JEE Main 2024 (Online) 31st January Morning Shift

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: Alcohols react both as nucleophiles and electrophiles.
Reason R: Alcohols react with active metals such as sodium, potassium ...

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: \(\mathrm{pK}_{\mathrm{a}}\) value of phenol is 10.0 while that of ethanol is 15.9 .
Reason R: Ethanol is stronger acid than ...

The product of the following reaction is P.

The number of hydroxyl groups present in the product P is ________.

A species having carbon with sextet of electrons and can act as electrophile is called

Given below are two statements:
Statement I: IUPAC name of \(\mathrm{HO}-\mathrm{CH}_2-\left(\mathrm{CH}_2\right)_3-\mathrm{CH}_2-\mathrm{COCH}_3\) is 7-hydroxyheptan-2-one.
Statement II: 2-oxoheptan-7-ol is the correct IUPAC name for above...

Match List I with List II

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...

The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining atomic orbitals
A. have the same energy
B. have the minimum overlap
C. have same symmetry about the molecular axis
D. have different sy...

The number of species from the following in which the central atom uses \(\mathrm{sp}^3\) hybrid orbitals in its bonding is __________.
$$\mathrm{NH}_3, \mathrm{SO}_2, \mathrm{SiO}_2, \mathrm{BeCl}_2, \mathrm{CO}_2, \mathrm{H}_2 \mathrm{O},...

For the given reaction, choose the correct expression of \(\mathrm{K}_{\mathrm{C}}\) from the following :-
\(\mathrm{Fe}_{(\mathrm{aq})}^{3+}+\mathrm{SCN}_{(\mathrm{aq})}^{-} \rightleftharpoons(\mathrm{FeSCN})_{(\mathrm{aq})}^{2+}\)

Integrated rate law equation for a first order gas phase reaction is given by (where \(\mathrm{P}_{\mathrm{i}}\) is initial pressure and \(\mathrm{P}_{\mathrm{t}}\) is total pressure at time \(t\))

The correct statements from following are:
A. The strength of anionic ligands can be explained by crystal field theory.
B. Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination compounds.
C. Th...

The 'Spin only' Magnetic moment for \(\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}\) is _________ \(\times 10^{-1} \mathrm{~BM}\). (given \(=\) Atomic number of \(\mathrm{Ni}: 28\))

Identify correct statements from below:
A. The chromate ion is square planar.
B. Dichromates are generally prepared from chromates.
C. The green manganate ion is diamagnetic.
D. Dark green coloured \(\mathrm{K}_2 \mathrm{MnO}_4\) disproport...

The metals that are employed in the battery industries are
A. \(\mathrm{Fe}\)
B. \(\mathrm{Mn}\)
C. \(\mathrm{Ni}\)
D. \(\mathrm{Cr}\)
E. \(\mathrm{Cd}\)
Choose the correct answer from the options given below:

Identify the factor from the following that does not affect electrolytic conductance of a solution.

Number of alkanes obtained on electrolysis of a mixture of \(\mathrm{CH}_3 \mathrm{COONa}\) and \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{COONa}\) is ________.

One Faraday of electricity liberates \(x \times 10^{-1}\) gram atom of copper from copper sulphate. \(x\) is ________.

The product (C) in the below mentioned reaction is :
$$\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{Br} \xrightarrow[\Delta]{\mathrm{KOH}_{(\text {alc) }}} \mathrm{A} \xrightarrow{\mathrm{HBr}} \mathrm{B} \xrightarrow[\mathrm{KOH}_{(\m...

The total number of hydrogen atoms in product A and product B is _________.

Consider the oxides of group 14 elements
\(\mathrm{SiO}_2, \mathrm{GeO}_2, \mathrm{SnO}_2, \mathrm{PbO}_2, \mathrm{CO}\) and \(\mathrm{GeO}\). The amphoteric oxides are

Give below are two statements:
Statement - I: Noble gases have very high boiling points.
Statement - II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low te...

The correct sequence of electron gain enthalpy of the elements listed below is
A. Ar
B. Br
C. F
D. S
Choose the most appropriate from the options given below:

Match List I with List II

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...

The compound that is white in color is

Identify the mixture that shows positive deviations from Raoult's Law

Number of moles of methane required to produce \(22 \mathrm{~g} \mathrm{~CO}_{2(\mathrm{~g})}\) after combustion is \(\mathrm{x} \times 10^{-2}\) moles. The value of \(\mathrm{x}\) is _________.

Molar mass of the salt from \(\mathrm{NaBr}, \mathrm{NaNO}_3, \mathrm{KI}\) and \(\mathrm{CaF}_2\) which does not evolve coloured vapours on heating with concentrated \(\mathrm{H}_2 \mathrm{SO}_4\) is ________ $$\mathrm{g} \mathrm{~mol}{ }^...

The ionization energy of sodium in \(\mathrm{~kJ} \mathrm{~mol}^{-1}\), if electromagnetic radiation of wavelength \(242 \mathrm{~nm}\) is just sufficient to ionize sodium atom is _______.

'Adsorption' principle is used for which of the following purification method?

Consider the following reaction at \(298 \mathrm{~K} \cdot \frac{3}{2} \mathrm{O}_{2(g)} \rightleftharpoons \mathrm{O}_{3(g)} \cdot \mathrm{K}_{\mathrm{P}}=2.47 \times 10^{-29}\). \(\Delta_r G^{\ominus}\) for the reaction is _________ $$\ma...

Let \(\mathrm{Q}\) and \(\mathrm{R}\) be the feet of perpendiculars from the point \(\mathrm{P}(a, a, a)\) on the lines \(x=y, z=1\) and \(x=-y, z=-1\) respectively. If \(\angle \mathrm{QPR}\) is a right angle, then \(12 a^2\) is equal to _...

$$\text { If } f(x)=\left|\begin{array}{ccc} x^3 & 2 x^2+1 & 1+3 x \\ 3 x^2+2 & 2 x & x^3+6 \\ x^3-x & 4 & x^2-2 \end{array}\right| \text { for all } x \in \mathbb{R} \text {, then } 2 f(0)+f^{\prime}(0) \text { is equal to }$$

The area of the region \(\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}\) is

Let \(a\) be the sum of all coefficients in the expansion of \(\left(1-2 x+2 x^2\right)^{2023}\left(3-4 x^2+2 x^3\right)^{2024}\) and \(b=\lim _\limits{x \rightarrow 0}\left(\frac{\int_0^x \frac{\log (1+t)}{t^{2024}+1} d t}{x^2}\right)\). I...

In the expansion of \((1+x)\left(1-x^2\right)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5, x \neq 0\), the sum of the coefficients of $x^3$ and \(x^{-13}\) is equal to __________.

If one of the diameters of the circle \(x^2+y^2-10 x+4 y+13=0\) is a chord of another circle \(\mathrm{C}\), whose center is the point of intersection of the lines \(2 x+3 y=12\) and \(3 x-2 y=5\), then the radius of the circle $$\mathrm{C}...

If \(\alpha\) denotes the number of solutions of \(|1-i|^x=2^x\) and \(\beta=\left(\frac{|z|}{\arg (z)}\right)\), where $$z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right], i=\sqrt{-1...

If the integral \(525 \int_\limits0^{\frac{\pi}{2}} \sin 2 x \cos ^{\frac{11}{2}} x\left(1+\operatorname{Cos}^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x\) is equal to \((n \sqrt{2}-64)\), then \(n\) is equal to _________.

Let \(S=(-1, \infty)\) and \(f: S \rightarrow \mathbb{R}\) be defined as
\(f(x)=\int_\limits{-1}^x\left(e^t-1\right)^{11}(2 t-1)^5(t-2)^7(t-3)^{12}(2 t-10)^{61} d t \text {, }\)
Let \(\mathrm{p}=\) Sum of squares of the values of \(x\), whe...

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\frac{4^x}{4^x+2}\) and \(M=\int_\limits{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d x, N=\int_\limits{f(a)}^{f(1-a)} \sin ^4(x(1-x)) d x ; a \neq \frac{1}{2}\). If $$\alph...

Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}, x \in\left(0, \frac{\pi}{2}\right)\) satisfying the condition \(y\left(\frac{\pi}{4}\right)=2\). Then, $$y\left(\...

The solution curve of the differential equation
\(y \frac{d x}{d y}=x\left(\log _e x-\log _e y+1\right), x>0, y>0\) passing through the point \((e, 1)\) is

If \(f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}\) and \((f \circ f)(x)=g(x)\), where \(g: \mathbb{R}-\left\{\frac{2}{3}\right\} \rightarrow \mathbb{R}-\left\{\frac{2}{3}\right\}\), then \((g ogog)(4)\) is equal to

If the foci of a hyperbola are same as that of the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) and the eccentricity of the hyperbola is \(\frac{15}{8}\) times the eccentricity of the ellipse, then the smaller focal distance of the point $$\l...

Let the foci and length of the latus rectum of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b b e( \pm 5,0)\) and \(\sqrt{50}\), respectively. Then, the square of the eccentricity of the hyperbola $$\frac{x^2}{b^2}-\frac{y^2}{a^2 b^2}=...

For \(\alpha, \beta, \gamma \neq 0\), if \(\sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pi\) and \((\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta\), then \(\gamma\) equals

\(\lim _\limits{x \rightarrow 0} \frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}\)

Let \(g(x)\) be a linear function and $$f(x)=\left\{\begin{array}{cl}g(x) & , x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}} & , x>0\end{array}\right.$$, is continuous at \(x=0\). If \(f^{\prime}(1)=f(-1)\), then the value \(g(3)\) ...

If the system of linear equations
$$\begin{aligned} & x-2 y+z=-4 \\ & 2 x+\alpha y+3 z=5 \\ & 3 x-y+\beta z=3 \end{aligned}$$
has infinitely many solutions, then \(12 \alpha+13 \beta\) is equal to

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to __________.