JEE Main 2024 (Online) 8th April Evening Shift

Which one the following compounds will readily react with dilute \(\mathrm{NaOH}\) ?

Match List I with List II

Choose the correct answer from the options given below :

Two moles of benzaldehyde and one mole of acetone under alkaline conditions using aqueous \(\mathrm{NaOH}\) after heating gives \(x\) as the major product. The number of \(\pi\) bonds in the product \(x\) is ______.

The correct sequence of acidic strength of the following aliphatic acids in their decreasing order is:
$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOH}, \mathrm{CH}_3 \mathrm{COOH}, \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{COOH}, \mathr...

Total number of aromatic compounds among the following compounds is ______.

IUPAC name of following hydrocarbon(X) is :

The number of optically active compounds from the following is _________.

The total number of carbon atoms present in tyrosine, an amino acid, is ________.

When \(\psi_{\mathrm{A}}\) and \(\psi_{\mathrm{B}}\) are the wave functions of atomic orbitals, then \(\sigma^*\) is represented by :

The shape of carbocation is :

Number of molecules having bond order 2 from the following molecules is _________. \(\mathrm{C}_2, \mathrm{O}_2, \mathrm{Be}_2, \mathrm{Li}_2, \mathrm{Ne}_2, \mathrm{~N}_2, \mathrm{He}_2\)

For a reaction \(A \xrightarrow{\mathrm{K}_1} \mathrm{~B} \xrightarrow{\mathrm{K}_2} \mathrm{C}\)
If the rate of formation of B is set to be zero then the concentration of B is given by :

Given below are two statements :
Statement (I) : All the following compounds react with p-toluenesulfonyl chloride.
$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2 \quad\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \mathrm{NH} \quad\left(\mathrm{C}_6 ...

Given below are two statements :
Statement (I) : Kjeldahl method is applicable to estimate nitrogen in pyridine.
Statement (II) : The nitrogen present in pyridine can easily be converted into ammonium sulphate in Kjeldahl method.
In the lig...

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;}
...

Total number of unpaired electrons in the complex ions \([\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}\) and \([\mathrm{NiCl}_4]^{2-}\) is ________.

The emf of cell \(\mathrm{Tl}\left|\underset{(0.001 \mathrm{M})}{\mathrm{Tl}^{+}}\right| \underset{(0.01 \mathrm{M})}{\mathrm{Cu}^{2+}} \mid \mathrm{Cu}\) is \(0.83 \mathrm{~V}\) at \(298 \mathrm{~K}\). It could be increased by :

The reaction;
\(\frac{1}{2} \mathrm{H}_{2(\mathrm{~g})}+\mathrm{AgCl}_{(\mathrm{s})} \rightarrow \mathrm{H}_{(\mathrm{aq})}^{+}+\mathrm{Cl}_{(\mathrm{aq})}^{-}+\mathrm{Ag}_{(\mathrm{s})}\)
occurs in which of the following galvanic cell :

Given below are two statements :
Statement (I) : Fusion of \(\mathrm{MnO}_2\) with \(\mathrm{KOH}\) and an oxidising agent gives dark green \(\mathrm{K}_2 \mathrm{MnO}_4\).
Statement (II) : Manganate ion on electrolytic oxidation in alkalin...

Given below are two statements :
Statement (I) : \(\mathrm{S}_{\mathrm{N}} 2\) reactions are 'stereospecific', indicating that they result in the formation of only one stereo-isomer as the product.
Statement (II) : $$\mathrm{S}_{\mathrm{N}}...

The equilibrium \(\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}\) is shifted to the right in :

Given below are two statements :
Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities
Statement (II) : Blood is naturally occurring buffer solution whose \(\mathrm{pH}\) is main...

Identify the correct statements about p-block elements and their compounds.
(A) Non metals have higher electronegativity than metals.
(B) Non metals have lower ionisation enthalpy than metals.
(C) Compounds formed between highly reactive no...

In qualitative test for identification of presence of phosphorous, the compound is heated with an oxidising agent. Which is further treated with nitric acid and ammonium molybdate respectively. The yellow coloured precipitate obtained is :

Identify the incorrect statements about group 15 elements :
(A) Dinitrogen is a diatomic gas which acts like an inert gas at room temperature.
(B) The common oxidation states of these elements are \(-3,+3\) and +5.
(C) Nitrogen has unique a...

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;}
...

A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is ________ (Integer answer) (Given : Molar mass in \(\mathrm{g} \mathrm{~mol}^{-1}\) Ethyl alcohol : 46 water : 18)

Molality of an aqueous solution of urea is \(4.44 \mathrm{~m}\). Mole fraction of urea in solution is \(x \times 10^{-3}\), Value of \(x\) is ________. (Integer answer)

Wavenumber for a radiation having 5800 \(\mathop A\limits^o\) wavelength is \(x \times 10 \mathrm{~cm}^{-1}\) The value of \(x\) is ________. (Integer answer)

\(\Delta_{\text {vap }} \mathrm{H}^{\ominus}\) for water is \(+40.79 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at 1 bar and \(100^{\circ} \mathrm{C}\). Change in internal energy for this vapourisation under same condition is ________ $$\mathrm{kJ} ...

If the shortest distance between the lines \(\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}\) is \(\frac{13}{\sqrt{29}}\), then a value of \(\lambda\) is :

Let \(\mathrm{P}(\alpha, \beta, \gamma)\) be the image of the point \(\mathrm{Q}(1,6,4)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\). Then \(2 \alpha+\beta+\gamma\) is equal to ________

If the function \(f(x)=2 x^3-9 \mathrm{ax}^2+12 \mathrm{a}^2 x+1, \mathrm{a}> 0\) has a local maximum at \(x=\alpha\) and a local minimum at \(x=\alpha^2\), then \(\alpha\) and \(\alpha^2\) are the roots of the equation :

Let \(\mathrm{A}\) be the region enclosed by the parabola \(y^2=2 x\) and the line \(x=24\). Then the maximum area of the rectangle inscribed in the region \(\mathrm{A}\) is ________.

The area of the region in the first quadrant inside the circle \(x^2+y^2=8\) and outside the parabola \(y^2=2 x\) is equal to :

If the term independent of \(x\) in the expansion of \(\left(\sqrt{\mathrm{a}} x^2+\frac{1}{2 x^3}\right)^{10}\) is 105 , then \(\mathrm{a}^2\) is equal to :

If the image of the point \((-4,5)\) in the line \(x+2 y=2\) lies on the circle \((x+4)^2+(y-3)^2=r^2\), then \(r\) is equal to:

The sum of all possible values of \(\theta \in[-\pi, 2 \pi]\), for which \(\frac{1+i \cos \theta}{1-2 i \cos \theta}\) is purely imaginary, is equal to :

Let \(\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}\). Then \(\mathrm{e}^\alpha\) and \(\mathrm{e}^{-\alpha}\) are the roots of the equation :

Let \(y=y(x)\) be the solution curve of the differential equation \(\sec y \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x \sin y=x^3 \cos y, y(1)=0\). Then \(y(\sqrt{3})\) is equal to:

Let \(\alpha|x|=|y| \mathrm{e}^{x y-\beta}, \alpha, \beta \in \mathbf{N}\) be the solution of the differential equation \(x \mathrm{~d} y-y \mathrm{~d} x+x y(x \mathrm{~d} y+y \mathrm{~d} x)=0,y(1)=2\). Then \(\alpha+\beta\) is equal to ___...

Let $$f(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if } & 0< x \leq \mathrm{a}\end{array}\right.$$ where \(\mathrm{a}> 0\) and \(\mathrm{g}(x)=(f(|x|)-|f(x)|) / 2\). Then the...

Let \(\mathrm{S}\) be the focus of the hyperbola \(\frac{x^2}{3}-\frac{y^2}{5}=1\), on the positive \(x\)-axis. Let \(\mathrm{C}\) be the circle with its centre at \(\mathrm{A}(\sqrt{6}, \sqrt{5})\) and passing through the point $$\mathrm{S...

If \(\int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} \mathrm{~d} x=\mathrm{A}\left(\frac{\alpha x-1}{\beta x+3}\right)^B+\mathrm{C}\), where \(\mathrm{C}\) is the constant of integration, then the value of \(\alpha+\beta+20 \mathrm{AB}\) is _______...

For \(\mathrm{a}, \mathrm{b}>0\), let $$f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x< 0 \\ 3, & x=0 \\ \frac{\sqrt{\mathrm{a} x+\mathrm{b}^2 x^2}-\sqrt{\mathrm{a} x}}{\mathrm{~b} \sqrt{\mathrm{a}} x \sqrt{x}},...

If \(\alpha=\lim _\limits{x \rightarrow 0^{+}}\left(\frac{\mathrm{e}^{\sqrt{\tan x}}-\mathrm{e}^{\sqrt{x}}}{\sqrt{\tan x}-\sqrt{x}}\right)\) and \(\beta=\lim _\limits{x \rightarrow 0}(1+\sin x)^{\frac{1}{2} \cot x}\) are the roots of the qu...

If the system of equations \(x+4 y-z=\lambda, 7 x+9 y+\mu z=-3,5 x+y+2 z=-1\) has infinitely many solutions, then \((2 \mu+3 \lambda)\) is equal to :

If \(\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}\) and $$\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0$$, then $...

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

There are three bags \(X, Y\) and \(Z\). Bag \(X\) contains 5 one-rupee coins and 4 five-rupee coins; Bag \(Y\) contains 4 one-rupee coins and 5 five-rupee coins and Bag \(Z\) contains 3 one-rupee coins and 6 five-rupee coins. A bag is sele...