JEE Main 2024 (Online) 29th January Evening Shift

Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid results

Match List I with List II

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Identify the reagents used for the following conversion

The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is _________.

According to IUPAC system, the compound

is named as

The ascending acidity order of the following H atoms is

Which one of the following will show geometrical isomerism?

Match List I with List II

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The total number of molecules with zero dipole moment among \(\mathrm{CH}_4, \mathrm{BF}_3, \mathrm{H}_2 \mathrm{O}, \mathrm{HF}, \mathrm{NH}_3, \mathrm{CO}_2\) and \(\mathrm{SO}_2\) is ________.

The total number of anti bonding molecular orbitals, formed from \(2 s\) and \(2 p\) atomic orbitals in a diatomic molecule is _______.

The following concentrations were observed at \(500 \mathrm{~K}\) for the formation of \(\mathrm{NH}_3\) from \(\mathrm{N}_2\) and \(\mathrm{H}_2\). At equilibrium ; $$\left[\mathrm{N}_2\right]=2 \times 10^{-2} \mathrm{M},\left[\mathrm{H}_2...

The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is ________ \(\times 10^{-2}\).
(Given antilog \(0.2006=1.587\))

Which of the following reaction is correct?

The product A formed in the following reaction is

A reagent which gives brilliant red precipitate with Nickel ions in basic medium is

Which of the following acts as a strong reducing agent? (Atomic number: \(\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{Gd}=64, \mathrm{Lu}=71\))

Which of the following statements are correct about \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) ?
A. They exhibit high enthalpy of atomization as the d-subshell is full.
B. \(\mathrm{Zn}\) and \(\mathrm{Cd}\) do not show variable oxida...

The correct IUPAC name of \(\mathrm{K}_2 \mathrm{MnO}_4\) is

A constant current was passed through a solution of \(\mathrm{AuCl}_4^{-}\) ion between gold electrodes. After a period of 10.0 minutes, the increase in mass of cathode was \(1.314 \mathrm{~g}\). The total charge passed through the solution...

Alkyl halide is converted into alkyl isocyanide by reaction with

On passing a gas, '\(\mathrm{X}\)', through Nessler's regent, a brown precipitate is obtained. The gas '\(\mathrm{X}\)' is

Given below are two statements:
Statement I : Fluorine has most negative electron gain enthalpy in its group.
Statement II : Oxygen has least negative electron gain enthalpy in its group.
In the light of the above statements, choose the mos...

The element having the highest first ionization enthalpy is

Anomalous behavior of oxygen is due to its

Chromatographic technique/s based on the principle of differential adsorption is / are
A. Column chromatography
B. Thin layer chromatography
C. Paper chromatography
Choose the most appropriate answer from the options given below:

The oxidation number of iron in the compound formed during brown ring test for NO\(_3^-\) iron is ________.

If \(50 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) oxalic acid is required to neutralise \(25 \mathrm{~mL}\) of \(\mathrm{NaOH}\) solution, the amount of \(\mathrm{NaOH}\) in \(50 \mathrm{~mL}\) of given \(\mathrm{NaOH}\) solution is ______ g.

Molality of 0.8 M H\(_2\)SO\(_4\) solution (density 1.06 g cm\(^{-3}\)) is ________ \(\times10^{-3}\) m.

Match List I with List II

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Standard enthalpy of vapourisation for \(\mathrm{CCl}_4\) is \(30.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Heat required for vapourisation of \(284 \mathrm{~g}\) of \(\mathrm{CCl}_4\) at constant temperature is ________ \(\mathrm{kJ}\).
(Given ...

Let \(\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)\) and \(\mathrm{R}(7,3,2)\) be the vertices of \(\triangle \mathrm{PQR}\). Then, the angle \(\angle \mathrm{QPR}\) is

Let O be the origin, and M and \(\mathrm{N}\) be the points on the lines \(\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}\) and \(\frac{x+8}{12}=\frac{y+2}{5}=\frac{z+11}{9}\) respectively such that \(\mathrm{MN}\) is the shortest distance betwe...

The function \(f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}\)

The function \(f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}\), has

Let the area of the region \(\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{x^2+2,2 x+2\right\}\right\}\) be A. Then \(12 \mathrm{~A}\) is equal to __________.

Remainder when \(64^{32^{32}}\) is divided by 9 is equal to ________.

Let \(\mathrm{r}\) and \(\theta\) respectively be the modulus and amplitude of the complex number \(z=2-i\left(2 \tan \frac{5 \pi}{8}\right)\), then \((\mathrm{r}, \theta)\) is equal to

Let \(\alpha, \beta\) be the roots of the equation \(x^2-\sqrt{6} x+3=0\) such that \(\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)\). Let \(a, b\) be integers not divisible by 3 and \(n\) be a natural number such that $$\frac{\alpha^{...

Let the slope of the line \(45 x+5 y+3=0\) be \(27 r_1+\frac{9 r_2}{2}\) for some \(r_1, r_2 \in \mathbb{R}\). Then \(\lim _\limits{x \rightarrow 3}\left(\int_3^x \frac{8 t^2}{\frac{3 r_2 x}{2}-r_2 x^2-r_1 x^3-3 x} d t\right)\) is equal to ...

If \(\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}\), where \(\alpha, \beta\) and \(\gamma\) are rational numbers, then
\(3 \alpha+4 \beta-\gamma\) is equal to _________.

If \(\sin \left(\frac{y}{x}\right)=\log _e|x|+\frac{\alpha}{2}\) is the solution of the differential equation \(x \cos \left(\frac{y}{x}\right) \frac{d y}{d x}=y \cos \left(\frac{y}{x}\right)+x\) and \(y(1)=\frac{\pi}{3}\), then $$\alpha^2$...

\(\text { Let } y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1 < x<1 \text {. Then at } x=\frac{1}{2} \text {, the value of } 225\left(y^{\prime}-y^{\prime \prime}\right) \text { is equal to }\)

If \(\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \cot x}+C\), where \(C\) is the integration constant, then ...

Let \(x=\frac{m}{n}\) (\(m, n\) are co-prime natural numbers) be a solution of the equation \(\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}\) and let \(\alpha, \beta(\alpha >\beta)\) be the roots of the equation \(m x^2-n x-m+ n=0\). Then th...

Let \(f(x)=\sqrt{\lim _\limits{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right\}}\) be differentiable in \((-\infty, 0) \cup(0, \infty)\) and \(f(1)=1\). Then the value of ea, such th...

Let $$A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$$ and $$P=\left[\begin{array}{lll}1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5\end{array}\right]$$. The sum of the prime factors of $$\left|P^{-1} A P-2 I\right|$...

Let for any three distinct consecutive terms \(a, b, c\) of an A.P, the lines \(a x+b y+c=0\) be concurrent at the point \(P\) and \(Q(\alpha, \beta)\) be a point such that the system of equations
$$\begin{aligned}
& x+y+z=6, \\
& 2 x+5 y+\...

Let \(P(\alpha, \beta)\) be a point on the parabola \(y^2=4 x\). If \(P\) also lies on the chord of the parabola \(x^2=8 y\) whose mid point is \(\left(1, \frac{5}{4}\right)\), then \((\alpha-28)(\beta-8)\) is equal to _________.

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

An integer is chosen at random from the integers \(1,2,3, \ldots, 50\). The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is