2$ is :
Let the area of the triangle formed by a straight line $\mathrm{L}: x+\mathrm{b} y+\mathrm{c}=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $45^{\circ}$ with the positive $x$-axis, then the value of $\mathrm{b}^2+\mathrm{c}^2$ is :
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The line $\mathrm{L}_1$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $\mathrm{L}_2$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :
The line $\mathrm{L}_1$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $\mathrm{L}_2$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :
The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the integral $\mathrm{I}=\int_{\mathrm{a}}^{\mathrm{b}} \frac{9 x^2}{1+5^x} \mathrm{~d} x$ is equal to :
Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the integral $\mathrm{I}=\int_{\mathrm{a}}^{\mathrm{b}} \frac{9 x^2}{1+5^x} \mathrm{~d} x$ is equal to :
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
$$If\,\sum\limits_{r = 0}^{10} {({{{{10}^{r + 1}} - 1} \over {{{10}^r}}}).{}^{11}{C_{r + 1}} = {{{}_\alpha 11 - {{11}^{11}}} \over {{{10}^{10}}}},\,then\,\,\alpha \,\,is\,\,equal\,\,to:} $$
$$If\,\sum\limits_{r = 0}^{10} {({{{{10}^{r + 1}} - 1} \over {{{10}^r}}}).{}^{11}{C_{r + 1}} = {{{}_\alpha 11 - {{11}^{11}}} \over {{{10}^{10}}}},\,then\,\,\alpha \,\,is\,\,equal\,\,to:} $$
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :
$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Let $\overrightarrow{\mathrm{a}}=2 \hat{i}-3 \hat{j}+\hat{k}, \quad \overrightarrow{\mathrm{~b}}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\overrightarrow{\mathrm{c}}$ be such that $(\vec{a}-\vec{c}) \times \vec{b}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$ and $\vec{a} \cdot \vec{c}=3$. If $\vec{b} \times \vec{c}=\vec{d}$, then $|\vec{a} \cdot \vec{d}|$ is equal to :
Let $\overrightarrow{\mathrm{a}}=2 \hat{i}-3 \hat{j}+\hat{k}, \quad \overrightarrow{\mathrm{~b}}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\overrightarrow{\mathrm{c}}$ be such that $(\vec{a}-\vec{c}) \times \vec{b}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$ and $\vec{a} \cdot \vec{c}=3$. If $\vec{b} \times \vec{c}=\vec{d}$, then $|\vec{a} \cdot \vec{d}|$ is equal to :
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

If the set of all $\mathrm{a} \in \mathbf{R}-\{1\}$, for which the roots of the equation $(1-\mathrm{a}) x^2+2(\mathrm{a}-3) x+9=0$ are positive is $(-\infty,-\alpha] \cup[\beta, \gamma)$, then $2 \alpha+\beta+\gamma$ is equal to $\qquad$ .

If the set of all $\mathrm{a} \in \mathbf{R}-\{1\}$, for which the roots of the equation $(1-\mathrm{a}) x^2+2(\mathrm{a}-3) x+9=0$ are positive is $(-\infty,-\alpha] \cup[\beta, \gamma)$, then $2 \alpha+\beta+\gamma$ is equal to $\qquad$ .
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1+4 \cdot 1^4}+\frac{4 \cdot 2}{1+4 \cdot 2^4}+\frac{4 \cdot 3}{1+4 \cdot 3^4}+\ldots .$. is $\frac{\mathrm{m}}{\mathrm{n}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to _______________
If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1+4 \cdot 1^4}+\frac{4 \cdot 2}{1+4 \cdot 2^4}+\frac{4 \cdot 3}{1+4 \cdot 3^4}+\ldots .$. is $\frac{\mathrm{m}}{\mathrm{n}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to _______________
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Let $y=y(x)$ be the solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$ such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)$ is equal to_____________________
Let $y=y(x)$ be the solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$ such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)$ is equal to_____________________
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Let $\mathrm{A}(4,-2), \mathrm{B}(1,1)$ and $\mathrm{C}(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and $A B$ of the triangle $A B C$ respectively, is___________
Let $\mathrm{A}(4,-2), \mathrm{B}(1,1)$ and $\mathrm{C}(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and $A B$ of the triangle $A B C$ respectively, is___________
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

Given below are two statements :

Statement (I) : Neopentane forms only one monosubstituted derivative.

Statement (II) : Melting point of neopentane is higher than n-pentane.

In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements :

Statement (I) : Neopentane forms only one monosubstituted derivative.

Statement (II) : Melting point of neopentane is higher than n-pentane.

In the light of the above statements, choose the most appropriate answer from the options given below :
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

Match List - I with List - II.

List - I
(Reaction)
 List - II
(Name of reaction)
(A) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Hydrocarbons Question 5 English (I) Lucas reaction
(B) $$
\mathrm{ArN}_2^{+} \mathrm{X}^{-} \xrightarrow[\mathrm{HCl}]{\mathrm{Cu}} \mathrm{ArCl}+\mathrm{N}_2 \uparrow+\mathrm{CuX}
$$
 (II) Finkelstein
reaction
(C) $$
\mathrm{C}_2 \mathrm{H}_5 \mathrm{Br}+\mathrm{NaI} \xrightarrow[\text { Acetone }]{\text { Dry }} \mathrm{C}_2 \mathrm{H}_5 \mathrm{I}+\mathrm{NaBr}
$$
 (III)
Fittig reaction
(D) $$
\mathrm{CH}_3 \mathrm{C}(\mathrm{OH})\left(\mathrm{CH}_3\right) \mathrm{CH}_3 \xrightarrow[\mathrm{ZnCl}_2]{\mathrm{HCl}} \mathrm{CH}_3 \mathrm{C}(\mathrm{Cl})\left(\mathrm{CH}_3\right) \mathrm{CH}_3
$$
 (IV)
Gatterman
reaction

$$ \text { Choose the correct answer from the options given below : } $$

Match List - I with List - II.

List - I
(Reaction)
 List - II
(Name of reaction)
(A) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Hydrocarbons Question 5 English (I) Lucas reaction
(B) $$
\mathrm{ArN}_2^{+} \mathrm{X}^{-} \xrightarrow[\mathrm{HCl}]{\mathrm{Cu}} \mathrm{ArCl}+\mathrm{N}_2 \uparrow+\mathrm{CuX}
$$
 (II) Finkelstein
reaction
(C) $$
\mathrm{C}_2 \mathrm{H}_5 \mathrm{Br}+\mathrm{NaI} \xrightarrow[\text { Acetone }]{\text { Dry }} \mathrm{C}_2 \mathrm{H}_5 \mathrm{I}+\mathrm{NaBr}
$$
 (III)
Fittig reaction
(D) $$
\mathrm{CH}_3 \mathrm{C}(\mathrm{OH})\left(\mathrm{CH}_3\right) \mathrm{CH}_3 \xrightarrow[\mathrm{ZnCl}_2]{\mathrm{HCl}} \mathrm{CH}_3 \mathrm{C}(\mathrm{Cl})\left(\mathrm{CH}_3\right) \mathrm{CH}_3
$$
 (IV)
Gatterman
reaction

$$ \text { Choose the correct answer from the options given below : } $$
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

Electronic configuration of four elements A, B, C and D are given below :

(A) $1 s^2 2 s^2 2 p^3$

(B) $1 s^2 2 s^2 2 p^4$

(C) $1 s^2 2 s^2 2 p^5$

(D) $1 s^2 2 s^2 2 p^2$

Which of the following is the correct order of increasing electronegativity (Pauling's scale)?

Electronic configuration of four elements A, B, C and D are given below :

(A) $1 s^2 2 s^2 2 p^3$

(B) $1 s^2 2 s^2 2 p^4$

(C) $1 s^2 2 s^2 2 p^5$

(D) $1 s^2 2 s^2 2 p^2$

Which of the following is the correct order of increasing electronegativity (Pauling's scale)?
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is :
A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is :
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Which among the following molecules is (a) involved in $\mathrm{sp}^3 \mathrm{~d}$ hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom?
Which among the following molecules is (a) involved in $\mathrm{sp}^3 \mathrm{~d}$ hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom?
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
In 3,3-dimethylhex-1-en-4-yne, there are _________$\mathrm{sp}^3$,_________$\mathrm{sp}^2$ and_________ sp hybridised carbon atoms respectively.
In 3,3-dimethylhex-1-en-4-yne, there are _________$\mathrm{sp}^3$,_________$\mathrm{sp}^2$ and_________ sp hybridised carbon atoms respectively.
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
In Dumas' method for estimation of nitrogen, 0.5 gram of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound (Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ ) is___________%.
In Dumas' method for estimation of nitrogen, 0.5 gram of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound (Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ ) is___________%.
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

Which of the following statements are true?

(A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron.

(B) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Structure of Atom Question 7 English is the boundary surface diagram of the $2 \mathrm{p}_x$ orbital.

(C) The + and - signs in the wave function of the $2 p_x$ orbital refer to charge.

(D) The wave function of $2 \mathrm{p}_x$ orbital is zero everywhere in the $x y$ plane.

Choose the correct answer from the options given below :

Which of the following statements are true?

(A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron.

(B) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Structure of Atom Question 7 English is the boundary surface diagram of the $2 \mathrm{p}_x$ orbital.

(C) The + and - signs in the wave function of the $2 p_x$ orbital refer to charge.

(D) The wave function of $2 \mathrm{p}_x$ orbital is zero everywhere in the $x y$ plane.

Choose the correct answer from the options given below :
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature.

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature.
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid $(273 \mathrm{~K})$ and acidified with acetic acid, the mass $(\mathrm{g})$ of 0.1 mole of product formed is :

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16, \mathrm{~S}: 32$ )

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid $(273 \mathrm{~K})$ and acidified with acetic acid, the mass $(\mathrm{g})$ of 0.1 mole of product formed is :

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16, \mathrm{~S}: 32$ )
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

Reactant A converts to product D through the given mechanism (with the net evolution of heat):

A → B     slow;     ΔH = +ve

B → C     fast;     ΔH = -ve

C → D     fast;     ΔH = -ve

Which of the following represents the above reaction mechanism?

Reactant A converts to product D through the given mechanism (with the net evolution of heat):

A → B     slow;     ΔH = +ve

B → C     fast;     ΔH = -ve

C → D     fast;     ΔH = -ve

Which of the following represents the above reaction mechanism?
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
Formation of $\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NOS}\right]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of :
Formation of $\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NOS}\right]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of :
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product ?

(A) $\quad \mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \stackrel{+}{\mathrm{H}} / \mathrm{H}_2 \mathrm{O}}$

(B) $\quad \mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}$

(C) $\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}$

(D) $\quad \mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}$

(E) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 8 English

Choose the correct answer from the options given below :

Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product ?

(A) $\quad \mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \stackrel{+}{\mathrm{H}} / \mathrm{H}_2 \mathrm{O}}$

(B) $\quad \mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}$

(C) $\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}$

(D) $\quad \mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}$

(E) JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 8 English

Choose the correct answer from the options given below :
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The nature of oxide $\left(\mathrm{TeO}_2\right)$ and hydride $\left(\mathrm{TeH}_2\right)$ formed by Te , respectively are :
The nature of oxide $\left(\mathrm{TeO}_2\right)$ and hydride $\left(\mathrm{TeH}_2\right)$ formed by Te , respectively are :
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

' $x$ ' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity $(\mathrm{M})$ of the solution with respect to temperature ?

[Consider the solubility of NaCl remains unchanged over the temperature range]

' $x$ ' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity $(\mathrm{M})$ of the solution with respect to temperature ?

[Consider the solubility of NaCl remains unchanged over the temperature range]
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
The type of hybridization and the magnetic property of $\left[\mathrm{MnCl}_6\right]^{3-}$ are,
The type of hybridization and the magnetic property of $\left[\mathrm{MnCl}_6\right]^{3-}$ are,
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
The d-orbital electronic configuration of the complex among $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+},\left[\mathrm{CoF}_6\right]^{3-}$, $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ and $\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ that has the highest CFSE is :
The d-orbital electronic configuration of the complex among $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+},\left[\mathrm{CoF}_6\right]^{3-}$, $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ and $\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ that has the highest CFSE is :
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

If $p$ being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

If $p$ being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

For the reaction $\mathrm{A} \rightarrow \mathrm{B}$ the following graph was obtained. The time required (in seconds) for the concentration of A to reduce to $2.5 \mathrm{~g} \mathrm{~L}^{-1}$ (if the initial concentration of A was $50 \mathrm{~g} \mathrm{~L}^{-1}$ ) is $\qquad$ . (Nearest integer)

Given : $\log 2=0.3010$

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 10 English

For the reaction $\mathrm{A} \rightarrow \mathrm{B}$ the following graph was obtained. The time required (in seconds) for the concentration of A to reduce to $2.5 \mathrm{~g} \mathrm{~L}^{-1}$ (if the initial concentration of A was $50 \mathrm{~g} \mathrm{~L}^{-1}$ ) is $\qquad$ . (Nearest integer)

Given : $\log 2=0.3010$

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 10 English
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

When 1 g each of compounds AB and $\mathrm{AB}_2$ are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in $a m u$ ) is____________ $\times 10^{-1}$ (Nearest integer)

(Given : Molal boiling point elevation constant is $0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )

When 1 g each of compounds AB and $\mathrm{AB}_2$ are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in $a m u$ ) is____________ $\times 10^{-1}$ (Nearest integer)

(Given : Molal boiling point elevation constant is $0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt

The spin-only magnetic moment value of $\mathrm{M}^{\mathrm{n}+}$ ion formed among $\mathrm{Ni}, \mathrm{Zn}, \mathrm{Mn}$ and Cu that has the least enthalpy of atomisation is_________ . (in nearest integer) Here n is equal to the number of diamagnetic complexes among $\mathrm{K}_2\left[\mathrm{NiCl}_4\right],\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2$, $\mathrm{K}_3\left[\mathrm{Mn}(\mathrm{CN})_6\right]$ and $\left[\mathrm{Cu}\left(\mathrm{PPh}_3\right)_3 \mathrm{I}\right]$

The spin-only magnetic moment value of $\mathrm{M}^{\mathrm{n}+}$ ion formed among $\mathrm{Ni}, \mathrm{Zn}, \mathrm{Mn}$ and Cu that has the least enthalpy of atomisation is_________ . (in nearest integer) Here n is equal to the number of diamagnetic complexes among $\mathrm{K}_2\left[\mathrm{NiCl}_4\right],\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2$, $\mathrm{K}_3\left[\mathrm{Mn}(\mathrm{CN})_6\right]$ and $\left[\mathrm{Cu}\left(\mathrm{PPh}_3\right)_3 \mathrm{I}\right]$
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of the solution will be__________$\times 10^2 \mathrm{mS} \mathrm{dm}^2 \mathrm{~mol}^{-1}$. (Nearest integer)

$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of the solution will be__________$\times 10^2 \mathrm{mS} \mathrm{dm}^2 \mathrm{~mol}^{-1}$. (Nearest integer)
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 4 English

Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is $80 \%$ whereas Q is $100 \%$.

Mass of product Q obtained is________ g.

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{O}: 16, \mathrm{Br}: 80$ )

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 4 English

Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is $80 \%$ whereas Q is $100 \%$.

Mass of product Q obtained is________ g.

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{O}: 16, \mathrm{Br}: 80$ )
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :
The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

In a moving coil galvanometer, two moving coils $\mathrm{M}_1$ and $\mathrm{M}_2$ have the following particulars :

$$ \begin{aligned} & \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\ & \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T} \end{aligned} $$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

In a moving coil galvanometer, two moving coils $\mathrm{M}_1$ and $\mathrm{M}_2$ have the following particulars :

$$ \begin{aligned} & \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\ & \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T} \end{aligned} $$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below :
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :
A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :
Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are JEE Main 2025 (Online) 2nd April Evening Shift Physics - Circular Motion Question 3 English
A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are JEE Main 2025 (Online) 2nd April Evening Shift Physics - Circular Motion Question 3 English
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Semiconductor Question 7 English

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Semiconductor Question 7 English
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is $\lambda_0$ then its value after time ' t ' would be :

An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is $\lambda_0$ then its value after time ' t ' would be :
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $\left(R_1 \neq R_2\right)$, without any change in lens power then possible combination of $R_1$ and $R_2$ is :
A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $\left(R_1 \neq R_2\right)$, without any change in lens power then possible combination of $R_1$ and $R_2$ is :
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and $B$ (shown in the figure) is :JEE Main 2025 (Online) 2nd April Evening Shift Physics - Electrostatics Question 9 English
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and $B$ (shown in the figure) is :JEE Main 2025 (Online) 2nd April Evening Shift Physics - Electrostatics Question 9 English
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :
Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
Energy released when two deuterons $\left({ }_1 \mathrm{H}^2\right)$ fuse to form a helium nucleus $\left({ }_2 \mathrm{He}^4\right)$ is : (Given : Binding energy per nucleon of ${ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}$ and binding energy per nucleon of ${ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}$ )
Energy released when two deuterons $\left({ }_1 \mathrm{H}^2\right)$ fuse to form a helium nucleus $\left({ }_2 \mathrm{He}^4\right)$ is : (Given : Binding energy per nucleon of ${ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}$ and binding energy per nucleon of ${ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}$ )
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
Consider a circular loop that is uniformly charged and has a radius $\mathrm{a} \sqrt{2}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin :
Consider a circular loop that is uniformly charged and has a radius $\mathrm{a} \sqrt{2}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin :
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Laws of Motion Question 5 English

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) :

(Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Laws of Motion Question 5 English

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) :

(Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$. Choose the correct answer from the options given below :
Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$. Choose the correct answer from the options given below :
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is__________
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is__________
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.
The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
JEE Main 2025 (Online) 2nd April Evening Shift Physics - Rotational Motion Question 8 English

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$. Moment of intertia of the wheel is___________ $\mathrm{kg} \mathrm{}\,\, \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Rotational Motion Question 8 English

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$. Moment of intertia of the wheel is___________ $\mathrm{kg} \mathrm{}\,\, \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be___________________$\times 10^6 \mathrm{~J}$

(Consider air as diatomic molecule)

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be___________________$\times 10^6 \mathrm{~J}$

(Consider air as diatomic molecule)
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.

(Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.

(Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )
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