JEE Main 2023 (Online) 13th April Morning Shift

2-Methyl propyl bromide reacts with \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-}\) and gives 'A' whereas on reaction with \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) it gives 'B'. The mechanism followed in these reactions and the produc...

In the reaction given below

'A' is

Among the following compounds, the one which shows highest dipole moment is

The products formed in the above reaction are

In which of the following processes, the bond order increases and paramagnetic character changes to diamagnetic one ?

\(\mathrm{ClF}_{5}\) at room temperature is a:

\(\mathrm{t}_{87.5}\) is the time required for the reaction to undergo \(87.5 \%\) completion and \(\mathrm{t}_{50}\) is the time required for the reaction to undergo \(50 \%\) completion. The relation between \(\mathrm{t}_{87.5}\) and $$\m...

In the reaction given below

'B' is

The mismatched combinations are
A. Chlorophyll - Co
B. Water hardness - EDTA
C. Photography \(-\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-}\)
D. Wilkinson catalyst \(-\left[\left(\mathrm{Ph}_{3} \mathrm{P}\right)_{3} \mathrm{RhCl}\right]\)...

The pair of lanthanides in which both elements have high third - ionization energy is :

A metal surface of \(100 \mathrm{~cm}^{2}\) area has to be coated with nickel layer of thickness \(0.001 \mathrm{~mm}\). A current of \(2 \mathrm{~A}\) was passed through a solution of \(\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}\) for '$$...

The radical which mainly causes ozone depletion in the presence of UV radiations is :

A certain quantity of real gas occupies a volume of \(0.15~ \mathrm{dm}^{3}\) at \(100 \mathrm{~atm}\) and \(500 \mathrm{~K}\) when its compressibility factor is 1.07 . Its volume at 300 atm and \(300 \mathrm{~K}\) (When its compressibility...

In the following reaction 'X' is

In the above reaction, left hand side and right hand side rings are named as '\(\mathrm{A}\)' and 'B' respectively. They undergo ring expansion. The correct statement for this process is:

For the given reaction

The total number of possible products formed by tertiary carbocation of A is ____________.

Given below are two statements :
Statement I : Permutit process is more efficient compared to the synthetic resin method for the softening of water.
Statement II : Synthetic resin method results in the formation of soluble sodium salts.
In ...

\(25.0 \mathrm{~mL}\) of \(0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) is mixed with \(25.0 \mathrm{~mL}\) of \(0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}\) of \(\mathrm{BaF}_{2}\) is $$0.5 \times 10^{-6...

Which one of the following is most likely a mismatch ?

The incorrect statement from the following for borazine is :

Which of the following statements are not correct?
A. The electron gain enthalpy of \(\mathrm{F}\) is more negative than that of \(\mathrm{Cl}\).
B. Ionization enthalpy decreases in a group of periodic table.
C. The electronegativity of an ...

Match the following

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\(\mathrm{KMnO}_{4}\) is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Number of water molecules produced for 2 molecules of \(\mathrm{KMnO}_{4}\) is ___________.

\(\mathrm{Be}(\mathrm{OH})_{2}\) reacts with \(\mathrm{Sr}(\mathrm{OH})_{2}\) to yield an ionic salt. Choose the incorrect option related to this reaction from the following :

Solution of \(12 \mathrm{~g}\) of non-electrolyte (A) prepared by dissolving it in \(1000 \mathrm{~mL}\) of water exerts the same osmotic pressure as that of \(0.05 ~\mathrm{M}\) glucose solution at the same temperature. The empirical formu...

An organic compound gives \(0.220 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.126 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) on complete combustion. If the \(\%\) of carbon is 24 then the \(\%\) of hydrogen is __________ $$\times 10^{-...

\(20 \mathrm{~mL}\) of calcium hydroxide was consumed when it was reacted with \(10 \mathrm{~mL}\) of unknown solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Also \(20 \mathrm{~mL}\) standard solution of \(0.5 ~\mathrm{M} ~\mathrm{HCl}\) co...

The energy of an electron in the first Bohr orbit of hydrogen atom is \(-2.18 \times 10^{-18} \mathrm{~J}\). Its energy in the third Bohr orbit is ____________.

What happens when a lyophilic sol is added to a lyophobic sol?

\(\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB} . \Delta H_{f}^{0}=-200 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
\(\mathrm{AB}, \mathrm{A}_{2}\) and \(\mathrm{B}_{2}\) are diatomic molecules. If the bond enthalpies of $$\mathrm{A}_{2}, \...

Let the equation of plane passing through the line of intersection of the planes \(x+2 y+a z=2\) and \(x-y+z=3\) be \(5 x-11 y+b z=6 a-1\). For \(c \in \mathbb{Z}\), if the distance of this plane from the point \((a,-c, c)\) is $$\frac{2}{\...

The distance of the point \((-1,2,3)\) from the plane \(\vec{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=10\) parallel to the line of the shortest distance between the lines \(\vec{r}=(\hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{k})\) and $$\vec{r}=(...

Let the image of the point \(\left(\frac{5}{3}, \frac{5}{3}, \frac{8}{3}\right)\) in the plane \(x-2 y+z-2=0\) be P. If the distance of the point \(Q(6,-2, \alpha), \alpha > 0\), from \(\mathrm{P}\) is 13 , then \(\alpha\) is equal to _____...

\(\max _\limits{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=\)

The area of the region enclosed by the curve
\(f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi\) and the \(x\)-axis is

Fractional part of the number \(\frac{4^{2022}}{15}\) is equal to

Let \(\alpha\) be the constant term in the binomial expansion of \(\left(\sqrt{x}-\frac{6}{x^{\frac{3}{2}}}\right)^{n}, n \leq 15\). If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of $$x^{-...

Let \(w=z \bar{z}+k_{1} z+k_{2} i z+\lambda(1+i), k_{1}, k_{2} \in \mathbb{R}\). Let \(\operatorname{Re}(w)=0\) be the circle \(\mathrm{C}\) of radius 1 in the first quadrant touching the line \(y=1\) and the \(y\)-axis. If the curve $$\ope...

Among
(S1): \(\lim_\limits{n \rightarrow \infty} \frac{1}{n^{2}}(2+4+6+\ldots \ldots+2 n)=1\)
(S2) : \(\lim_\limits{n \rightarrow \infty} \frac{1}{n^{16}}\left(1^{15}+2^{15}+3^{15}+\ldots \ldots+n^{15}\right)=\frac{1}{16}\)

\(\int_\limits{0}^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+11 e^{x}+6} d x=\)

Let for \(x \in \mathbb{R}, S_{0}(x)=x, S_{k}(x)=C_{k} x+k \int_{0}^{x} S_{k-1}(t) d t\), where
\(C_{0}=1, C_{k}=1-\int_{0}^{1} S_{k-1}(x) d x, k=1,2,3, \ldots\) Then \(S_{2}(3)+6 C_{3}\) is equal to ____________.

Let \(y=y_{1}(x)\) and \(y=y_{2}(x)\) be the solution curves of the differential equation \(\frac{d y}{d x}=y+7\) with initial conditions \(y_{1}(0)=0\) and \(y_{2}(0)=1\) respectively. Then the curves \(y=y_{1}(x)\) and \(y=y_{2}(x)\) inte...

For the differentiable function \(f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\), let \(3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10\), then \(\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|\) is equal to

Let the tangent and normal at the point \((3 \sqrt{3}, 1)\) on the ellipse \(\frac{x^{2}}{36}+\frac{y^{2}}{4}=1\) meet the \(y\)-axis at the points \(A\) and \(B\) respectively. Let the circle \(C\) be drawn taking \(A B\) as a diameter and...

For \(x \in \mathbb{R}\), two real valued functions \(f(x)\) and \(g(x)\) are such that, \(g(x)=\sqrt{x}+1\) and \(f \circ g(x)=x+3-\sqrt{x}\). Then \(f(0)\) is equal to

Let \(m_{1}\) and \(m_{2}\) be the slopes of the tangents drawn from the point \(\mathrm{P}(4,1)\) to the hyperbola \(H: \frac{y^{2}}{25}-\frac{x^{2}}{16}=1\). If \(\mathrm{Q}\) is the point from which the tangents drawn to \(\mathrm{H}\) h...

If \(S=\left\{x \in \mathbb{R}: \sin ^{-1}\left(\frac{x+1}{\sqrt{x^{2}+2 x+2}}\right)-\sin ^{-1}\left(\frac{x}{\sqrt{x^{2}+1}}\right)=\frac{\pi}{4}\right\}\), then $$\sum_\limits{x \in s}\left(\sin \left(\left(x^{2}+x+5\right) \frac{\pi}{2}...

The negation of the statement \(((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A\) is

For the system of linear equations
\(2 x+4 y+2 a z=b\)
\(x+2 y+3 z=4\)
\(2 x-5 y+2 z=8\)
which of the following is NOT correct?

Let $$B=\left[\begin{array}{lll}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4\end{array}\right], \alpha > 2$$ be the adjoint of a matrix \(A\) and \(|A|=2\). Then
$$\left[\begin{array}{ccc}\alpha & -2 \alpha & \alpha\end{array}\right]...