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

$$ \text { If the domain of the function } f(x)=\log _e\left(\frac{2 x-3}{5+4 x}\right)+\sin ^{-1}\left(\frac{4+3 x}{2-x}\right) \text { is }[\alpha, \beta) \text {, then } \alpha^2+4 \beta \text { is equal to } $$

$$ \text { If the domain of the function } f(x)=\log _e\left(\frac{2 x-3}{5+4 x}\right)+\sin ^{-1}\left(\frac{4+3 x}{2-x}\right) \text { is }[\alpha, \beta) \text {, then } \alpha^2+4 \beta \text { is equal to } $$
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
Let $a_1, a_2, a_3, \ldots$. be a G.P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to
Let $a_1, a_2, a_3, \ldots$. be a G.P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
The sum $1+3+11+25+45+71+\ldots$ upto 20 terms, is equal to
The sum $1+3+11+25+45+71+\ldots$ upto 20 terms, is equal to
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $0 \leq x^2+2 y \leq 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l+m$ is equal to

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $0 \leq x^2+2 y \leq 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l+m$ is equal to
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is
The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

Let the domain of the function $f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $(a, b)$. If $\int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in \mathbb{N}, \operatorname{gcd}(p, q, r)=1$, where $[\cdot]$ is the greatest integer function, then $p+q+r$ is equal to

Let the domain of the function $f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $(a, b)$. If $\int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in \mathbb{N}, \operatorname{gcd}(p, q, r)=1$, where $[\cdot]$ is the greatest integer function, then $p+q+r$ is equal to
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3} x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3 x-1=0$. If $P_n=$ $\alpha^n+\beta^n$ and $Q_n=\gamma^n+\hat{o}^n$, then $\frac{P_{25}+\sqrt{3} P_{24}}{2 P_{23}}+\frac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3} x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3 x-1=0$. If $P_n=$ $\alpha^n+\beta^n$ and $Q_n=\gamma^n+\hat{o}^n$, then $\frac{P_{25}+\sqrt{3} P_{24}}{2 P_{23}}+\frac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

Let a line passing through the point $(4,1,0)$ intersect the line $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha, \beta, \gamma)$ and the line $\mathrm{L}_2: x-6=y=-z+4$ at the point $B(a, b, c)$. Then $\left|\begin{array}{lll}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{array}\right|$ is equal to

Let a line passing through the point $(4,1,0)$ intersect the line $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha, \beta, \gamma)$ and the line $\mathrm{L}_2: x-6=y=-z+4$ at the point $B(a, b, c)$. Then $\left|\begin{array}{lll}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{array}\right|$ is equal to
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

Let $\quad f(x)= \begin{cases}(1+a x)^{1 / x} & , x<0 \\ 1+b, & x=0 \\ \frac{(x+4)^{1 / 2}-2}{(x+c)^{1 / 3}-2}, & x>0\end{cases}$ be continuous at $x=0$. Then $e^a b c$ is equal to:

Let $\quad f(x)= \begin{cases}(1+a x)^{1 / x} & , x<0 \\ 1+b, & x=0 \\ \frac{(x+4)^{1 / 2}-2}{(x+c)^{1 / 3}-2}, & x>0\end{cases}$ be continuous at $x=0$. Then $e^a b c$ is equal to:
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse $\frac{x^2}{36}+\frac{y^2}{25}=1$ at $A$ and $B$ such that $(P A) \cdot(P B)$ is maximum. Then $5\left(P A^2+P B^2\right)$ is equal to :

A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse $\frac{x^2}{36}+\frac{y^2}{25}=1$ at $A$ and $B$ such that $(P A) \cdot(P B)$ is maximum. Then $5\left(P A^2+P B^2\right)$ is equal to :
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to $z$-axis. Line $L_2$ passes through the point $(\lambda, 5,6)$ and is parallel to $y$-axis. Let for $\lambda=\lambda_1, \lambda_2, \lambda_2<\lambda_1$, the shortest distance between the two lines be 3 . Then the square of the distance of the point $\left(\lambda_1, \lambda_2, 7\right)$ from the line $L_1$ is

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to $z$-axis. Line $L_2$ passes through the point $(\lambda, 5,6)$ and is parallel to $y$-axis. Let for $\lambda=\lambda_1, \lambda_2, \lambda_2<\lambda_1$, the shortest distance between the two lines be 3 . Then the square of the distance of the point $\left(\lambda_1, \lambda_2, 7\right)$ from the line $L_1$ is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
Let $g$ be a differentiable function such that $\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0$ and let $y=y(x)$ satisfy the differential equation $\frac{d y}{d x}-y \tan x=2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\right)$. If $y(0)=0$, then $y\left(\frac{\pi}{3}\right)$ is equal to
Let $g$ be a differentiable function such that $\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0$ and let $y=y(x)$ satisfy the differential equation $\frac{d y}{d x}-y \tan x=2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\right)$. If $y(0)=0$, then $y\left(\frac{\pi}{3}\right)$ is equal to
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is :
The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is :
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

If $\sum\limits_{r=1}^9\left(\frac{r+3}{2^r}\right) \cdot{ }^9 C_r=\alpha\left(\frac{3}{2}\right)^9-\beta, \alpha, \beta \in \mathbb{N}$, then $(\alpha+\beta)^2$ is equal to

If $\sum\limits_{r=1}^9\left(\frac{r+3}{2^r}\right) \cdot{ }^9 C_r=\alpha\left(\frac{3}{2}\right)^9-\beta, \alpha, \beta \in \mathbb{N}$, then $(\alpha+\beta)^2$ is equal to
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Let $z \in C$ be such that $\frac{z^2+3 i}{z-2+i}=2+3 i$. Then the sum of all possible values of $z^2$ is :
Let $z \in C$ be such that $\frac{z^2+3 i}{z-2+i}=2+3 i$. Then the sum of all possible values of $z^2$ is :
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $\mathrm{L}_1: 2 x+y+6=0$ and $\mathrm{L}_2: 4 x+2 y-p=0, p>0$, at the points A and B , respectively. If $A B=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\frac{A M}{B M}$ is equal to

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $\mathrm{L}_1: 2 x+y+6=0$ and $\mathrm{L}_2: 4 x+2 y-p=0, p>0$, at the points A and B , respectively. If $A B=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\frac{A M}{B M}$ is equal to
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

Let $A$ be a matrix of order $3 \times 3$ and $|A|=5$. If $|2 \operatorname{adj}(3 A \operatorname{adj}(2 A))|=2^\alpha \cdot 3^\beta \cdot 5^\gamma, \alpha, \beta, \gamma \in N$, then $\alpha+\beta+\gamma$ is equal to

Let $A$ be a matrix of order $3 \times 3$ and $|A|=5$. If $|2 \operatorname{adj}(3 A \operatorname{adj}(2 A))|=2^\alpha \cdot 3^\beta \cdot 5^\gamma, \alpha, \beta, \gamma \in N$, then $\alpha+\beta+\gamma$ is equal to
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $\mathrm{W}_{\mathrm{n}}$. Let the probability $\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)$ of choosing the word $\mathrm{W}_{\mathrm{n}}$ satisfy $\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n}>1$.

If $\mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal to :____________

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $\mathrm{W}_{\mathrm{n}}$. Let the probability $\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)$ of choosing the word $\mathrm{W}_{\mathrm{n}}$ satisfy $\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n}>1$.

If $\mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal to :____________
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k}, \vec{c}=\lambda \hat{j}+\mu \hat{k}$ and $\hat{d}$ be a unit vector such that $\vec{a} \times \hat{d}=\vec{b} \times \hat{d}$ and $\vec{c} \cdot \hat{d}=1$. If $\vec{c}$ is perpendicular to $\vec{a}$, then $|3 \lambda \hat{d}+\mu \vec{c}|^2$ is equal to________

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k}, \vec{c}=\lambda \hat{j}+\mu \hat{k}$ and $\hat{d}$ be a unit vector such that $\vec{a} \times \hat{d}=\vec{b} \times \hat{d}$ and $\vec{c} \cdot \hat{d}=1$. If $\vec{c}$ is perpendicular to $\vec{a}$, then $|3 \lambda \hat{d}+\mu \vec{c}|^2$ is equal to________
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt

Let the product of the focal distances of the point $\mathbf{P}(4,2 \sqrt{3})$ on the hyperbola $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be 32 . Let the length of the conjugate axis of H be $p$ and the length of its latus rectum be $q$. Then $p^2+q^2$ is equal to__________

Let the product of the focal distances of the point $\mathbf{P}(4,2 \sqrt{3})$ on the hyperbola $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be 32 . Let the length of the conjugate axis of H be $p$ and the length of its latus rectum be $q$. Then $p^2+q^2$ is equal to__________
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, the $x$-axis and the lines $x=-2$ and $x=4$ is equal to__________

The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, the $x$-axis and the lines $x=-2$ and $x=4$ is equal to__________
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
The correct order of the complexes $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}(\mathrm{A}),\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}(\mathrm{B}),\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}(\mathrm{C})$ and $\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}(\mathrm{D})$ in terms of wavelength of light absorbed is
The correct order of the complexes $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}(\mathrm{A}),\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}(\mathrm{B}),\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}(\mathrm{C})$ and $\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}(\mathrm{D})$ in terms of wavelength of light absorbed is
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

Which of the following statements are correct?

A. The process of adding an electron to a neutral gaseous atom is always exothermic.

B. The process of removing an electron from an isolated gaseous atom is always endothermic.

C. The $1^{\text {st }}$ ionization energy of boron is less than that of beryllium.

D. The electronegativity of C is 2.5 in $\mathrm{CH}_4$ and $\mathrm{CCl}_4$

E. Li is the most electropositive among elements of group I.

Choose the correct answer from the options given below:

Which of the following statements are correct?

A. The process of adding an electron to a neutral gaseous atom is always exothermic.

B. The process of removing an electron from an isolated gaseous atom is always endothermic.

C. The $1^{\text {st }}$ ionization energy of boron is less than that of beryllium.

D. The electronegativity of C is 2.5 in $\mathrm{CH}_4$ and $\mathrm{CCl}_4$

E. Li is the most electropositive among elements of group I.

Choose the correct answer from the options given below:
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Compounds Containing Nitrogen Question 4 English

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Compounds Containing Nitrogen Question 4 English
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

$$ \text { Match the LIST-I with LIST-II } $$

LIST-I
(Molecules/ion)
 LIST-II
(Hybridisation of central atom)
A. $$
\mathrm{PF}_5
$$		 I $$
\mathrm{dsp}^2
$$
B $$
\mathrm{SF}_6
$$		 II $$
\mathrm{sp}^3 \mathrm{~d}
$$
C $$
\mathrm{Ni}(\mathrm{CO})_4
$$		 III $$
\mathrm{sp}^3 \mathrm{~d}^2
$$
D $$
\left[\mathrm{PtCl}_4\right]^{2-}
$$		 IV $$
\mathrm{sp}^3
$$

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

$$ \text { Match the LIST-I with LIST-II } $$

LIST-I
(Molecules/ion)
 LIST-II
(Hybridisation of central atom)
A. $$
\mathrm{PF}_5
$$		 I $$
\mathrm{dsp}^2
$$
B $$
\mathrm{SF}_6
$$		 II $$
\mathrm{sp}^3 \mathrm{~d}
$$
C $$
\mathrm{Ni}(\mathrm{CO})_4
$$		 III $$
\mathrm{sp}^3 \mathrm{~d}^2
$$
D $$
\left[\mathrm{PtCl}_4\right]^{2-}
$$		 IV $$
\mathrm{sp}^3
$$

$$ \text { Choose the correct answer from the options given below: } $$
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom?
Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom?
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
In the following system, $\mathrm{PCl}_5(\mathrm{~g}) \leftrightharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ at equilibrium, upon addition of xenon gas at constant T \& p , the concentration of
In the following system, $\mathrm{PCl}_5(\mathrm{~g}) \leftrightharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ at equilibrium, upon addition of xenon gas at constant T \& p , the concentration of
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

$$ \text { In the following reactions, which one is NOT correct? } $$

$$ \text { In the following reactions, which one is NOT correct? } $$
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

Given below are two statements :

Statement I : The N - N single bond is weaker and longer than that of P - P single bond.

Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.

In the light of the above statements, choose the correct answer from the options given below

Given below are two statements :

Statement I : The N - N single bond is weaker and longer than that of P - P single bond.

Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.

In the light of the above statements, choose the correct answer from the options given below
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

$$ \text { Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis? } $$

$$ \text { Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis? } $$
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is: (Given : Ebullioscopic constant of water $=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )
2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is: (Given : Ebullioscopic constant of water $=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

Which of the following properties will change when system containing solution 1 will become solution 2 ?

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Solutions Question 4 English

Which of the following properties will change when system containing solution 1 will become solution 2 ?

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Solutions Question 4 English
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

$$ \text {Identify the correct statements from the following. } $$

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Basics of Organic Chemistry Question 7 English

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

$$ \text {Identify the correct statements from the following. } $$

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Basics of Organic Chemistry Question 7 English

$$ \text {Choose the correct answer from the options given below: } $$
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

$$ \text { The least acidic compound, among the following is: } $$

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 2 English

$$ \text { The least acidic compound, among the following is: } $$

JEE Main 2025 (Online) 3rd April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 2 English
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

Among $10^{-9} \mathrm{~g}$ (each) of the following elements, which one will have the highest number of atoms?

Element: $\mathrm{Pb}, \mathrm{Po}, \mathrm{Pr}$ and Pt

Among $10^{-9} \mathrm{~g}$ (each) of the following elements, which one will have the highest number of atoms?

Element: $\mathrm{Pb}, \mathrm{Po}, \mathrm{Pr}$ and Pt
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt

The metal ions that have the calculated spin-only magnetic moment value of 4.9 B.M. are :

A. $\mathrm{Cr}^{2+}$

B. $\mathrm{Fe}^{2+}$

C. $\mathrm{Fe}^{3+}$

D. $\mathrm{Co}^{2+}$

E. $\mathrm{Mn}^{3+}$

Choose the correct answer from the options given below:

The metal ions that have the calculated spin-only magnetic moment value of 4.9 B.M. are :

A. $\mathrm{Cr}^{2+}$

B. $\mathrm{Fe}^{2+}$

C. $\mathrm{Fe}^{3+}$

D. $\mathrm{Co}^{2+}$

E. $\mathrm{Mn}^{3+}$

Choose the correct answer from the options given below:
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

$$ \text { Which of the following is the correct structure of L-Fructose? } $$

$$ \text { Which of the following is the correct structure of L-Fructose? } $$
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt

Given below are two statements :

Statement I : A catalyst cannot alter the equilibrium constant $\left(\mathrm{K}_{\mathrm{c}}\right)$ of the reaction, temperature remaining constant.

Statement II : A homogenous catalyst can change the equilibrium composition of a system, temperature remaining constant.

In the light of the above statements, choose the correct answer from the options given below

Given below are two statements :

Statement I : A catalyst cannot alter the equilibrium constant $\left(\mathrm{K}_{\mathrm{c}}\right)$ of the reaction, temperature remaining constant.

Statement II : A homogenous catalyst can change the equilibrium composition of a system, temperature remaining constant.

In the light of the above statements, choose the correct answer from the options given below
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Correct order of limiting molar conductivity for cations in water at 298 K is :
Correct order of limiting molar conductivity for cations in water at 298 K is :
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

In a reaction $A+B \rightarrow C$, initial concentrations of $A$ and $B$ are related as $[A]_0=8[B]_0$. The half lives of $A$ and $B$ are 10 min and 40 min , respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

In a reaction $A+B \rightarrow C$, initial concentrations of $A$ and $B$ are related as $[A]_0=8[B]_0$. The half lives of $A$ and $B$ are 10 min and 40 min , respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

Number of molecules from below which cannot give iodoform reaction is :

Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol.

Number of molecules from below which cannot give iodoform reaction is :

Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol.
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

_________mL of $\mathrm{N}_2$ gas will be liberated at STP. (nearest integer)

 

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

 

_________mL of $\mathrm{N}_2$ gas will be liberated at STP. (nearest integer)

 

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

 
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt

0.5 g of an organic compound on combustion gave 1.46 g of $\mathrm{CO}_2$ and 0.9 g of $\mathrm{H}_2 \mathrm{O}$. The percentage of carbon in the compound is _______________. (Nearest integer)

[Given : Molar mass (in $\left.\mathrm{g} \mathrm{mol}^{-1}\right) \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16$ ]

0.5 g of an organic compound on combustion gave 1.46 g of $\mathrm{CO}_2$ and 0.9 g of $\mathrm{H}_2 \mathrm{O}$. The percentage of carbon in the compound is _______________. (Nearest integer)

[Given : Molar mass (in $\left.\mathrm{g} \mathrm{mol}^{-1}\right) \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16$ ]
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

The number of optical isomers exhibited by the iron complex $(\mathrm{A})$ obtained from the following reaction is___________.

$$ \mathrm{FeCl}_3+\mathrm{KOH}+\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \rightarrow \mathrm{~A} $$

The number of optical isomers exhibited by the iron complex $(\mathrm{A})$ obtained from the following reaction is___________.

$$ \mathrm{FeCl}_3+\mathrm{KOH}+\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \rightarrow \mathrm{~A} $$
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is:

(Take $\gamma=1.5 ; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is:

(Take $\gamma=1.5 ; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.

A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
A wire of length 25 m and cross-sectional area $5 \mathrm{~mm}^2$ having resistivity of $2 \times 10^{-6} \Omega \mathrm{~m}$ is bent into a complete circle. The resistance between diametrically opposite points will be
A wire of length 25 m and cross-sectional area $5 \mathrm{~mm}^2$ having resistivity of $2 \times 10^{-6} \Omega \mathrm{~m}$ is bent into a complete circle. The resistance between diametrically opposite points will be
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $\mathrm{h}_{\mathrm{m}}$. Here $\mathrm{h}_{\mathrm{m}}$ as function of $\phi$ can be presented as

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $\mathrm{h}_{\mathrm{m}}$. Here $\mathrm{h}_{\mathrm{m}}$ as function of $\phi$ can be presented as
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
The work function of a metal is 3 eV . The color of the visible light that is required to cause emission of photoelectrons is
The work function of a metal is 3 eV . The color of the visible light that is required to cause emission of photoelectrons is
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:

$$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $$

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:

$$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $$
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

Consider following statements for refraction of light through prism, when angle of deviation is minimum.

A. The refracted ray inside prism becomes parallel to the base.

B. Larger angle prisms provide smaller angle of minimum deviation.

C. Angle of incidence and angle of emergence becomes equal.

D. There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.

E. Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below :

Consider following statements for refraction of light through prism, when angle of deviation is minimum.

A. The refracted ray inside prism becomes parallel to the base.

B. Larger angle prisms provide smaller angle of minimum deviation.

C. Angle of incidence and angle of emergence becomes equal.

D. There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.

E. Angle of refraction becomes double of prism angle.

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

A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants $\varepsilon_1$ and $\varepsilon_2$, as shown in figures. The distance between the plates is $d$ and area of each plate is $A$. If capacitance in first configuration and second configuration are $\mathrm{C}_1$ and $\mathrm{C}_2$ respectively, then $\frac{C_1}{C_2}$ is:

First Configuration

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Capacitor Question 4 English 1

Second Configuration

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Capacitor Question 4 English 2

A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants $\varepsilon_1$ and $\varepsilon_2$, as shown in figures. The distance between the plates is $d$ and area of each plate is $A$. If capacitance in first configuration and second configuration are $\mathrm{C}_1$ and $\mathrm{C}_2$ respectively, then $\frac{C_1}{C_2}$ is:

First Configuration

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Capacitor Question 4 English 1

Second Configuration

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Capacitor Question 4 English 2
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
During the melting of a slab of ice at 273 K at atmospheric pressure :
During the melting of a slab of ice at 273 K at atmospheric pressure :
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Rotational Motion Question 5 English

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Rotational Motion Question 5 English
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
JEE Main 2025 (Online) 3rd April Morning Shift Physics - Heat and Thermodynamics Question 8 English

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F=-k x^3$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' $n$ ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $\mathrm{L}_0$ to $\mathrm{L}_1$, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Heat and Thermodynamics Question 8 English

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F=-k x^3$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' $n$ ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $\mathrm{L}_0$ to $\mathrm{L}_1$, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
JEE Main 2025 (Online) 3rd April Morning Shift Physics - Simple Harmonic Motion Question 2 English

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Simple Harmonic Motion Question 2 English

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

$$ \text {Which of the following curves possibly represent one-dimensional motion of a particle? } $$

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 1JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 2JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 3JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 4

Choose the correct answer from the options given below :

$$ \text {Which of the following curves possibly represent one-dimensional motion of a particle? } $$

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 1JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 2JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 3JEE Main 2025 (Online) 3rd April Morning Shift Physics - Motion in a Straight Line Question 3 English 4

Choose the correct answer from the options given below :
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is
The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10 \mathrm{~cm}$ is 120 V . The potential at the centre of shell, at a distance $\mathrm{r}=5 \mathrm{~cm}$ from centre, and at a distance $\mathrm{r}=15$ cm from the centre of the shell respectively, are:

The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10 \mathrm{~cm}$ is 120 V . The potential at the centre of shell, at a distance $\mathrm{r}=5 \mathrm{~cm}$ from centre, and at a distance $\mathrm{r}=15$ cm from the centre of the shell respectively, are:
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is
The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

In the figure shown below, a resistance of $150.4 \Omega$ is connected in series to an ammeter A of resistance $240 \Omega$. A shunt resistance of $10 \Omega$ is connected in parallel with the ammeter. The reading of the ammeter is___________mA .

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Current Electricity Question 6 English

In the figure shown below, a resistance of $150.4 \Omega$ is connected in series to an ammeter A of resistance $240 \Omega$. A shunt resistance of $10 \Omega$ is connected in parallel with the ammeter. The reading of the ammeter is___________mA .

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Current Electricity Question 6 English
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1=6 \pi \mathrm{~m}$ and $\mathrm{R}_2=4 \pi \mathrm{~m}$. The magnitude of the resultant magnetic field at center O is $\mathrm{k} \times 10^{-7} \mathrm{~T}$. The value of k is_________.

( Given $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$ )

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Magnetic Effect of Current Question 4 English

A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1=6 \pi \mathrm{~m}$ and $\mathrm{R}_2=4 \pi \mathrm{~m}$. The magnitude of the resultant magnetic field at center O is $\mathrm{k} \times 10^{-7} \mathrm{~T}$. The value of k is_________.

( Given $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$ )

JEE Main 2025 (Online) 3rd April Morning Shift Physics - Magnetic Effect of Current Question 4 English
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $x \mathrm{I}$. The value of $x$ is___________ .
Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $x \mathrm{I}$. The value of $x$ is___________ .
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after__________seconds.
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after__________seconds.
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T . The magnetic force on the wire is ________mN .
A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T . The magnetic force on the wire is ________mN .
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