JEE Main 2024 (Online) 27th January Evening Shift

Major product formed in the following reaction is a mixture of :

Phenolic group can be identified by a positive:

Match List - I with List - II.

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The molecular formula of second homologue in the homologous series of mono carboxylic acids is

The order of relative stability of the contributing structure is :

Choose the correct answer from the options given below :

The incorrect statement regarding conformations of ethane is :

Bond line formula of HOCH(CN)\(_2\) is :

Total number of compounds with Chiral carbon atoms from following is _________.

Which structure of protein remains intact after coagulation of egg white on boiling?

The number of non-polar molecules from the following is _________. \(\mathrm{HF}, \mathrm{H}_2 \mathrm{O}, \mathrm{SO}_2, \mathrm{H}_2, \mathrm{CO}_2, \mathrm{CH}_4, \mathrm{NH}_3, \mathrm{HCl}, \mathrm{CHCl}_3, \mathrm{BF}_3\)

Time required for completion of \(99.9 \%\) of a First order reaction is ________ times of half life \(\left(t_{1 / 2}\right)\) of the reaction.

Identity the incorrect pair from the following :

Identify from the following species in which \(\mathrm{d}^2 \mathrm{sp}^3\) hybridization is shown by central atom :

The Spin only magnetic moment value of square planar complex \(\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}\left(\mathrm{NH}_2 \mathrm{CH}_3\right)\right] \mathrm{Cl}\) is _________ B.M. (Nearest integer)
(Given atomic number f...

Given below are two statements :
Statement (I) : In the Lanthanoids, the formation \(\mathrm{Ce}^{+4}\) is favoured by its noble gas configuration.
Statement (II) : \(\mathrm{Ce}^{+4}\) is a strong oxidant reverting to the common +3 state.
...

Choose the correct option having all the elements with \(\mathrm{d}^{10}\) electronic configuration from the following :

Total number of ions from the following with noble gas configuration is _________. \(\mathrm{Sr}^{2+}(z=38), \mathrm{Cs}^{+}(z=55), \mathrm{La}^{2+}(z=57), \mathrm{Pb}^{2+}(z=82), \mathrm{Yb}^{2+}(z=70)\) and \(\mathrm{Fe}^{2+}(z=26)\)

Which of the following statements is not correct about rusting of iron?

The hydrogen electrode is dipped in a solution of \(\mathrm{pH}=3\) at \(25^{\circ} \mathrm{C}\). The potential of the electrode will be _________ \(\times 10^{-2} \mathrm{~V}\).
$$\left(\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V...

Identify B formed in the reaction.
\(\mathrm{Cl}-\left(\mathrm{CH}_2\right)_4-\mathrm{Cl} \xrightarrow{\text { excess } \mathrm{NH}_3} \mathrm{~A} \xrightarrow{\mathrm{NaOH}} \mathrm{B}+\mathrm{H}_2 \mathrm{O}+\mathrm{NaCl}\)

Which among the following halide/s will not show \(\mathrm{S_N 1}\) reaction:
(A) \(\mathrm{H}_2 \mathrm{C}=\mathrm{CH}-\mathrm{CH}_2 \mathrm{Cl}\)
(B) \(\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{Cl}\)
(C)
(D)
Choose the most appropri...

The final product A, formed in the following reaction sequence is:

Given below are two statements :
Statement (I) : Oxygen being the first member of group 16 exhibits only -2 oxidation state.
Statement (II) : Down the group 16 stability of +4 oxidation state decreases and +6 oxidation state increases.
In t...

1 mole of \(\mathrm{PbS}\) is oxidised by "\(\mathrm{X}\)" moles of \(\mathrm{O}_3\) to get "\(\mathrm{Y}\)" moles of \(\mathrm{O}_2\). \(\mathrm{X}+\mathrm{Y}=\) _________.

The technique used for purification of steam volatile water immiscible substances is :

Which of the following cannot function as an oxidising agent?

The quantity which changes with temperature is :

\(9.3 \mathrm{~g}\) of aniline is subjected to reaction with excess of acetic anhydride to prepare acetanilide. The mass of acetanilide produced if the reaction is \(100 \%\) completed is _________ \(\times 10^{-1} \mathrm{~g}\).
(Given mol...

Volume of \(3 \mathrm{M} \mathrm{~NaOH}\) (formula weight \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) ) which can be prepared from \(84 \mathrm{~g}\) of \(\mathrm{NaOH}\) is __________ \(\times 10^{-1} \mathrm{dm}^3\).

For a certain thermochemical reaction \(\mathrm{M} \rightarrow \mathrm{N}\) at \(\mathrm{T}=400 \mathrm{~K}, \Delta \mathrm{H}^{\ominus}=77.2 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}=122 \mathrm{~JK}^{-1}, \log\) equilibrium const...

Let the image of the point \((1,0,7)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) be the point \((\alpha, \beta, \gamma)\). Then which one of the following points lies on the line passing through \((\alpha, \beta, \gamma)\) and...

The lines \(\frac{x-2}{2}=\frac{y}{-2}=\frac{z-7}{16}\) and \(\frac{x+3}{4}=\frac{y+2}{3}=\frac{z+2}{1}\) intersect at the point \(P\). If the distance of \(\mathrm{P}\) from the line \(\frac{x+1}{2}=\frac{y-1}{3}=\frac{z-1}{1}\) is \(l\), ...

Let \(g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)\) and \(f^{\prime \prime}(x)>0\) for all \(x \in(0,3)\). If \(g\) is decreasing in \((0, \alpha)\) and increasing in \((\alpha, 3)\), then \(8 \alpha\) is :

If the area of the region \(\left\{(x, y): 0 \leq y \leq \min \left\{2 x, 6 x-x^2\right\}\right\}\) is \(\mathrm{A}\), then \(12 \mathrm{~A}\) is equal to ________.

The coefficient of \(x^{2012}\) in the expansion of \((1-x)^{2008}\left(1+x+x^2\right)^{2007}\) is equal to _________.

Consider a circle \((x-\alpha)^2+(y-\beta)^2=50\), where \(\alpha, \beta>0\). If the circle touches the line \(y+x=0\) at the point \(P\), whose distance from the origin is \(4 \sqrt{2}\), then \((\alpha+\beta)^2\) is equal to __________.

Let the complex numbers \(\alpha\) and \(\frac{1}{\bar{\alpha}}\) lie on the circles \(\left|z-z_0\right|^2=4\) and \(\left|z-z_0\right|^2=16\) respectively, where \(z_0=1+i\). Then, the value of \(100|\alpha|^2\) is __________.

For \(0 < \mathrm{a} < 1\), the value of the integral \(\int_\limits0^\pi \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\mathrm{a}^2}\) is :

Let \(f(x)=\int_\limits0^x g(t) \log _{\mathrm{e}}\left(\frac{1-\mathrm{t}}{1+\mathrm{t}}\right) \mathrm{dt}\), where \(g\) is a continuous odd function.
If $$\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+\mathrm{e}^x}\right) \mat...

If \(y=y(x)\) is the solution curve of the differential equation \(\left(x^2-4\right) \mathrm{d} y-\left(y^2-3 y\right) \mathrm{d} x=0, x>2, y(4)=\frac{3}{2}\) and the slope of the curve is never zero, then the value of \(y(10)\) equals :

If the solution curve, of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y-2}{x-y}\) passing through the point \((2,1)\) is $$\tan ^{-1}\left(\frac{y-1}{x-1}\right)-\frac{1}{\beta} \log _{\mathrm{e}}\left(\alpha+\lef...

Let \(f: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}\) and \(g: \mathbf{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathbf{R}\) be defined as \(f(x)=\frac{2 x+3}{2 x+1}\) and \(g(x)=\frac{|x|+1}{2 x+5}\). Then, the domain ...

Let \(e_1\) be the eccentricity of the hyperbola \(\frac{x^2}{16}-\frac{y^2}{9}=1\) and \(e_2\) be the eccentricity of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a} > \mathrm{b}\), which passes through the foci of the hyperbol...

\(\text { The integral } \int \frac{\left(x^8-x^2\right) \mathrm{d} x}{\left(x^{12}+3 x^6+1\right) \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)} \text { is equal to : }\)

Considering only the principal values of inverse trigonometric functions, the number of positive real values of \(x\) satisfying \(\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}\) is :

Consider the function \(f:(0,2) \rightarrow \mathbf{R}\) defined by \(f(x)=\frac{x}{2}+\frac{2}{x}\) and the function \(g(x)\) defined by
$$g(x)=\left\{\begin{array}{ll}
\min \lfloor f(t)\}, & 0<\mathrm{t} \leq x \text { and } 0 < x \leq 1 ...

\(\text { If } \lim _\limits{x \rightarrow 0} \frac{3+\alpha \sin x+\beta \cos x+\log _e(1-x)}{3 \tan ^2 x}=\frac{1}{3} \text {, then } 2 \alpha-\beta \text { is equal to : }\)

The values of \(\alpha\), for which $$\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$$, lie in the interval

Let \(A\) be a \(2 \times 2\) real matrix and \(I\) be the identity matrix of order 2. If the roots of the equation \(|\mathrm{A}-x \mathrm{I}|=0\) be \(-1\) and 3, then the sum of the diagonal elements of the matrix \(\mathrm{A}^2\) is

Let \(\alpha=\frac{(4 !) !}{(4 !)^{3 !}}\) and \(\beta=\frac{(5 !) !}{(5 !)^{4 !}}\). Then :