JEE Main 2023 (Online) 25th January Morning Shift

In the cumene to phenol preparation in presence of air, the intermediate is

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : Acetal / Ketal is stable in basic medium.
Reason R : The high leaving tendency of alkoxide ion gives the stability to acet...

Identify the product formed (A and E)

Which of the following conformations will be the most stable?

The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

Match items of Row I with those of Row II.
Row I :

Row II :
(i) \(\alpha\)-\(\mathrm{D}\)-\((-)\)-\(\mathrm{Fructofuranose}\)
(ii) \(\beta\)-D-\((-)\)-Fructofuranose
(iii) \(\alpha\)-D-\((-)\) Glucopyranose
(iv) \(\beta\)-D-\((-)\)-Glucopy...

The total number of lone pairs of electrons on oxygen atoms of ozone is __________.

For the first order reaction A \(\to\) B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest integer)
Given : log 2 = 0.3010
log 3 = 0.4771
log 5 = 0.6989

Which of the following statements is incorrect for antibiotics?

The number of paramagnetic species from the following is _____________.
\(\mathrm{{[Ni{(CN)_4}]^{2 - }},[Ni{(CO)_4}],{[NiC{l_4}]^{2 - }}}\)
\(\mathrm{{[Fe{(CN)_6}]^{4 - }},{[Cu{(N{H_3})_4}]^{2 + }}}\)
$$\mathrm{{[Fe{(CN)_6}]^{3 - }}\,and\,{...

How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ______________
(Given : Atomic number V, 23; Cr, 24; Fe, 26; Ni, 28)
V\(^{3+}\), Cr\(^{3+}\), Fe\(^{2+}\), Ni\(^{3+}\)

Consider the cell
\(\mathrm{Pt(s)|{H_2}(g)\,(1\,atm)|{H^ + }\,(aq,[{H^ + }] = 1)||F{e^{3 + }}(aq),F{e^{2 + }}(aq)|Pt(s)}\)
Given \(\mathrm{E_{F{e^{3 + }}/F{e^{2 + }}}^o = 0.771\,V}\) and $$\mathrm{E_{{H^ + }/1/2\,{H_2}}^o = 0\,V,\,T = 298\,...

Some reactions of NO\(_2\) relevant to photochemical smog formation are

Identify A, B, X and Y :

The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH\(^-\) is

The correct sequence of reagents for the preparation of Q and R is :

A litre of buffer solution contains 0.1 mole of each of NH\(_3\) and NH\(_4\)Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____________ \(\times\) 10\(^{-3}\) (Nearest integer)
[Gi...

Which one of the following reactions does not occur during extraction of copper?

Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A] and [B] are respectively :

Compound A reacts with NH\(_4\)Cl and forms a compound B. Compound B reacts with H\(_2\)O and excess of CO\(_2\) to form compound C which on passing through or reaction with saturated NaCl solution forms sodium hydrogen carbonate. Compound ...

Inert gases have positive electron gain enthalpy. Its correct order is :

The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume of its solution required for the complete neutralization of 25 mL of 0.24 M NaOH is __________ \(\times\) 10\(^{-2}\) mL (Nearest integer)

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

Match the List-I with List-II :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:nor...

A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at \(\frac{1}{3}^{\mathrm{rd}}\) of the total faces. The empirical formula of the compound is :

The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph.
The molar mass of PVC is ____________ g mol\(^{-1}\) (Nearest integer)

(Given : R = 0.083 L atm K\(^{-1}\) mol\(^{-1}\))

'25 volume' hydrogen peroxide means

In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in the compound is ____________ (Nearest Integer)
(Given : Atomic mass Ba: 137 u, S: 32 u, O: 16 u)

The radius of the \(\mathrm{2^{nd}}\) orbit of \(\mathrm{Li^{2+}}\) is \(x\). The expected radius of the \(\mathrm{3^{rd}}\) orbit of \(\mathrm{Be^{3+}}\) is

The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph :

An athlete is given 100 g of glucose (C\(_6\)H\(_{12}\)O\(_6\)) for energy. This is equivalent to 1800kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of en...

The distance of the point P(4, 6, \(-\)2) from the line passing through the point (\(-\)3, 2, 3) and parallel to a line with direction ratios 3, 3, \(-\)1 is equal to :

Consider the lines \(L_1\) and \(L_2\) given by
\({L_1}:{{x - 1} \over 2} = {{y - 3} \over 1} = {{z - 2} \over 2}\)
\({L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}\).
A line \(L_3\) having direction ratios 1, \(-\)1, \(-\)...

Let the equation of the plane passing through the line \(x - 2y - z - 5 = 0 = x + y + 3z - 5\) and parallel to the line \(x + y + 2z - 7 = 0 = 2x + 3y + z - 2\) be \(ax + by + cz = 65\). Then the distance of the point (a, b, c) from the pla...

Let \(x=2\) be a local minima of the function \(f(x)=2x^4-18x^2+8x+12,x\in(-4,4)\). If M is local maximum value of the function \(f\) in (\(-4,4)\), then M =

Let \(f:(0,1)\to\mathbb{R}\) be a function defined \(f(x) = {1 \over {1 - {e^{ - x}}}}\), and \(g(x) = \left( {f( - x) - f(x)} \right)\). Consider two statements
(I) g is an increasing function in (0, 1)
(II) g is one-one in (0, 1)
Then,

If the area enclosed by the parabolas \(\mathrm{P_1:2y=5x^2}\) and \(\mathrm{P_2:x^2-y+6=0}\) is equal to the area enclosed by \(\mathrm{P_1}\) and \(\mathrm{y=\alpha x,\alpha > 0}\), then \(\alpha^3\) is equal to ____________.

If \(a_r\) is the coefficient of \(x^{10-r}\) in the Binomial expansion of \((1 + x)^{10}\), then \(\sum\limits_{r = 1}^{10} {{r^3}{{\left( {{{{a_r}} \over {{a_{r - 1}}}}} \right)}^2}}\) is equal to

The constant term in the expansion of \({\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}\) is ___________.

The points of intersection of the line \(ax + by = 0,(a \ne b)\) and the circle \({x^2} + {y^2} - 2x = 0\) are \(A(\alpha ,0)\) and \(B(1,\beta )\). The image of the circle with AB as a diameter in the line \(x + y + 2 = 0\) is :

Let \(\mathrm{z_1=2+3i}\) and \(\mathrm{z_2=3+4i}\). The set \(\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}\) represents a

The minimum value of the function \(f(x) = \int\limits_0^2 {{e^{|x - t|}}dt}\) is :

Let \(y = y(x)\) be the solution curve of the differential equation \({{dy} \over {dx}} = {y \over x}\left( {1 + x{y^2}(1 + {{\log }_e}x)} \right),x > 0,y(1) = 3\). Then \({{{y^2}(x)} \over 9}\) is equal to :

Let \(y(x) = (1 + x)(1 + {x^2})(1 + {x^4})(1 + {x^8})(1 + {x^{16}})\). Then \(y' - y''\) at \(x = - 1\) is equal to

For some a, b, c \(\in\mathbb{N}\), let \(f(x) = ax - 3\) and \(\mathrm{g(x)=x^b+c,x\in\mathbb{R}}\). If \({(fog)^{ - 1}}(x) = {\left( {{{x - 7} \over 2}} \right)^{1/3}}\), then \((fog)(ac) + (gof)(b)\) is equal to ____________.

The vertices of a hyperbola H are (\(\pm\) 6, 0) and its eccentricity is \({{\sqrt 5 } \over 2}\). Let N be the normal to H at a point in the first quadrant and parallel to the line \(\sqrt 2 x + y = 2\sqrt 2\). If d is the length of the l...

Let \(f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx}\). If \(f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)\), then \(f(4)\) is equal to

If the sum of all the solutions of \({\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right) + {\cot ^{ - 1}}\left( {{{1 - {x^2}} \over {2x}}} \right) = {\pi \over 3}, - 1 < x < 1,x \ne 0\), is \(\alpha - {4 \over {\sqrt 3 }}\), then $$\a...

The value of \(\mathop {\lim }\limits_{n \to \infty } {{1 + 2 - 3 + 4 + 5 - 6\, + \,.....\, + \,(3n - 2) + (3n - 1) - 3n} \over {\sqrt {2{n^4} + 4n + 3} - \sqrt {{n^4} + 5n + 4} }}\) is :

Let \(S = \left\{ {\alpha :{{\log }_2}({9^{2\alpha - 4}} + 13) - {{\log }_2}\left( {{5 \over 2}.\,{3^{2\alpha - 4}} + 1} \right) = 2} \right\}\). Then the maximum value of \(\beta\) for which the equation $${x^2} - 2{\left( {\sum\limits_{...

The statement \(\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)\) is