JEE Main 2023 (Online) 30th January Morning Shift

What is the correct order of acidity of the protons marked \(\mathrm{A}-\mathrm{D}\) in the given compounds ?

Which of the following compounds would give the following set of qualitative analysis ?
(i) Fehling's Test : Positive
(ii) Na fusion extract upon treatment with sodium nitroprusside gives a blood red colour but not prussian blue.

A trisubstituted compound '\(\mathrm{A}\)', \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\) gives neutral \(\mathrm{FeCl}_{3}\) test positive. Treatment of compound 'A' with \(\mathrm{NaOH}\) and \(\mathrm{CH}_{3} \mathrm{Br}\) gives $$\...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Ketoses give Seliwanoff's test faster than Aldoses.
Reason (R) : Ketoses undergo \(\beta\)-elimination followed by fo...

For \(\mathrm{OF}_{2}\) molecule consider the following :
A. Number of lone pairs on oxygen is 2 .
B. FOF angle is less than \(104.5^{\circ}\).
C. Oxidation state of \(\mathrm{O}\) is \(-2\).
D. Molecule is bent '\(\mathrm{V}\)' shaped.
E. ...

Match List I with List II

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...

If compound A reacts with B following first order kinetics with rate constant \(2.011 \times 10^{-3} \mathrm{~s}^{-1}\). The time taken by \(\mathrm{A}\) (in seconds) to reduce from \(7 \mathrm{~g}\) to \(2 \mathrm{~g}\) will be ___________...

Amongst the following compounds, which one is an antacid?

Benzyl isocyanide can be obtained by :
A.
B.
C.
D.
Choose the correct answer from the options given below :

To inhibit the growth of tumours, identify the compounds used from the following :
A. EDTA
B. Coordination Compounds of Pt
C. D - Penicillamine
D. Cis - Platin
Choose the correct answer from the option given below :

Which of the following is correct order of ligand field strength?

During the qualitative analysis of \(\mathrm{SO}_{3}^{2-}\) using dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{2}\) gas is evolved which turns \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) solution (acidified with dilute $$\mat...

The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is _____________.

Consider the cell
$$\mathrm{Pt}_{(\mathrm{s})}\left|\mathrm{H}_{2}(\mathrm{~g}, 1 \mathrm{~atm})\right| \mathrm{H}^{+}(\mathrm{aq}, 1 \mathrm{M})|| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \operatorname{Pt}(\mathrm{...

Formation of photochemical smog involves the following reaction in which \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are respectively.
$$
\begin{aligned}
& \text { i. } \mathrm{NO}_{2} \stackrel{\mathrm{h} v}{\longrightarrow} \mathrm{A}+\...

A \(300 \mathrm{~mL}\) bottle of soft drink has \(0.2 ~\mathrm{M}~ \mathrm{CO}_{2}\) dissolved in it. Assuming \(\mathrm{CO}_{2}\) behaves as an ideal gas, the volume of the dissolved \(\mathrm{CO}_{2}\) at \(\mathrm{STP}\) is ____________ ...

Match List I with List II

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...

The major products 'A' and 'B', respectively, are

\(600 \mathrm{~mL}\) 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 ___________ \(\times 10^{-2}\). (Nearest integer)
[Gi...

In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to:

Match List I with List II

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...

Caprolactam when heated at high temperature in presence of water, gives

Lithium aluminium hydride can be prepared from the reaction of :

The alkaline earth metal sulphate(s) which are readily soluble in water is/are :
A. \(\mathrm{BeSO}_{4}\)
B. \(\mathrm{MgSO}_{4}\)
C. \(\mathrm{CaSO}_{4}\)
D. \(\mathrm{SrSO}_{4}\)
E. \(\mathrm{BaSO}_{4}\)
Choose the correct answer from the...

In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic analysis?

A solution containing \(2 \mathrm{~g}\) of a non-volatile solute in \(20 \mathrm{~g}\) of water boils at \(373.52 \mathrm{~K}\). The molecular mass of the solute is ___________ \(\mathrm{g} ~\mathrm{mol}^{-1}\). (Nearest integer)
Given, wat...

Some amount of dichloromethane \(\left(\mathrm{CH}_{2} \mathrm{Cl}_{2}\right)\) is added to \(671.141 \mathrm{~mL}\) of chloroform \(\left(\mathrm{CHCl}_{3}\right)\) to prepare \(2.6 \times 10^{-3} \mathrm{M}\) solution of $$\mathrm{CH}_{2}...

The energy of one mole of photons of radiation of frequency \(2 \times 10^{12} \mathrm{~Hz}\) in \(\mathrm{J} ~\mathrm{mol}^{-1}\) is ___________. (Nearest integer)
[Given : \(\mathrm{h}=6.626 \times 10^{-34} ~\mathrm{Js}\)
$$\mathrm{N}_{\m...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In expensive scientific instruments, silica gel is kept in watch-glasses or in semipermeable membrane bags.
Reason (R...

When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ____________ J. (Nearest integer)

The line \(l_1\) passes through the point (2, 6, 2) and is perpendicular to the plane \(2x+y-2z=10\). Then the shortest distance between the line \(l_1\) and the line \(\frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2}\) is :

If the equation of the plane passing through the point \((1,1,2)\) and perpendicular to the line \(x-3 y+ 2 z-1=0=4 x-y+z\) is \(\mathrm{A} x+\mathrm{B} y+\mathrm{C} z=1\), then \(140(\mathrm{C}-\mathrm{B}+\mathrm{A})\) is equal to ________...

If \(\lambda_{1} < \lambda_{2}\) are two values of \(\lambda\) such that the angle between the planes \(P_{1}: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7\) and
\(P_{2}: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9\) is $$\sin ^{-1}\left(...

The number of points on the curve \(y=54 x^{5}-135 x^{4}-70 x^{3}+180 x^{2}+210 x\) at which the normal lines are parallel to \(x+90 y+2=0\) is :

Let \(\alpha\) be the area of the larger region bounded by the curve \(y^{2}=8 x\) and the lines \(y=x\) and \(x=2\), which lies in the first quadrant. Then the value of \(3 \alpha\) is equal to ___________.

If the coefficient of \(x^{15}\) in the expansion of \(\left(\mathrm{a} x^{3}+\frac{1}{\mathrm{~b} x^{1 / 3}}\right)^{15}\) is equal to the coefficient of \(x^{-15}\) in the expansion of \(\left(a x^{1 / 3}-\frac{1}{b x^{3}}\right)^{15}\), ...

The coefficient of \({x^{301}}\) in \({(1 + x)^{500}} + x{(1 + x)^{499}} + {x^2}{(1 + x)^{498}}\, + \,...\, + \,{x^{500}}\) is :

Let \(y=x+2,4y=3x+6\) and \(3y=4x+1\) be three tangent lines to the circle \((x-h)^2+(y-k)^2=r^2\). Then \(h+k\) is equal to :

Let \(z=1+i\) and \(z_{1}=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}\). Then \(\frac{12}{\pi} \arg \left(z_{1}\right)\) is equal to __________.

If [t] denotes the greatest integer \(\le \mathrm{t}\), then the value of \({{3(e - 1)} \over e}\int\limits_1^2 {{x^2}{e^{[x] + [{x^3}]}}dx}\) is :

\(\lim_\limits{x \rightarrow 0} \frac{48}{x^{4}} \int_\limits{0}^{x} \frac{t^{3}}{t^{6}+1} \mathrm{~d} t\) is equal to ___________.

Let the solution curve \(y=y(x)\) of the differential equation $$
\frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan ^{-1}\left(x^{3}\right)}{\left(1+x^{6}\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^{3}-\tan ^{-1} x^{3}}{\sqrt{\left(1+x^{...

Let \(f^{1}(x)=\frac{3 x+2}{2 x+3}, x \in \mathbf{R}-\left\{\frac{-3}{2}\right\}\) For \(\mathrm{n} \geq 2\), define \(f^{\mathrm{n}}(x)=f^{1} \mathrm{o} f^{\mathrm{n}-1}(x)\). If $$f^{5}(x)=\frac{\mathrm{a} x+\mathrm{b}}{\mathrm{b} x+\math...

Let \(S=\{1,2,3,4,5,6\}\). Then the number of one-one functions \(f: \mathrm{S} \rightarrow \mathrm{P}(\mathrm{S})\), where \(\mathrm{P}(\mathrm{S})\) denote the power set of \(\mathrm{S}\), such that \(f(n) \subset f(\mathrm{~m})\) where $...

Suppose \(f: \mathbb{R} \rightarrow(0, \infty)\) be a differentiable function such that \(5 f(x+y)=f(x) \cdot f(y), \forall x, y \in \mathbb{R}\). If \(f(3)=320\), then \(\sum_\limits{n=0}^{5} f(n)\) is equal to :

If the solution of the equation \(\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)\), is \(\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)\), where \(\alpha\), \(\beta\) are integers, then $$\alpha+\b...

Among the statements :
\((\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})\)
$$(\mathrm{S} 2)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow((\math...

Let the system of linear equations
\(x+y+kz=2\)
\(2x+3y-z=1\)
\(3x+4y+2z=k\)
have infinitely many solutions. Then the system
\((k+1)x+(2k-1)y=7\)
\((2k+1)x+(k+5)y=10\)
has :

Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm{A}| \neq 0$$ and \(\mathrm{|A-d(A d j A)|=0}\). Then

If \(\mathrm{P}(\mathrm{h}, \mathrm{k})\) be a point on the parabola \(x=4 y^{2}\), which is nearest to the point \(\mathrm{Q}(0,33)\), then the distance of \(\mathrm{P}\) from the directrix of the parabola \(\quad y^{2}=4(x+y)\) is equal t...