JEE Main 2023 (Online) 12th April Morning Shift

Correct statements for the given reaction are :

A. Compound '\(\mathrm{B}\)' is aromatic
B. The completion of above reaction is very slow
C. 'A' shows tautomerism
D. The bond lengths of C-C in compound $B$ are found to be same
Choose the c...

The two products formed in above reaction are -

'A' in the above reaction is:

In the following reaction

'A' is

The major product 'P' formed in the following sequence of reactions is

The value of \(x\) in compound 'D' is _________.

The mass of NH\(_3\) produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ________ kg. (Nearest Integer)
Molar Mass of
C = 12g/mol
N = 14g/mol
O = 16g/mol

Three organic compounds A, B and \(\mathrm{C}\) were allowed to run in thin layer chromatography using hexane and gave the following result (see figure). The \(\mathrm{R}_{\mathrm{f}}\) value of the most polar compound is ____________ $$\ti...

In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of \(\mathrm{sp}^{2}\) hybridised carbons is __________.

The bond order and magnetic property of acetylide ion are same as that of

The reaction \(2 \mathrm{NO}+\mathrm{Br}_{2} \rightarrow 2 \mathrm{NOBr}\)
takes places through the mechanism given below:
\(\mathrm{NO}+\mathrm{Br}_{2} \Leftrightarrow \mathrm{NOBr}_{2}\) (fast)
$$\mathrm{NOBr}_{2}+\mathrm{NO} \rightarrow ...

The incorrect statement regarding the reaction given below is

Match List I with List II

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...

Given below are two statement: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A: \(5 \mathrm{f}\) electrons can participate in bonding to a far greater extent than \(4 \mathrm{f}\) e...

For lead storage battery pick the correct statements
A. During charging of battery, \(\mathrm{PbSO}_{4}\) on anode is converted into \(\mathrm{PbO}_{2}\)
B. During charging of battery, \(\mathrm{PbSO}_{4}\) on cathode is converted into $$\m...

Match List I with List II

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...

At \(600 \mathrm{~K}\), the root mean square (rms) speed of gas \(\mathrm{X}\) (molar mass \(=40\) ) is equal to the most probable speed of gas \(\mathrm{Y}\) at \(90 \mathrm{~K}\). The molar mass of the gas \(\mathrm{Y}\) is ___________ $$...

Match List I with List II

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...

An analyst wants to convert \(1 \mathrm{~L} \mathrm{~HCl}\) of \(\mathrm{pH}=1\) to a solution of \(\mathrm{HCl}\) of \(\mathrm{pH} ~2\). The volume of water needed to do this dilution is __________ \(\mathrm{mL}\). (Nearest integer)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : In the Ellingham diagram, a sharp change in slope of the line is observed for \(\mathrm{Mg} \rightarrow \mathrm{MgO}\) at $$\...

Given below are two statements :
Statement I : Boron is extremely hard indicating its high lattice energy.
Statement II : Boron has highest melting and boiling point compared to its other group members.
In the light of the above statements,...

Given below are two statements :
Statement I : \(\mathrm{SbCl}_{5}\) is more covalent than \(\mathrm{SbCl}_{3}\)
Statement II: The higher oxides of halogens also tend to be more stable than the lower ones.
In the light of the above statemen...

Match List I with List II

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...

The density of alkali metals is in the order :

In the given reaction cycle

X, Y and Z respectively are :

80 mole percent of \(\mathrm{MgCl}_{2}\) is dissociated in aqueous solution. The vapour pressure of \(1.0 ~\mathrm{molal}\) aqueous solution of \(\mathrm{MgCl}_{2}\) at \(38^{\circ} \mathrm{C}\) is ____________ $$\mathrm{mm} ~\mathrm{Hg.} ~...

A metal chloride contains \(55.0 \%\) of chlorine by weight . \(100 \mathrm{~mL}\) vapours of the metal chloride at STP weigh \(0.57 \mathrm{~g}\). The molecular formula of the metal chloride is
(Given: Atomic mass of chlorine is $$35.5 \ma...

Values of work function (W\(_0\)) for a few metals are given below

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Four gases A, B, C and D have critical temperatures \(5.3,33.2,126.0\) and \(154.3 \mathrm{~K}\) respectively. For their adsorption on a fixed amount of charcoal, the correct order is:

One mole of an ideal gas at \(350 \mathrm{~K}\) is in a \(2.0 \mathrm{~L}\) vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0 L to \(3.0 \mathrm{~L}\) aga...

Let the lines \(l_{1}: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}\) and \(l_{2}: 3 x+2 y+z-2=0=x-3 y+2 z-13\) be coplanar. If the point \(\mathrm{P}(a, b, c)\) on \(l_{1}\) is nearest to the point \(\mathrm{Q}(-4,-3,2)\), then $$|a|+|b...

Let the plane P: \(4 x-y+z=10\) be rotated by an angle \(\frac{\pi}{2}\) about its line of intersection with the plane \(x+y-z=4\). If \(\alpha\) is the distance of the point \((2,3,-4)\) from the new position of the plane \(\mathrm{P}\), t...

Let the plane \(x+3 y-2 z+6=0\) meet the co-ordinate axes at the points A, B, C. If the orthocenter of the triangle \(\mathrm{ABC}\) is \(\left(\alpha, \beta, \frac{6}{7}\right)\), then \(98(\alpha+\beta)^{2}\) is equal to ___________.

If the local maximum value of the function \(f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right)\) , is \(\frac{k}{e}\), then \(\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}\) is equal to

The area of the region enclosed by the curve \(y=x^{3}\) and its tangent at the point \((-1,-1)\) is :

If \(\frac{1}{n+1}{ }^{n} \mathrm{C}_{n}+\frac{1}{n}{ }^{n} \mathrm{C}_{n-1}+\ldots+\frac{1}{2}{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{0}=\frac{1023}{10}\) then \(n\) is equal to :

The sum, of the coefficients of the first 50 terms in the binomial expansion of \((1-x)^{100}\), is equal to

Two circles in the first quadrant of radii \(r_{1}\) and \(r_{2}\) touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line \(x+y=2\). Then \(r_{1}^{2}+r_{2}^{2}-r_{1} r_{2}\) is equal to ___________.

Let \(\mathrm{C}\) be the circle in the complex plane with centre \(\mathrm{z}_{0}=\frac{1}{2}(1+3 i)\) and radius \(r=1\). Let \(\mathrm{z}_{1}=1+\mathrm{i}\) and the complex number \(z_{2}\) be outside the circle \(C\) such that $$\left|z...

If \(\int_\limits{-0.15}^{0.15}\left|100 x^{2}-1\right| d x=\frac{k}{3000}\), then \(k\) is equal to ___________.

Let \(y=y(x), y > 0\), be a solution curve of the differential equation \(\left(1+x^{2}\right) \mathrm{d} y=y(x-y) \mathrm{d} x\). If \(y(0)=1\) and \(y(2 \sqrt{2})=\beta\), then

Let \(\mathrm{P}\left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), \mathrm{Q}, \mathrm{R}\) and \(\mathrm{S}\) be four points on the ellipse \(9 x^{2}+4 y^{2}=36\). Let \(\mathrm{PQ}\) and \(\mathrm{RS}\) be mutually perpendicula...

Let \(\mathrm{D}\) be the domain of the function \(f(x)=\sin ^{-1}\left(\log _{3 x}\left(\frac{6+2 \log _{3} x}{-5 x}\right)\right)\). If the range of the function \(\mathrm{g}: \mathrm{D} \rightarrow \mathbb{R}\) defined by $$\mathrm{g}(x)...

Let \(I(x)=\int \sqrt{\frac{x+7}{x}} \mathrm{~d} x\) and \(I(9)=12+7 \log _{e} 7\). If \(I(1)=\alpha+7 \log _{e}(1+2 \sqrt{2})\), then \(\alpha^{4}\) is equal to _________.

Let \([x]\) be the greatest integer \(\leq x\). Then the number of points in the interval \((-2,1)\), where the function \(f(x)=|[x]|+\sqrt{x-[x]}\) is discontinuous, is ___________.

Among the two statements
\((\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))\) is a contradiction and
\((\mathrm{S} 2):(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee((\sim p) \wedge(\sim q))\) is a tautology

Let $$A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$$. If $$\mathrm{B}=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A\left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]$$, then the sum of all the el...

Let $$\mathrm{D}_{\mathrm{k}}=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^{2}+n+2 & n^{2} \\ n & n^{2}+n & n^{2}+n+2\end{array}\right|$$. If \(\sum_\limits{k=1}^{n} \mathrm{D}_{\mathrm{k}}=96\), then \(n\) is equal to _____________.

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits \(0,1,3,5,7\) and 9 without repetition, is equal to :

Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?