JEE Main 2022 (Online) 29th July Evening Shift

When ethanol is heated with conc. \(\mathrm{H}_{2} \mathrm{SO}_{4}\), a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer's reagent, is

Correct structure of \(\gamma\)-methylcyclohexane carbaldehyde is

The number of stereoisomers formed in a reaction of \((±)\mathrm{Ph}(\mathrm{C}=\mathrm{O}) \mathrm{C}(\mathrm{OH})(\mathrm{CN}) \mathrm{Ph}\) with \(\mathrm{HCN}\) is ___________.
\(\left[\right.\)where \(\mathrm{Ph}\) is $$-\mathrm{C}_{6}...

Given below are two statements.
Statement I : The compound is optically active.
Statement II : is mirror image of above compound A.
In the light of the above statement, choose the most appropriate answer from the options given below.

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Amylose is insoluble in water.
Reason R: Amylose is a long linear molecule with more than 200 glucose units.
In the light of ...

Consider, \(\mathrm{PF}_{5}, \mathrm{BrF}_{5}, \mathrm{PCl}_{3}, \mathrm{SF}_{6},\left[\mathrm{ICl}_{4}\right]^{-}, \mathrm{ClF}_{3}\) and \(\mathrm{IF}_{5}\).
Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having $$...

Assuming \(1 \,\mu \mathrm{g}\) of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ______ \(\times\, 10^{-1} \mu \mathrm{g}\).
[Given : ln 10 =...

The number of chlorine atoms in bithionol is __________.

The Hinsberg reagent is

Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion? (en - ethylenediamine; $$\mathrm{H}_{2} \mathrm{~N}_{-} \mathrm{CH}_{2...

Sum of oxidation state (magnitude) and coordination number of cobalt in \(\mathrm{Na}\left[\mathrm{Co}(\mathrm{bpy}) \mathrm{Cl}_{4}\right]\) is _________.

Which of the following \(3\mathrm{d}\)-metal ion will give the lowest enthalpy of hydration \(\left(\Delta_{\text {hyd }} \mathrm{H}\right)\) when dissolved in water ?

For a cell, \(\mathrm{Cu}(\mathrm{s})\left|\mathrm{Cu}^{2+}(0.001 \,\mathrm{M}) \| \mathrm{Ag}^{+}(0.01 \,\mathrm{M})\right| \mathrm{Ag}(\mathrm{s})\)
the cell potential is found to be \(0.43 \mathrm{~V}\) at \(298 \mathrm{~K}\). The magnit...

'x' g of molecular oxygen \(\left(\mathrm{O}_{2}\right)\) is mixed with \(200 \mathrm{~g}\) of neon (Ne). The total pressure of the non-reactive mixture of \(\mathrm{O}_{2}\) and Ne in the cylinder is 25 bar. The partial pressure of Ne is 2...

Compound 'A' undergoes following sequence of reactions to give compound 'B'.
The correct structure and chirality of compound 'B' is
[where Et is \(\left.-\mathrm{C}_{2} \mathrm{H}_{5}\right]\)

\(200 \mathrm{~mL}\) of \(0.01 \,\mathrm{M} \,\mathrm{HCl}\) is mixed with \(400 \mathrm{~mL}\) of \(0.01 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}\). The \(\mathrm{pH}\) of the mixture is _________.
Given: $$\log {2}=0.30, \log 3=0.48,...

In liquation process used for tin (Sn), the metal :

Given below are two statements.
Statement I : Stannane is an example of a molecular hydride.
Statement II : Stannane is a planar molecule.
In the light of the above statement, choose the most appropriate answer from the options given below.

When borax is heated with \(\mathrm{CoO}\) on a platinum loop, blue coloured bead formed is largely due to :

Dinitrogen is a robust compound, but reacts at high altitudes to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is :

Consider the following sulphur based oxoacids.
\(\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8}\) and \(\mathrm{H}_{2}\mathrm{S}_{2} \mathrm{O}_{7}\).
Amongst these oxoacids, the...

Which of the following is NOT a natural polymer?

A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with \(\mathrm{CH}_{3} \mathrm{COOH}\). Compound 'X' exists in ionized form in basic medium. The compound 'X' is

Portland cement contains 'X' to enhance the setting time. What is 'X'?

\(1.80 \mathrm{~g}\) of solute A was dissolved in \(62.5 \mathrm{~cm}^{3}\) of ethanol and freezing point of the solution was found to be \(155.1 \mathrm{~K}\). The molar mass of solute A is ________ g \(\mathrm{mol}^{-1}\).
[Given : Freezi...

Consider the reaction
\(4 \mathrm{HNO}_{3}(1)+3 \mathrm{KCl}(\mathrm{s}) \rightarrow \mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{NOCl}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{KNO}_{3}(\mathrm{~s})\)
The amount of $$\mathrm{HN...

$$
\begin{aligned}
&\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+400 \mathrm{~kJ} \\
&\mathrm{C}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g})+100 \mat...

A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave 1.344 mL of \(\mathrm{H}_{2}\) gas at STP. The number of alcoholic hydrogens present in compound 'X' is ________.

Given below are the quantum numbers for 4 electrons.
A. \(\mathrm{n}=3,l=2, \mathrm{~m}_{1}=1, \mathrm{~m}_{\mathrm{s}}=+1 / 2\)
B. \(\mathrm{n}=4,l=1, \mathrm{~m}_{1}=0, \mathrm{~m}_{\mathrm{s}}=+1 / 2\)
C. $$\mathrm{n}=4,l=2, \mathrm{~m}_...

Given below are the critical temperatures of some of the gases:

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Let \(Q\) be the foot of perpendicular drawn from the point \(P(1,2,3)\) to the plane \(x+2 y+z=14\). If \(R\) is a point on the plane such that \(\angle P R Q=60^{\circ}\), then the area of \(\triangle P Q R\) is equal to :

If \((2,3,9),(5,2,1),(1, \lambda, 8)\) and \((\lambda, 2,3)\) are coplanar, then the product of all possible values of \(\lambda\) is:

If the tangent to the curve \(y=x^{3}-x^{2}+x\) at the point \((a, b)\) is also tangent to the curve \(y = 5{x^2} + 2x - 25\) at the point (2, \(-\)1), then \(|2a + 9b|\) is equal to __________.

\(\sum\limits_{r=1}^{20}\left(r^{2}+1\right)(r !)\) is equal to

\(\text { If } \sum\limits_{k=1}^{10} K^{2}\left(10_{C_{K}}\right)^{2}=22000 L \text {, then } L \text { is equal to }\) ________.

Let \(A B\) be a chord of length 12 of the circle \((x-2)^{2}+(y+1)^{2}=\frac{169}{4}\). If tangents drawn to the circle at points \(A\) and \(B\) intersect at the point \(P\), then five times the distance of point \(P\) from chord \(A B\) ...

\(\text { Let } S=\left\{(x, y) \in \mathbb{N} \times \mathbb{N}: 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}\) and
\(T=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:(x-7)^{2}+(y-4)^{2} \leq 36\right\}\). Then \(n(S \cap T)\) is equal to _____...

If \(z \neq 0\) be a complex number such that \(\left|z-\frac{1}{z}\right|=2\), then the maximum value of \(|z|\) is :

Let \(\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=|z-1|\}\). Then the set of all values of \(x\), for which \(w=2 x+i y \in \mathrm{S}\) for some \(y \in \mathbb{R}\), is :

If \([t]\) denotes the greatest integer \(\leq t\), then the value of \(\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] \mathrm{d} x\) is :

If the solution curve of the differential equation \(\frac{d y}{d x}=\frac{x+y-2}{x-y}\) passes through the points \((2,1)\) and \((\mathrm{k}+1,2), \mathrm{k}>0\), then

Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}+\left(\frac{2 x^{2}+11 x+13}{x^{3}+6 x^{2}+11 x+6}\right) y=\frac{(x+3)}{x+1}, x>-1\), which passes through the point \((0,1)\). Then \(y(1)\) is equal to ...

For \(I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x\), if \(I\left(\frac{\pi}{4}\right)=2^{1011}\), then

The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)\) is :

$$ \text { Let the function } f(x)=\left\{\begin{array}{cl} \frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & ;\text { if } x \neq 0 \\ 10 & ; \text { if } x=0 \end{array} \text { be continuous at } x=0 .\right. $$
Then \(\alpha\) is equal...

If \([t]\) denotes the greatest integer \(\leq t\), then the number of points, at which the function \(f(x)=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]\) is not differentiable in the open interval \((-20,20)\), is __________.

The statement \((p \Rightarrow q) \vee(p \Rightarrow r)\) is NOT equivalent to

Which of the following matrices can NOT be obtained from the matrix $$\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$$ by a single elementary row operation ?

If the system of equations
$$ \begin{aligned} &x+y+z=6 \\ &2 x+5 y+\alpha z=\beta \\ &x+2 y+3 z=14 \end{aligned} $$
has infinitely many solutions, then \(\alpha+\beta\) is equal to

Let $$X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$$ and $$A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]$$. For \(\mathrm{k} \in N\), if \(X^{\prime} A^{k} X=33\), then \(\mathrm{k}\) is equal to...