JEE Main 2024 (Online) 4th April Morning Shift

Given below are two statements :
Statements I : Acidity of \(\alpha\)-hydrogens of aldehydes and ketones is responsible for Aldol reaction.
Statement II : Reaction between benzaldehyde and ethanal will NOT give Cross - Aldol product.
In the...

Identify the product in the following reaction:

What will be the decreasing order of basic strength of the following conjugate bases? \({ }^{-} \mathrm{OH}, \mathrm{R} \overline{\mathrm{O}}, \mathrm{CH}_3 \mathrm{CO} \overline{\mathrm{O}}, \mathrm{Cl}\)

Which among the following is incorrect statement?

The number of different chain isomers for C\(_7\)H\(_{16}\) is __________.

Match List I with List II :

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Which of the following is the correct structure of L-Glucose?

Number of molecules/ions from the following in which the central atom is involved in \(\mathrm{sp}^3\) hybridization is ________.
\(\mathrm{NO}_3^{-}, \mathrm{BCl}_3, \mathrm{ClO}_2^{-}, \mathrm{ClO}_3^{-}\)

Which one of the following molecules has maximum dipole moment?

Number of molecules/species from the following having one unpaired electron is ________.
\(\mathrm{O}_2, \mathrm{O}_2^{-1}, \mathrm{NO}, \mathrm{CN}^{-1}, \mathrm{O}_2^{2-}\)

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.

Some details of the above reactions are listed below.

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Which of the following nitrogen containing compound does not give Lassaigne's test ?

The number of the correct reaction(s) among the following is _______.

Number of complexes from the following with even number of unpaired "\(\mathrm{d}\)" electrons is ________ $$[\mathrm{V}(\mathrm{H}_2 \mathrm{O})_6]^{3+},[\mathrm{Cr}(\mathrm{H}_2 \mathrm{O})_6]^{2+},[\mathrm{Fe}(\mathrm{H}_2 \mathrm{O})_6]...

The correct sequence of ligands in the order of decreasing field strength is :

The element which shows only one oxidation state other than its elemental form is :

Consider the following reaction
\(\mathrm{MnO}_2+\mathrm{KOH}+\mathrm{O}_2 \rightarrow \mathrm{A}+\mathrm{H}_2 \mathrm{O} \text {. }\)
Product '\(\mathrm{A}\)' in neutral or acidic medium disproportionate to give products '\(\mathrm{B}\)' a...

One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode comes?

What pressure (bar) of \(\mathrm{H}_2\) would be required to make emf of hydrogen electrode zero in pure water at \(25^{\circ} \mathrm{C}\) ?

Identify B and C and how are A and C related?

Identify the correct set of reagents or reaction conditions '\(X\)' and '\(Y\)' in the following set of transformation.

The correct order of first ionization enthalpy values of the following elements is :
(A) O
(B) N
(C) Be
(D) F
(E) B
Choose the correct answer from the options given below :

Number of elements from the following that CANNOT form compounds with valencies which match with their respective group valencies is ________. B, C, N, S, O, F, P, Al, Si

Only \(2 \mathrm{~mL}\) of \(\mathrm{KMnO}_4\) solution of unknown molarity is required to reach the end point of a titration of \(20 \mathrm{~mL}\) of oxalic acid \((2 \mathrm{M})\) in acidic medium. The molarity of \(\mathrm{KMnO}_4\) sol...

In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to :

\(2.5 \mathrm{~g}\) of a non-volatile, non-electrolyte is dissolved in \(100 \mathrm{~g}\) of water at \(25^{\circ} \mathrm{C}\). The solution showed a boiling point elevation by \(2^{\circ} \mathrm{C}\). Assuming the solute concentration i...

The Molarity (M) of an aqueous solution containing \(5.85 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(500 \mathrm{~mL}\) water is : (Given : Molar Mass \(\mathrm{Na}: 23\) and \(\mathrm{Cl}: 35.5 \mathrm{~gmol}^{-1}\))

\(\mathrm{Xg}\) of ethylamine is subjected to reaction with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) followed by water; evolved dinitrogen gas which occupied \(2.24 \mathrm{~L}\) volume at STP. X is _________ \(\times 10^{-1} \mathrm{~g}\).

The de-Broglie's wavelength of an electron in the \(4^{\text {th }}\) orbit is ________ \(\pi \mathrm{a}_0\). (\(\mathrm{a}_0=\) Bohr's radius)

The enthalpy of formation of ethane \((\mathrm{C}_2 \mathrm{H}_6)\) from ethylene by addition of hydrogen where the bond-energies of \(\mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{H}-\mathrm{H}\) are $$414 \m...

Let the point, on the line passing through the points \(P(1,-2,3)\) and \(Q(5,-4,7)\), farther from the origin and at a distance of 9 units from the point \(P\), be \((\alpha, \beta, \gamma)\). Then \(\alpha^2+\beta^2+\gamma^2\) is equal to...

Let the sum of the maximum and the minimum values of the function \(f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}\) be \(\frac{m}{n}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\). Then \(\mathrm{m}+\mathrm{n}\) is equal to :

One of the points of intersection of the curves \(y=1+3 x-2 x^2\) and \(y=\frac{1}{x}\) is \(\left(\frac{1}{2}, 2\right)\). Let the area of the region enclosed by these curves be $$\frac{1}{24}(l \sqrt{5}+\mathrm{m})-\mathrm{n} \log _{\math...

The sum of all rational terms in the expansion of \(\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}\) is equal to :

Let $$a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1 !}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2 !}...

A square is inscribed in the circle \(x^2+y^2-10 x-6 y+30=0\). One side of this square is parallel to \(y=x+3\). If \(\left(x_i, y_i\right)\) are the vertices of the square, then \(\Sigma\left(x_i^2+y_i^2\right)\) is equal to:

Let \(\alpha\) and \(\beta\) be the sum and the product of all the non-zero solutions of the equation \((\bar{z})^2+|z|=0, z \in C\). Then \(4(\alpha^2+\beta^2)\) is equal to :

$$\text { Let } f(x)=\left\{\begin{array}{lr} -2, & -2 \leq x \leq 0 \\ x-2, & 0< x \leq 2 \end{array} \text { and } \mathrm{h}(x)=f(|x|)+|f(x)| \text {. Then } \int_\limits{-2}^2 \mathrm{~h}(x) \mathrm{d} x\right. \text { is equal to: }$$

If the shortest distance between the lines \(\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}\) and \(\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}\) is \(\frac{38}{3 \sqrt{5}} \mathrm{k}\), and $$\int_\limits 0^{\mathrm{k}}\left[x^2\right] \mathrm{d...

If \(\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} \mathrm{~d} x=\frac{1}{\mathrm{a}} \log _{\mathrm{e}}\left(\frac{\mathrm{a}}{3}\right)+\frac{\pi}{\mathrm{b} \sqrt{3}}\), where \(\mathrm{a}, \mathrm{b} \in \mathrm{N}\), then $$...

If the solution \(y=y(x)\) of the differential equation \((x^4+2 x^3+3 x^2+2 x+2) \mathrm{d} y-(2 x^2+2 x+3) \mathrm{d} x=0\) satisfies \(y(-1)=-\frac{\pi}{4}\), then \(y(0)\) is equal to :

Let the solution \(y=y(x)\) of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}-y=1+4 \sin x\) satisfy \(y(\pi)=1\). Then \(y\left(\frac{\pi}{2}\right)+10\) is equal to __________.

Let \(f(x)=x^5+2 \mathrm{e}^{x / 4}\) for all \(x \in \mathbf{R}\). Consider a function \(g(x)\) such that \((g \circ f)(x)=x\) for all \(x \in \mathbf{R}\). Then the value of \(8 g^{\prime}(2)\) is :

If the domain of the function \(\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _{\mathrm{e}}\left(\frac{3 x^2-8 x+5}{x^2-3 x-10}\right)\) is \((\alpha, \beta]\), then \(3 \alpha+10 \beta\) is equal to:

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a function given by
$$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2}, & x < 0 \\ \alpha, & x=0, \\ \frac{\beta \sqrt{1-\cos x}}{x}, & x>0\end{cases}$$
where \(\alpha, \beta \in \mathbf{R}\). If $$f...

If \(\lim _\limits{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{\mathrm{m} \sqrt{5}}{\mathrm{n}(2 \mathrm{n})^{2 / 3}}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then $$8 \mathrm...

Let \(\alpha \in(0, \infty)\) and $$A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$$. If $$\operatorname{det}\left(\operatorname{adj}\left(2 A-A^T\right) \cdot \operatorname{adj}\left(A-2 A^T\right)\rig...

If the system of equations
$$\begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & x+(\cos \alpha) y+(\sin \alpha) z=0 \\ & x+(\sin \alpha) y-(\cos \alpha) z=0 \end{aligned}$$
has a non-trivial solution, then $$\alpha...

Let \(A\) be a square matrix of order 2 such that \(|A|=2\) and the sum of its diagonal elements is \(-\)3 . If the points \((x, y)\) satisfying \(\mathrm{A}^2+x \mathrm{~A}+y \mathrm{I}=\mathrm{O}\) lie on a hyperbola, whose transverse axi...

Let \(A\) be a \(3 \times 3\) matrix of non-negative real elements such that $$A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$$. Then the maximum value of $$\operatorname{det}(\math...