JEE Main 2024 (Online) 6th April Morning Shift

In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of intermediate is __________.

Which among the following aldehydes is most reactive towards nucleophilic addition reactions?

Functional group present in sulphonic acids is :

Which of the following is metamer of the given compound (X) ?

DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorrect base structure.

Match List I with List II

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Match List I with List II

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Number of molecules from the following which can exhibit hydrogen bonding is
_________. (nearest integer)

At \(-20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure, a cylinder is filled with equal number of \(\mathrm{H}_2, \mathrm{I}_2\) and \(\mathrm{HI}\) molecules for the reaction
$$\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \r...

Time required for \(99.9 \%\) completion of a first order reaction is _________ times the time required for completion of \(90 \%\) reaction.(nearest integer)

Match List I with List II

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Given below are two statements :
Statement I : Piciric acid is 2,4,6 - trinitrotoluene.
Statement II : Phenol - 2,4 - disulphonic acid is treated with Conc. \(\mathrm{HNO}_3\) to get picric acid.
In the light of the above statements, choose...

\(9.3 \mathrm{~g}\) of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100% yield/conversion) is ________ g. (nearest integer)

Match List I with List II

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The difference in the 'spin-only' magnetic moment values of \(\mathrm{KMnO}_4\) and the manganese product formed during titration of \(\mathrm{KMnO}_4\) against oxalic acid in acidic medium is ________ \(\mathrm{BM}\). (nearest integer)

Consider the following complexes
(A) \(\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}\), (B) \(\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}\), (C) $$
\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\ri...

The number of element from the following that do not belong to lanthanoids is \(\mathrm{Eu}, \mathrm{Cm}, \mathrm{Er}, \mathrm{Tb}, \mathrm{Yb}\) and \(\mathrm{Lu}\)

Among \(\mathrm{CrO}, \mathrm{Cr}_2 \mathrm{O}_3\) and \(\mathrm{CrO}_3\), the sum of spin-only magnetic moment values of basic and amphoteric oxides is _________ \(10^{-2} \mathrm{BM}\) (nearest integer).
(Given atomic number of $$\mathrm{...

A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will -

The major product of the following reaction is P.
\(\mathrm{CH}_3 \mathrm{C}\equiv\mathrm{C}-\mathrm{CH}_3\) $$\xrightarrow[\substack{\text { (ii) dil. } \mathrm{KMnO}_4 \\ 273 \mathrm{~K}}]{\text { (i) } \mathrm{Na} \text { /liq. } \mathrm...

The major products from the following reaction sequence are product A and product B.

The total sum of \(\pi\) electrons in product A and product B are __________ (nearest integer)

Consider the dissociation of the weak acid HX as given below
\(\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}), \mathrm{Ka}=1.2 \times 10^{-5}\)
[\(\mathrm{K}_{\mathrm{a}}\) : dissociation...

Given below are two statements :
Statement I : Gallium is used in the manufacturing of thermometers.
Statement II : A thermometer containing gallium is useful for measuring the freezing point \((256 \mathrm{~K})\) of brine solution.
In the ...

Which of the following material is not a semiconductor.

The electron affinity value are negative for
A. \(\mathrm{Be} \rightarrow \mathrm{Be}^{-}\)
B. \(\mathrm{N} \rightarrow \mathrm{N}^{-}\)
C. \(\mathrm{O} \rightarrow \mathrm{O}^{2-}\)
D. \(\mathrm{Na} \rightarrow \mathrm{Na}^{-}\)
E. $$\math...

Which of the following statements are correct?
A. Glycerol is purified by vacuum distillation because it decomposes at its normal boiling point.
B. Aniline can be purified by steam distillation as aniline is miscible in water.
C. Ethanol ca...

Match List I with List II

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The density of '\(x\)' \(\mathrm{M}\) solution ('\(x\)' molar) of \(\mathrm{NaOH}\) is \(1.12 \mathrm{~g} \mathrm{~mL}^{-1}\), while in molality, the concentration of the solution is \(3 \mathrm{~m}\) ( 3 molal). Then \(x\) is
(Given : Mola...

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ \(\times 10^{13} \mathrm{~Hz}\) (nearest integer).
[Given : \(\mathrm{R}_{\mathrm{H}}\) (Rydberg constant) $$=2.18 \times 10^{-18} \mathrm{~J},...

An ideal gas, \(\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}\), is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is \(298 \mathrm{~K}\) and $$5 ...

If \(A(3,1,-1), B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), C(2,2,1)\) and \(D\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right)\) are the vertices of a quadrilateral \(A B C D\), then its area is

The shortest distance between the lines \(\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}\) and \(\frac{x+1}{2}=\frac{y-1}{1}=\frac{z-9}{-3}\) is

Let \(P\) be the point \((10,-2,-1)\) and \(Q\) be the foot of the perpendicular drawn from the point \(R(1,7,6)\) on the line passing through the points \((2,-5,11)\) and \((-6,7,-5)\). Then the length of the line segment \(P Q\) is equal ...

The interval in which the function \(f(x)=x^x, x>0\), is strictly increasing is

Let the area of the region enclosed by the curves \(y=3 x, 2 y=27-3 x\) and \(y=3 x-x \sqrt{x}\) be \(A\). Then \(10 A\) is equal to

If the second, third and fourth terms in the expansion of \((x+y)^n\) are 135, 30 and \(\frac{10}{3}\), respectively, then \(6\left(n^3+x^2+y\right)\) is equal to __________.

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are \(m\) and \(n\), respectively, then \(m+n^2\) is equal to

\(\int_\limits0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x \text { is equal to }\)

Let \(r_k=\frac{\int_0^1\left(1-x^7\right)^k d x}{\int_0^1\left(1-x^7\right)^{k+1} d x}, k \in \mathbb{N}\). Then the value of \(\sum_\limits{k=1}^{10} \frac{1}{7\left(r_k-1\right)}\) is equal to _________.

Let \(y=y(x)\) be the solution of the differential equation \(\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x} \log _e x, x>0\) and \(y\left(e^{-1}\right)=0\). Then, \(y(e)\) is equal to

Let \(y=y(x)\) be the solution of the differential equation \(\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}\), \(y(1)=0\). Then \(y(0)\) is

$$\text { If } f(x)=\left\{\begin{array}{ll} x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0 & , x=0 \end{array}\right. \text {, then }$$

Let \(f:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R}\) be a differentiable function such that \(f^{\prime}(1)=\lim _\limits{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right)\). Then $$\lim _\limits{a \rightarrow \infty} \frac{a(a+1)}{2}...

The function \(f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}\) is

For \(n \in \mathrm{N}\), if \(\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^{-1} n=\frac{\pi}{4}\), then \(n\) is equal to ________.

For \(\alpha, \beta \in \mathbb{R}\) and a natural number \(n\), let $$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}+\alpha \\ 2 r & 2 & n^2-\beta \\ 3 r-2 & 3 & \frac{n(3 n-1)}{2}\end{array}\right|$$. Then \(2 A_{10}-A_8\) is

Let \(\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}\). If \(x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)=(0,0,0)\) for some \(x, y, z \in \mathbb{R}, x y z \neq 0\), then \(6 \alpha+4 \beta+\gamma\) is equal to _________.

Let \(C\) be the circle of minimum area touching the parabola \(y=6-x^2\) and the lines \(y=\sqrt{3}|x|\). Then, which one of the following points lies on the circle \(C\) ?

Let a conic \(C\) pass through the point \((4,-2)\) and \(P(x, y), x \geq 3\), be any point on \(C\). Let the slope of the line touching the conic \(C\) only at a single point \(P\) be half the slope of the line joining the points \(P\) and...

Let \(L_1, L_2\) be the lines passing through the point \(P(0,1)\) and touching the parabola \(9 x^2+12 x+18 y-14=0\). Let \(Q\) and \(R\) be the points on the lines \(L_1\) and \(L_2\) such that the \(\triangle P Q R\) is an isosceles tria...