JEE Main 2025 (Online) 28th January Morning Shift

Given below are two statements :
Statement I :
Statement II : In , intramolecular substitution takes place first by involving lone pair of electrons on nitrogen.
In the light of the above statements, choose the most appropriate answer from...

Both acetaldehyde and acetone (individually) undergo which of the following reactions?
A. Iodoform Reaction
B. Cannizaro Reaction
C. Aldol Condensation
D. Tollen's Test
E. Clemmensen Reduction
Choose the correct answer from the options give...

A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q"). ("Q") on ozonolysis followed by reflux under alkaline condition gives (" $R$ "). The structure of (" $R$ ") is given below.

The structure of ("P") is

The compounds that produce $\mathrm{CO}_2$ with aqueous $\mathrm{NaHCO}_3$ solution are:

Choose the correct answer from the options given below:

The correct order of stability of following carbocations is :

Given below are two statements:
Statement I : D-glucose pentaacetate reacts with 2,4 -dinitrophenylhydrazine
Statement II : Starch, on heating with concentrated sulfuric acid at $100^{\circ} \mathrm{C}$ and $2-3 \mathrm{atmosphere}$ pressur...

Consider ' n ' is the number of lone pair of electrons present in the equatorial position of the most stable structure of $\mathrm{ClF}_3$. The ions from the following with ' n ' number of unpaired electrons are
A. $\mathrm{V}^{3+}$
B. $\ma...

The molecules having square pyramidal geometry are

For a given reaction $\mathrm{R} \rightarrow \mathrm{P}, \mathrm{t}_{1 / 2}$ is related to $[\mathrm{A}]_0$ as given in table.
Given: $\log 2=0.30$
Which of the following is true?
A. The order of the reaction is $1 / 2$.
B. If $[\mathrm{A}...

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

Given below is the plot of the molar conductivity vs $\sqrt{\text { concentration }}$ for KCl in aqueous solution.

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is $100 \Omega$, then the resistan...

The products A and B in the following reactions, respectively are
$\mathrm{A} \stackrel{\mathrm{Ag}-\mathrm{NO}_2}{\longleftrightarrow} \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{Br} \xrightarrow{\mathrm{AgCN}} \mathrm{B}$

Consider the following sequence of reactions:

11.25 mg of chlorobenzene will produce ___________$\times 10^{-1} \mathrm{mg}$ of product B.
(Consider the reactions result in complete conversion.)
[Given molar mass of $\mathrm{C}, \mathrm{H...

A weak acid HA has degree of dissociation x . Which option gives the correct expression of ( pH - $\mathrm{pK}_{\mathrm{a}}$)?

The incorrect decreasing order of atomic radii is

Consider the following elements $\mathrm{In}, \mathrm{Tl}, \mathrm{Al}, \mathrm{Pb}, \mathrm{Sn}$ and Ge .
The most stable oxidation states of elements with highest and lowest first ionisation enthalpies, respectively, are

Given below are two statements:
Statement I: In the oxalic acid vs $\mathrm{KMnO}_4$ (in the presence of dil $\mathrm{H}_2 \mathrm{SO}_4$ ) titration the solution needs to be heated initially to $60^{\circ} \mathrm{C}$, but no heating is re...

Match the List - I with List - II

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Which of the following oxidation reactions are carried out by both $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ and $\mathrm{KMnO}_4$ in acidic medium?
A. $\Gamma^{-} \rightarrow \mathrm{I}_2$
B. $\mathrm{S}^{2-} \rightarrow \mathrm{S}$
C. $\m...

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass $256 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and the decrease in freezing point is 0.40 K ?

The molarity of a $70 \%$ (mass/mass) aqueous solution of a monobasic acid (X) is _________ $\times 10^{-1}$ M (Nearest integer)
[Given: Density of aqueous solution of (X) is $1.25 \mathrm{~g} \mathrm{~mL}^{-1}$
Molar mass of the acid is $7...

Quantitative analysis of an organic compound (X) shows following % composition.
C : $14.5 \%$
Cl : 64.46%
H: 1.8 %
(Empirical formula mass of the compound $(\mathrm{X})$ is _________ $\times 10^{-1}$
(Given molar mass in $\mathrm{g} \mathrm...

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. $\mathrm{n}=1, \mathrm{l}=0, \mathrm{~m}_1=0$
B. $\mathrm{n}=2, \mathrm{l}=0, \...

The formation enthalpies, $\Delta \mathrm{H}_{\mathrm{f}}^{\ominus}$ for $\mathrm{H}_{(\mathrm{g})}$ and $\mathrm{O}_{(\mathrm{g})}$ are 220.0 and $250.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively, at 298.15 K , and $\Delta \mathrm{H}_{...

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following

If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

Let $\mathrm{A}(x, y, z)$ be a point in $x y$-plane, which is equidistant from three points $(0,3,2),(2,0,3)$ and $(0,0,1)$.
Let $\mathrm{B}=(1,4,-1)$ and $\mathrm{C}=(2,0,-2)$. Then among the statements
(S1) : $\triangle \mathrm{ABC}$ is a...

The sum of all local minimum values of the function
$$\mathrm{f}(x)=\left\{\begin{array}{lr} 1-2 x, & x<-1 \\ \frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\ \frac{11}{18}(x-4)(x-5), & x>2 \end{array}\right.$$
is

The area (in sq. units) of the region $\left\{(x, \mathrm{y}): 0 \leq \mathrm{y} \leq 2|x|+1,0 \leq \mathrm{y} \leq x^2+1,|x| \leq 3\right\}$ is

If $\alpha=1+\sum\limits_{r=1}^6(-3)^{r-1} \quad{ }^{12} \mathrm{C}_{2 r-1}$,
then the distance of the point $(12, \sqrt{3})$ from the line $\alpha x-\sqrt{3} y+1=0$ is ________.

Let the equation of the circle, which touches $x$-axis at the point $(a, 0), a>0$ and cuts off an intercept of length $b$ on $y-a x i s$ be $x^2+y^2-\alpha x+\beta y+\gamma=0$. If the circle lies below $x-a x i s$, then the ordered pair $\l...

Let $O$ be the origin, the point $A$ be $z_1=\sqrt{3}+2 \sqrt{2} i$, the point $B\left(z_2\right)$ be such that $\sqrt{3}\left|z_2\right|=\left|z_1\right|$ and $\arg \left(z_2\right)=\arg \left(z_1\right)+\frac{\pi}{6}$. Then

If $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96 x^2 \cos ^2 x}{\left(1+e^x\right)} \mathrm{d} x=\pi\left(\alpha \pi^2+\beta\right), \alpha, \beta \in \mathbb{Z}$, then $(\alpha+\beta)^2$ equals

Let for some function $\mathrm{y}=f(x), \int_0^x t f(t) d t=x^2 f(x), x>0$ and $f(2)=3$. Then $f(6)$ is equal to

Let $\mathrm{E}_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $\mathrm{E}_{\mathrm{i}}$ 's are constructed such that their centres and eccentricities are same as that of $\mathrm{E}_1$, and the length of minor axis of $\mathrm{E...

If $f(x)=\frac{2^x}{2^x+\sqrt{2}}, \mathrm{x} \in \mathbb{R}$, then $\sum_\limits{\mathrm{k}=1}^{81} f\left(\frac{\mathrm{k}}{82}\right)$ is equal to

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $f(x)=(2+3 a) x^2+\left(\frac{a+2}{a-1}\right) x+b, a \neq 1$. If $f(x+y)=f(x)+f(\mathrm{y})+1-\frac{2}{7} x \mathrm{y}$, then the value of $28 \sum\limits_{i=1}^5|f(i)|$ i...

$\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)$ is equal to:

Let $\mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x<0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x>2\end{array}\right.$
where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where $f$ is...

Let M denote the set of all real matrices of order $3 \times 3$ and let $\mathrm{S}=\{-3,-2,-1,1,2\}$. Let
$$\begin{aligned}
& \mathrm{S}_1=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=\mathrm{A}^{\mathrm{T}} \t...

Let ABCD be a trapezium whose vertices lie on the parabola $\mathrm{y}^2=4 \mathrm{x}$. Let the sides AD and BC of the trapezium be parallel to $y$-axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point $(1,0)$...

Let ${ }^n C_{r-1}=28,{ }^n C_r=56$ and ${ }^n C_{r+1}=70$. Let $A(4 \operatorname{cost}, 4 \sin t), B(2 \sin t,-2 \cos t)$ and $C\left(3 r-n, r^2-n-1\right)$ be the vertices of a triangle $A B C$, where $t$ is a parameter. If $(3 x-1)^2+(3...

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1,2,3,4,5,6,7$, such that the sum of their first and last digits should not be more than 8 , is

Two number $\mathrm{k}_1$ and $\mathrm{k}_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $\mathrm{i}^{\mathrm{k}_1}+\mathrm{i}^{\mathrm{k}_2},(\mathrm{i}=\sqrt{-1})$ is non-zero, equals

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denote the number of defective oranges, then th...

The sum, of the squares of all the roots of the equation $x^2+|2 x-3|-4=0$, is

Let $\mathrm{T}_{\mathrm{r}}$ be the $\mathrm{r}^{\text {th }}$ term of an A.P. If for some $\mathrm{m}, \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}$, and $20 \sum\limits_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=...

Let $\left\langle a_{\mathrm{n}}\right\rangle$ be a sequence such that $a_0=0, a_1=\frac{1}{2}$ and $2 a_{\mathrm{n}+2}=5 a_{\mathrm{n}+1}-3 a_{\mathrm{n}}, \mathrm{n}=0,1,2,3, \ldots$. Then $\sum\limits_{k=1}^{100} a_k$ is equal to

The relation $R=\{(x, y): x, y \in \mathbb{Z}$ and $x+y$ is even $\}$ is:

Let $\vec{a}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{d}}=\vec{a} \times \overrightarrow{\mathrm{b}}$. If $\overrigh...