JEE Main 2023 (Online) 31st January Morning Shift

An organic compound 'A' with emperical formula \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\) gives sooty flame on burning. Its reaction with bromine solution in low polarity solvent results in high yield of B. B is

Consider the following reaction

The correct statement for product B is. It is

Match items of column I and II

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A protein '\(\mathrm{X}\)' with molecular weight of \(70,000 \mathrm{~u}\), on hydrolysis gives amino acids. One of these amino acid is

Match List I with List II

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For reaction : \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g})\)
\(\mathrm{K}_{\mathrm{p}}=2 \times 10^{12}\) at \(27^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressu...

A \(\to\) B
The rate constants of the above reaction at 200 K and 300 K are 0.03 min\(^{-1}\) and 0.05 min\(^{-1}\) respectively. The activation energy for the reaction is ___________ J (Nearest integer)
(Given : \(\mathrm{ln10=2.3}\)
$$\ma...

Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar ?

Consider the above reaction and identify the product B.

How many of the transformations given below would result in aromatic amines?

Cobalt chloride when dissolved in water forms pink colored complex \(\underline{\mathrm{X}}\) which has
octahedral geometry. This solution on treating with conc \(\mathrm{HCl}\) forms deep blue complex, \(\underline{\mathrm{Y}}\) which has ...

When \(\mathrm{Cu}^{2+}\) ion is treated with \(\mathrm{KI}\), a white precipitate, \(\mathrm{X}\) appears in solution. The solution is titrated with sodium thiosulphate, the compound \(\mathrm{Y}\) is formed. \(\mathrm{X}\) and $$\mathrm{Y...

\(\mathrm{Nd^{2+}}\) = __________

The correct order of basicity of oxides of vanadium is :

Which one of the following statements is correct for electrolysis of brine solution?

The logarithm of equilibrium constant for the reaction \(\mathrm{Pd}^{2+}+4 \mathrm{Cl}^{-} \rightleftharpoons \mathrm{PdCl}_{4}^{2-}\) is ___________ (Nearest integer)
Given : \(\frac{2.303 R \mathrm{~T}}{\mathrm{~F}}=0.06 \mathrm{~V}\)
$$...

Identify X, Y and Z in the following reaction. (Equation not balanced)

The total pressure of a mixture of non-reacting gases \(\mathrm{X}(0.6 \mathrm{~g})\) and \(\mathrm{Y}(0.45 \mathrm{~g})\) in a vessel is \(740 \mathrm{~mm}\) of \(\mathrm{Hg}\). The partial pressure of the gas \(\mathrm{X}\) is _______ $$\...

The correct order of melting points of dichlorobenzenes is

Choose the correct set of reagents for the following conversion.
trans \(\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\right) \rightarrow \operatorname{cis}\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\right)\)

\(\mathrm{H}_{2} \mathrm{O}_{2}\) acts as a reducing agent in :

The methods NOT involved in concentration of ore are
A. Liquation
B. Leaching
C. Electrolysis
D. Hydraulic washing
E. Froth floatation
Choose the correct answer from the options given below :

The correct increasing order of the ionic radii is

The oxidation state of phosphorus in hypophosphoric acid is + _____________.

At \(27^{\circ} \mathrm{C}\), a solution containing \(2.5 \mathrm{~g}\) of solute in \(250.0 \mathrm{~mL}\) of solution exerts an osmotic pressure of \(400 \mathrm{~Pa}\). The molar mass of the solute is ___________ $$\mathrm{g} \mathrm{~mo...

Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of \(11.5 \mathrm{~g}\) of zinc with excess \(\mathrm{HCl}\) is __________ L (Nearest integer)
(Given : Mola...

On complete combustion, \(0.492 \mathrm{~g}\) of an organic compound gave \(0.792 \mathrm{~g}\) of \(\mathrm{CO}_{2}\). The % of carbon in the organic compound is ___________ (Nearest integer)

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from \(\mathrm{n=4}\) to \(\mathrm{n}=2\) of \(\mathrm{He}^{+}\) spectrum

Adding surfactants in non polar solvent, the micelles structure will look like

The enthalpy change for the conversion of \(\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g})\) to \(\mathrm{Cl}^{-}\)(aq) is (\(-\)) ___________
\(\mathrm{kJ} \mathrm{mol}^{-1}\) (Nearest integer)
Given : $$\Delta_{\mathrm{dis}} \mathrm{H}_{\mathr...

Let the shortest distance between the lines
\(L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0\) and
\(L_{1}: x+1=y-1=4-z\) be \(2 \sqrt{6}\). If \((\alpha, \beta, \gamma)\) lies on \(L\),
then which of the follo...

Let the line \(L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}\) intersect the plane \(2 x+y+3 z=16\) at the point
\(P\). Let the point \(Q\) be the foot of perpendicular from the point \(R(1,-1,-3)\) on the line \(L\). If \(\alpha\) is the ...

Let \(\theta\) be the angle between the planes \(P_{1}: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9\) and \(P_{2}: \vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15\). Let \(\mathrm{L}\) be the line that meets \(P_{2}\) at the point \((4,-2,5)\) a...

A wire of length \(20 \mathrm{~m}\) is to be cut into two pieces. A piece of length \(l_{1}\) is bent to make a square of area \(A_{1}\) and the other piece of length \(l_{2}\) is made into a circle of area \(A_{2}\). If \(2 A_{1}+3 A_{2}\)...

Let for \(x \in \mathbb{R}\),
$$ f(x)=\frac{x+|x|}{2} \text { and } g(x)=\left\{\begin{array}{cc} x, & x<0 \\ x^{2}, & x \geq 0 \end{array}\right. \text {. } $$
Then area bounded by the curve \(y=(f \circ g)(x)\) and the lines $$y=0,2 y-x=1...

The remainder on dividing \(5^{99}\) by 11 is ____________.

Let \(\alpha>0\), be the smallest number such that the expansion of \(\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}\) has a term \(\beta x^{-\alpha}, \beta \in \mathbb{N}\). Then \(\alpha\) is equal to ___________.

Let a circle \(C_{1}\) be obtained on rolling the circle \(x^{2}+y^{2}-4 x-6 y+11=0\) upwards 4 units on the tangent \(\mathrm{T}\) to it at the point \((3,2)\). Let \(C_{2}\) be the image of \(C_{1}\) in \(\mathrm{T}\). Let \(A\) and \(B\)...

For all \(z \in C\) on the curve \(C_{1}:|z|=4\), let the locus of the point \(z+\frac{1}{z}\) be the curve \(\mathrm{C}_{2}\). Then :

Let \(\alpha \in (0,1)\) and \(\beta = {\log _e}(1 - \alpha )\). Let \({P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \over 3}\, + \,...\, + \,{{{x^n}} \over n},x \in (0,1)\). Then the integral $$\int\limits_0^\alpha {{{{t^{50}}} \over {1 -...

The value of \(\int_\limits{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x\) is equal to :

Let a differentiable function \(f\) satisfy \(f(x)+\int_\limits{3}^{x} \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3\). Then \(12 f(8)\) is equal to :

Let \(y=f(x)=\sin ^{3}\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^{3}+5 x^{2}+1\right)^{\frac{3}{2}}\right)\right)\right)\). Then, at x = 1,

If the maximum distance of normal to the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{b^{2}}=1, b < 2\), from the origin is 1, then the eccentricity of the ellipse is :

If the domain of the function \(f(x)=\frac{[x]}{1+x^{2}}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

If \({\sin ^{ - 1}}{\alpha \over {17}} + {\cos ^{ - 1}}{4 \over 5} - {\tan ^{ - 1}}{{77} \over {36}} = 0,0 < \alpha < 13\), then \({\sin ^{ - 1}}(\sin \alpha ) + {\cos ^{ - 1}}(\cos \alpha )\) is equal to :

\((\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))\) is a tautology
\((\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)\) is a contradiction.
Then

For the system of linear equations
\(x+y+z=6\)
\(\alpha x+\beta y+7 z=3\)
\(x+2 y+3 z=14\)
which of the following is NOT true ?

Let \(A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 1} \cr 0 & {12} & { - 3} \cr } } \right)\). Then the sum of the diagonal elements of the matrix \({(A + I)^{11}}\) is equal to :

Let \(\mathrm{y}=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y=-\frac{1}{2}\). Then
\(S=\left\{x \in \mathbb{R}: \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}\) :