JEE Main 2022 (Online) 25th July Morning Shift

Most stable product of the following reaction is:

Given below are two statements :
Statement I : On heating with \(\mathrm{KHSO}_{4}\), glycerol is dehydrated and acrolein is formed.
Statement II : Acrolein has fruity odour and can be used to test glycerol's presence.
Choose the correct op...

Which one of the following reactions does not represent correct combination of substrate and product under the given conditions?

In the given reaction

The number of chiral carbon/s in product A is ___________.

During the denaturation of proteins, which of these structures will remain intact?

Among the following species
\(\mathrm{N}_{2}, \mathrm{~N}_{2}^{+}, \mathrm{N}_{2}^{-}, \mathrm{N}_{2}^{2-}, \mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}, \mathrm{O}_{2}^{2-}\)
the number of species showing diamagnesim is _________...

The half life for the decomposition of gaseous compound \(\mathrm{A}\) is \(240 \mathrm{~s}\) when the gaseous pressure was 500 Torr initially. When the pressure was 250 Torr, the half life was found to be \(4.0\) min. The order of the reac...

Drugs used to bind to receptors, inhibiting is natural function and blocking a message are called:

An organic compound 'A' on reaction with NH3 followed by heating gives compound B. Which on further strong heating gives compound C (C8H5NO2). Compound C on sequential reaction with ethanolic KOH, alkyl chloride and hydrolysis with alkali g...

The number of sp3 hybridised carbons in an acyclic neutral compound with molecular formula C4H5N is ___________.

Consider the following metal complexes :
\(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)
\(\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\)
\(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\)
$$\left[\mathr...

Among Co3+, Ti2+, V2+ and Cr2+ ions, one if used as a reagent cannot liberate H2 from dilute mineral acid solution, its spin-only magnetic moment in gaseous state is ___________ B.M. (Nearest integer)

The cell potential for \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{aq})\right|\left|\mathrm{Sn}^{x+}\right| \mathrm{Sn}\) is \(0.801 \mathrm{~V}\) at \(298 \mathrm{~K}\). The reaction quotient for the above reaction is \(10^{-2}\). The numb...

The photochemical smog does not generally contain :

The pressure of a moist gas at \(27^{\circ} \mathrm{C}\) is \(4 \mathrm{~atm}\). The volume of the container is doubled at the same temperature. The new pressure of the moist gas is ________________ \(\times 10^{-1} \mathrm{~atm}\). (Neares...

A compound ‘\(\mathrm{A}\)’ on reaction with ‘\(\mathrm{X}\)’ and ‘\(\mathrm{Y}\)’ produces the same major product but different by product '\(a\)' and '\(b^{\prime}\). Oxidation of '\(a\)' gives a substance produced by ants.

'X' and 'Y' r...

The reaction of \(\mathrm{H}_{2} \mathrm{O}_{2}\) with potassium permanganate in acidic medium leads to the formation of mainly :

\(20 \mathrm{~mL}\) of \(0.1\, \mathrm{M} \,\mathrm{NH}_{4} \mathrm{OH}\) is mixed with \(40 \mathrm{~mL}\) of \(0.05 \mathrm{M} \mathrm{HCl}\). The \(\mathrm{pH}\) of the mixture is nearest to :
(Given : $$\mathrm{K}_{\mathrm{b}}\left(\mat...

The compound(s) that is (are) removed as slag during the extraction of copper is :
(A) CaO
(B) FeO
(C) Al2O3
(D) ZnO
(E) NiO
Choose the correct answer from the options given below:

Match List I with List II

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The geometry around boron in the product 'B' formed from the following reaction is
$$
\begin{aligned}
&\mathrm{BF}_{3}+\mathrm{NaH} \stackrel{450 \mathrm{~K}}{\rightarrow} \mathrm{A}+\mathrm{NaF} \\\\
&\mathrm{A}+\mathrm{NMe}_{3} \rightarro...

The interhalogen compound formed from the reaction of bromine with excess of fluorine is a :

The IUPAC nomenclature of an element with electronic configuration [Rn] \(5 \mathrm{f}^{14} 6 \mathrm{d}^{1} 7 \mathrm{s}^{2}\) is :

Melamine polymer is formed by the condensation of:

While estimating the nitrogen present in an organic compound by Kjeldahl's method, the ammonia evolved from \(0.25 \mathrm{~g}\) of the compound neutralized \(2.5 \mathrm{~mL}\) of \(2 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}\). The pe...

Choose the correct order of density of the alkali metals :

The depression in freezing point observed for a formic acid solution of concentration \(0.5 \mathrm{~mL} \mathrm{~L}^{-1}\) is \(0.0405^{\circ} \mathrm{C}\). Density of formic acid is \(1.05 \mathrm{~g} \mathrm{~mL}^{-1}\). The Van't Hoff f...

\(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) on reaction with excess of water results into acidic mixture

\(\mathrm{SO}_{2} \mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+2 \mathrm{HCl}\)

16 moles of $$\math...

Which of the following sets of quantum numbers is not allowed?

The enthalpy of combustion of propane, graphite and dihydrogen at \(298 \mathrm{~K}\) are \(-2220.0 \mathrm{~kJ} \mathrm{~mol}^{-1},-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The ma...

Let \(\mathrm{P}\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and $$\frac{x}{3}=\frac{y}{7}=...

The line of shortest distance between the lines \(\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}\) and \(\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}\) makes an angle of \(\cos ^{-1}\left(\sqrt{\frac{2}{27}}\right)\) with the plane $$\mathrm{P}: \mat...

If the absolute maximum value of the function \(f(x)=\left(x^{2}-2 x+7\right) \mathrm{e}^{\left(4 x^{3}-12 x^{2}-180 x+31\right)}\) in the interval \([-3,0]\) is \(f(\alpha)\), then :

The curve \(y(x)=a x^{3}+b x^{2}+c x+5\) touches the \(x\)-axis at the point \(\mathrm{P}(-2,0)\) and cuts the \(y\)-axis at the point \(Q\), where \(y^{\prime}\) is equal to 3 . Then the local maximum value of \(y(x)\) is:

The area of the region given by
\(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}\) is :

Let the locus of the centre \((\alpha, \beta), \beta>0\), of the circle which touches the circle \(x^{2}+(y-1)^{2}=1\) externally and also touches the \(x\)-axis be \(\mathrm{L}\). Then the area bounded by \(\mathrm{L}\) and the line $$y=4$...

If the maximum value of the term independent of \(t\) in the expansion of \(\left(\mathrm{t}^{2} x^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{\mathrm{t}}\right)^{15}, x \geqslant 0\), is \(\mathrm{K}\), then \(8 \mathrm{~K}\) is equal to ___...

For \(\mathrm{n} \in \mathbf{N}\), let \(\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}\) and \(\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}\). Then the numbe...

For any real number \(x\), let \([x]\) denote the largest integer less than equal to \(x\). Let \(f\) be a real valued function defined on the interval \([-10,10]\) by $$f(x)=\left\{\begin{array}{l}x-[x], \text { if }[x] \text { is odd } \\...

$$
\begin{aligned}
&\text { If } \lim _{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(n k+1)+(n k+2)+\ldots+(n k+n)] \\
&=33 \cdot \lim _{n \rightarrow \infty} \frac{1}{n^{k+1}} \cdot\left[1^{k}+2^{k}+3^{k}+\ldots+n^{k}\right]
\end{ali...

The slope of the tangent to a curve \(C: y=y(x)\) at any point \((x, y)\) on it is \(\frac{2 \mathrm{e}^{2 x}-6 \mathrm{e}^{-x}+9}{2+9 \mathrm{e}^{-2 x}}\).

If \(C\) passes through the points $$\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\r...

The general solution of the differential equation \(\left(x-y^{2}\right) \mathrm{d} x+y\left(5 x+y^{2}\right) \mathrm{d} y=0\) is :

The total number of functions,
\(f:\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}\)
such that \(f(1)+f(2)=f(3)\), is equal to :

A tower PQ stands on a horizontal ground with base \(Q\) on the ground. The point \(R\) divides the tower in two parts such that \(Q R=15 \mathrm{~m}\). If from a point \(A\) on the ground the angle of elevation of \(R\) is \(60^{\circ}\) a...

Let the equation of two diameters of a circle \(x^{2}+y^{2}-2 x+2 f y+1=0\) be \(2 p x-y=1\) and \(2 x+p y=4 p\). Then the slope m \(\in\) \((0, \infty)\) of the tangent to the hyperbola \(3 x^{2}-y^{2}=3\) passing through the centre of t...

If \(\mathop {\lim }\limits_{n \to \infty } \left( {\sqrt {{n^2} - n - 1} + n\alpha + \beta } \right) = 0\), then \(8(\alpha+\beta)\) is equal to :

Let $$f(x)=\left\{\begin{array}{l}\left|4 x^{2}-8 x+5\right|, \text { if } 8 x^{2}-6 x+1 \geqslant 0 \\ {\left[4 x^{2}-8 x+5\right], \text { if } 8 x^{2}-6 x+1<0,}\end{array}\right.$$ where \([\alpha]\) denotes the greatest integer less tha...

Which of the following statements is a tautology ?

The number of \(\theta \in(0,4 \pi)\) for which the system of linear equations

$$ \begin{aligned} &3(\sin 3 \theta) x-y+z=2 \\\\ &3(\cos 2 \theta) x+4 y+3 z=3 \\\\ &6 x+7 y+7 z=9 \end{aligned} $$
has no solution, is :

Let $$A=\left(\begin{array}{rrr}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right)$$ and \(B=A-I\). If \(\omega=\frac{\sqrt{3} i-1}{2}\), then the number of elements in the $$\operatorname{set}\left\{n \in\{1,2, \ldots, 100\}: A^{n}+...