JEE Main 2024 (Online) 4th April Evening Shift

Common name of Benzene - 1,2 - diol is -

Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and \(\pi\) electrons is __________.

The total number of 'sigma' and 'pi' bonds in 2-oxohex-4-ynoic acid is ______.

Correct order of stability of carbanion is :

Match List I with List II

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The correct statement/s about Hydrogen bonding is/are
A. Hydrogen bonding exists when H is covalently bonded to the highly electro negative atom.
B. Intermolecular H bonding is present in \(o\)-nitro phenol
C. Intramolecular \(\mathrm{H}\) ...

Number of compounds / species from the following with non-zero dipole moment is _________.
$$\mathrm{BeCl}_2, \mathrm{BCl}_3, \mathrm{NF}_3, \mathrm{XeF}_4, \mathrm{CCl}_4, \mathrm{H}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{~S}, \mathrm{HBr}, \m...

The number of species from the following that have pyramidal geometry around the central atom is _________
\(\mathrm{S}_2 \mathrm{O}_3^{2-}, \mathrm{SO}_4^{2-}, \mathrm{SO}_3^{2-}, \mathrm{S}_2 \mathrm{O}_7^{2-}\)

The equilibrium constant for the reaction
\(\mathrm{SO}_3(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\)
is \(\mathrm{K}_{\mathrm{c}}=4.9 \times 10^{-2}\). The value of $$\mathrm{K}_{\math...

Consider the following reaction, the rate expression of which is given below
$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \\ & \text { rate }=\mathrm{k}[\mathrm{A}]^{1 / 2}[\mathrm{~B}]^{1 / 2} \end{aligned}$$
The reacti...

Phthalimide is made to undergo following sequence of reactions.

Total number of \(\pi\) bonds present in product 'P' is/are ________.

The number of unpaired d-electrons in \(\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\) is ________.

A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of \(3.86 \mathrm{~BM}\). The atomic number of the metal is

If an iron (III) complex with the formula \(\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_x(\mathrm{CN})_y\right]^-\) has no electron in its \(e_g\) orbital, then the value of \(x+y\) is

A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of formula \(\mathrm{M}_2 \mathrm{O}_{\mathrm{n}}\) (where \(\mathrm{n}=3,4,5\)). The 'spin-only' magnetic moment ...

Fuel cell, using hydrogen and oxygen as fuels,
A. has been used in spaceship
B. has as efficiency of \(40 \%\) to produce electricity
C. uses aluminum as catalysts
D. is eco-friendly
E. is actually a type of Galvanic cell only
Choose the co...

For a strong electrolyte, a plot of molar conductivity against (concentration) \({ }^{1 / 2}\) is a straight line, with a negative slope, the correct unit for the slope is

Find out the major product formed from the following reaction. \([\mathrm{Me}:-\mathrm{CH}_3]\)

\(\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{Br}+\mathrm{NaOH} \xrightarrow{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}} \text { Product 'A' }\)

Consider the above reactions, identify product B and product C.

Product P is

In the above chemical reaction sequence "\(\mathrm{A}\)" and "\(\mathrm{B}\)" respectively are

Given below are two statements :
Statement I : The correct order of first ionization enthalpy values of \(\mathrm{Li}, \mathrm{Na}, \mathrm{F}\) and \(\mathrm{Cl}\) is \(\mathrm{Na}<\mathrm{Li}<\mathrm{Cl}<\mathrm{F}\).
Statement II : The c...

The correct order of the first ionization enthalpy is

When \(\mathrm{MnO}_2\) and \(\mathrm{H}_2 \mathrm{SO}_4\) is added to a salt \((\mathrm{A})\), the greenish yellow gas liberated as salt (A) is :

\(2.7 \mathrm{~kg}\) of each of water and acetic acid are mixed. The freezing point of the solution will be \(-x^{\circ} \mathrm{C}\). Consider the acetic acid does not dimerise in water, nor dissociates in water. \(x=\) ________ (nearest i...

From \(6.55 \mathrm{~g}\) of aniline, the maximum amount of acetanilide that can be prepared will be ________ \(\times 10^{-1} \mathrm{~g}\).

Choose the Incorrect Statement about Dalton's Atomic Theory

The maximum number of orbitals which can be identified with \(\mathrm{n}=4\) and \(m_l=0\) is _________.

The adsorbent used in adsorption chromatography is/are -
A. silica gel
B. alumina
C. quick lime
D. magnesia
Choose the most appropriate answer from the options given below :

Three moles of an ideal gas are compressed isothermally from \(60 \mathrm{~L}\) to \(20 \mathrm{~L}\) using constant pressure of \(5 \mathrm{~atm}\). Heat exchange \(\mathrm{Q}\) for the compression is - _________ Lit. atm.

Let \(\mathrm{P}\) be the point of intersection of the lines \(\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}\) and \(\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}\). Then, the shortest distance of \(\mathrm{P}\) from the line \(4 x=2 y=z\) is

Consider a line \(\mathrm{L}\) passing through the points \(\mathrm{P}(1,2,1)\) and \(\mathrm{Q}(2,1,-1)\). If the mirror image of the point \(\mathrm{A}(2,2,2)\) in the line \(\mathrm{L}\) is \((\alpha, \beta, \gamma)\), then $$\alpha+\bet...

Let \(f(x)=3 \sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum and the maximum values of \(f\), then \(\alpha^2+2 \beta^2\) is equal to

The area (in sq. units) of the region described by \(\left\{(x, y): y^2 \leq 2 x \text {, and } y \geq 4 x-1\right\}\) is

If the coefficients of \(x^4, x^5\) and \(x^6\) in the expansion of \((1+x)^n\) are in the arithmetic progression, then the maximum value of \(n\) is:

Let \(\mathrm{C}\) be a circle with radius \(\sqrt{10}\) units and centre at the origin. Let the line \(x+y=2\) intersects the circle \(\mathrm{C}\) at the points \(\mathrm{P}\) and \(\mathrm{Q}\). Let \(\mathrm{MN}\) be a chord of $$\mathr...

The area (in sq. units) of the region \(S=\{z \in \mathbb{C}:|z-1| \leq 2 ;(z+\bar{z})+i(z-\bar{z}) \leq 2, \operatorname{lm}(z) \geq 0\}\) is

Let \(f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}\). Then, \(\lim _\limits{x \rightarrow 0} \frac{f(x)}{x^3}\) is equal to

If the value of the integral \(\int\limits_{-1}^1 \frac{\cos \alpha x}{1+3^x} d x\) is \(\frac{2}{\pi}\).Then, a value of \(\alpha\) is

Let \(y=y(x)\) be the solution of the differential equation \((x+y+2)^2 d x=d y, y(0)=-2\). Let the maximum and minimum values of the function \(y=y(x)\) in \(\left[0, \frac{\pi}{3}\right]\) be \(\alpha\) and \(\beta\), respectively. If $$(...

Let \(y=y(x)\) be the solution of the differential equation \((x^2+4)^2 d y+(2 x^3 y+8 x y-2) d x=0\). If \(y(0)=0\), then \(y(2)\) is equal to

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a thrice differentiable function such that \(f(0)=0, f(1)=1, f(2)=-1, f(3)=2\) and \(f(4)=-2\). Then, the minimum number of zeros of $$\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \...

Consider the function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(f(x)=\frac{2 x}{\sqrt{1+9 x^2}}\). If the composition of $$f, \underbrace{(f \circ f \circ f \circ \cdots \circ f)}_{10 \text { times }}(x)=\frac{2^{10} x}{\sqrt{1+...

Consider a hyperbola \(\mathrm{H}\) having centre at the origin and foci on the \(\mathrm{x}\)-axis. Let \(\mathrm{C}_1\) be the circle touching the hyperbola \(\mathrm{H}\) and having the centre at the origin. Let \(\mathrm{C}_2\) be the c...

If \(\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _x\left|\tan \frac{x}{2}\right|+\mathrm{C}\)
where \(\alpha, \beta \in \mathbb{R}\) and \(\mathrm{C}\) i...

Given that the inverse trigonometric function assumes principal values only. Let \(x, y\) be any two real numbers in \([-1,1]\) such that \(\cos ^{-1} x-\sin ^{-1} y=\alpha, \frac{-\pi}{2} \leq \alpha \leq \pi\).
Then, the minimum value of ...

If the function
$$f(x)= \begin{cases}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ a \log _e 2 \log _e 3 & , x=0\end{cases}$$
is continuous at \(x=0\), then the value of \(a^2\) is equal to

Let \(A\) be a \(2 \times 2\) symmetric matrix such that $$A\left[\begin{array}{l}1 \\ 1\end{array}\right]=\left[\begin{array}{l}3 \\ 7\end{array}\right]$$ and the determinant of \(A\) be 1 . If \(A^{-1}=\alpha A+\beta I\), where \(I\) is a...

Let $$A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$$ and \(B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\ldots+(\operatorname{adj} A)^{10}\).
Then, the sum of all the elements of the matrix \(B\) is:

Let \(P Q\) be a chord of the parabola \(y^2=12 x\) and the midpoint of \(P Q\) be at \((4,1)\). Then, which of the following point lies on the line passing through the points \(\mathrm{P}\) and \(\mathrm{Q}\) ?