JEE Main 2024 (Online) 30th January Evening Shift

Salicylaldehyde is synthesized from phenol, when reacted with

m-chlorobenzaldehyde on treatment with 50% KOH solution yields :

The correct stability order of carbocations is

Which among the following purification methods is based on the principle of "Solubility" in two different solvents?

IUPAC name of following compound is :

Number of geometrical isomers possible for the given structure is/are _________.

The total number of correct statements, regarding the nucleic acids is _________.
A. RNA is regarded as the reserve of genetic information
B. DNA molecule self-duplicates during cell division
C. DNA synthesizes proteins in the cell
D. The m...

Given below are two statements:
Statement - I: Since Fluorine is more electronegative than nitrogen, the net dipole moment of \(\mathrm{NF}_3\) is greater than \(\mathrm{NH}_3\).
Statement - II: In \(\mathrm{NH}_3\), the orbital dipole due ...

The molecule / ion with square pyramidal shape is

\(\mathrm{NO}_2\) required for a reaction is produced by decomposition of \(\mathrm{N}_2 \mathrm{O}_5\) in \(\mathrm{CCl}_4\) as by equation
$$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}...

The products A and B formed in the following reaction scheme are respectively

The coordination geometry around the manganese in decacarbonyldimanganese \((0)\) is

Number of complexes which show optical isomerism among the following is ________.
$$\text { cis- }\left[\mathrm{Cr}(\mathrm{ox})_2 \mathrm{Cl}_2\right]^{3-},\left[\mathrm{Co}(\text {en})_3\right]^{3+}, \text { cis- }\left[\mathrm{Pt}(\text ...

The orange colour of \(\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) and purple colour of \(\mathrm{KMnO}_4\) is due to

Alkaline oxidative fusion of \(\mathrm{MnO}_2\) gives "A" which on electrolytic oxidation in alkaline solution produces B. A and B respectively are

Reduction potential of ions are given below:
$$\begin{array}{ccc}
\mathrm{ClO}_4^{-} & \mathrm{IO}_4^{-} & \mathrm{BrO}_4^{-} \\
\mathrm{E}^{\circ}=1.19 \mathrm{~V} & \mathrm{E}^{\circ}=1.65 \mathrm{~V} & \mathrm{E}^{\circ}=1.74 \mathrm{~V}...

Given below are two statements:
Statement - I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow \(\mathrm{S}_{\mathrm{N}}{ }^2\) mechanism.
Statement - II: A sec...

2-chlorobutane \(+\mathrm{Cl}_2 \rightarrow \mathrm{C}_4 \mathrm{H}_8 \mathrm{Cl}_2\) (isomers)
Total number of optically active isomers shown by \(\mathrm{C}_4 \mathrm{H}_8 \mathrm{Cl}_2\), obtained in the above reaction is _________.

Products A and B formed in the following set of reactions are

The \(\mathrm{pH}\) of an aqueous solution containing \(1 \mathrm{M}\) benzoic acid \(\left(\mathrm{pK}_{\mathrm{a}}=4.20\right)\) and \(1 \mathrm{M}\) sodium benzoate is 4.5. The volume of benzoic acid solution in \(300 \mathrm{~mL}\) of t...

A and B formed in the following reactions are:
$$\begin{aligned}
& \mathrm{CrO}_2 \mathrm{Cl}_2+4 \mathrm{NaOH} \rightarrow \mathrm{A}+2 \mathrm{NaCl}+2 \mathrm{H}_2 \mathrm{O}, \\
& \mathrm{A}+2 \mathrm{HCl}+2 \mathrm{H}_2 \mathrm{O}_2 \ri...

Choose the correct statements about the hydrides of group 15 elements.
A. The stability of the hydrides decreases in the order \(\mathrm{NH}_3>\mathrm{PH}_3>\mathrm{AsH}_3> \mathrm{SbH}_3>\mathrm{BiH}_3\).
B. The reducing ability of the hyd...

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: \(\mathrm{H}_2 \mathrm{Te}\) is more acidic than \(\mathrm{H}_2 \mathrm{~S}\).
Reason R: Bond dissociation enthalpy of $$\mat...

Given below are two statements:
Statement - I: Along the period, the chemical reactivity of the elements gradually increases from group 1 to group 18 .
Statement - II: The nature of oxides formed by group 1 elements is basic while that of g...

Total number of species from the following which can undergo disproportionation reaction is ________.
$$\mathrm{H}_2 \mathrm{O}_2, \mathrm{ClO}_3^{-}, \mathrm{P}_4, \mathrm{Cl}_2, \mathrm{Ag}, \mathrm{Cu}^{+1}, \mathrm{~F}_2, \mathrm{NO}_2,...

Number of metal ions characterized by flame test among the following is ________.
\(\mathrm{Sr}^{2+}, \mathrm{Ba}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Cu}^{2+}, \mathrm{Zn}^{2+}, \mathrm{Co}^{2+}, \mathrm{Fe}^{2+}\)

The solution from the following with highest depression in freezing point/lowest freezing point is

If a substance '\(A\)' dissolves in solution of a mixture of '\(B\)' and '\(C\)' with their respective number of moles as \(\mathrm{n}_{\mathrm{A}}, \mathrm{n}_{\mathrm{B}}\) and \(\mathrm{n}_{\mathrm{C}_3}\). Mole fraction of $$\mathrm{C}$...

Number of spectral lines obtained in \(\mathrm{He}^{+}\) spectra, when an electron makes transition from fifth excited state to first excited state will be

Two reactions are given below:
$$\begin{aligned}
& 2 \mathrm{Fe}_{(\mathrm{s})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{Fe}_2 \mathrm{O}_{3(\mathrm{~s})}, \Delta \mathrm{H}^{\circ}=-822 \mathrm{~kJ} / \mathrm{mol} \\
& \...

Let \(L_1: \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\lambda(\hat{i}-\hat{j}+2 \hat{k}), \lambda \in \mathbb{R}\),
$$L_2: \vec{r}=(\hat{j}-\hat{k})+\mu(3 \hat{i}+\hat{j}+p \hat{k}), \mu \in \mathbb{R} \text {, and } L_3: \vec{r}=\delta(\ell \hat{...

Let a line passing through the point \((-1,2,3)\) intersect the lines \(L_1: \frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}\) at \(M(\alpha, \beta, \gamma)\) and \(L_2: \frac{x+2}{-3}=\frac{y-2}{-2}=\frac{z-1}{4}\) at \(N(a, b, c)\). Then, the ...

Let \(f(x)=(x+3)^2(x-2)^3, x \in[-4,4]\). If \(M\) and \(m\) are the maximum and minimum values of \(f\), respectively in \([-4,4]\), then the value of \(M-m\) is

The area of the region enclosed by the parabola \((y-2)^2=x-1\), the line \(x-2 y+4=0\) and the positive coordinate axes is _________.

Suppose \(2-p, p, 2-\alpha, \alpha\) are the coefficients of four consecutive terms in the expansion of \((1+x)^n\). Then the value of \(p^2-\alpha^2+6 \alpha+2 p\) equals

Let \(\alpha=\sum_\limits{k=0}^n\left(\frac{\left({ }^n C_k\right)^2}{k+1}\right)\) and \(\beta=\sum_\limits{k=0}^{n-1}\left(\frac{{ }^n C_k{ }^n C_{k+1}}{k+2}\right)\) If \(5 \alpha=6 \beta\), then \(n\) equals _______.

Consider two circles \(C_1: x^2+y^2=25\) and \(C_2:(x-\alpha)^2+y^2=16\), where \(\alpha \in(5,9)\). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of \(C_1\) and \(C_2\) be $$\sin ^{-1}\l...

If \(z\) is a complex number, then the number of common roots of the equations \(z^{1985}+z^{100}+1=0\) and \(z^3+2 z^2+2 z+1=0\), is equal to

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\frac{x}{\left(1+x^4\right)^{1 / 4}}\), and \(g(x)=f(f(f(f(x))))\). Then, \(18 \int_0^{\sqrt{2 \sqrt{5}}} x^2 g(x) d x\) is equal to

Let \(y=f(x)\) be a thrice differentiable function in \((-5,5)\). Let the tangents to the curve \(y=f(x)\) at \((1, f(1))\) and \((3, f(3))\) make angles \(\pi / 6\) and \(\pi / 4\), respectively with positive \(x\)-axis. If $$27 \int_\limi...

Let \(a\) and \(b\) be real constants such that the function \(f\) defined by $$f(x)=\left\{\begin{array}{ll}x^2+3 x+a & , x \leq 1 \\ b x+2 & , x>1\end{array}\right.$$ be differentiable on \(\mathbb{R}\). Then, the value of $$\int_\limits{...

Let \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) be defined as \(f(x)=a e^{2 x}+b e^x+c x\). If \(f(0)=-1, f^{\prime}\left(\log _e 2\right)=21\) and \(\int_0^{\log _e 4}(f(x)-c x) d x=\frac{39}{2}\), then the value of \(|a+b+c|\) equal...

Let \(Y=Y(X)\) be a curve lying in the first quadrant such that the area enclosed by the line \(Y-y=Y^{\prime}(x)(X-x)\) and the co-ordinate axes, where \((x, y)\) is any point on the curve, is always $$\frac{-y^2}{2 Y^{\prime}(x)}+1, Y^{\p...

Let \(f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) be a function satisfying \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}\) for all \(x, y, f(y) \neq 0\). If \(f^{\prime}(1)=2024\), then

Let \(A(\alpha, 0)\) and \(B(0, \beta)\) be the points on the line \(5 x+7 y=50\). Let the point \(P\) divide the line segment \(A B\) internally in the ratio \(7:3\). Let \(3 x-25=0\) be a directrix of the ellipse $$E: \frac{x^2}{a^2}+\fra...

If the domain of the function \(f(x)=\log _e\left(\frac{2 x+3}{4 x^2+x-3}\right)+\cos ^{-1}\left(\frac{2 x-1}{x+2}\right)\) is \((\alpha, \beta]\), then the value of \(5 \beta-4 \alpha\) is equal to

Let \(P\) be a point on the hyperbola \(H: \frac{x^2}{9}-\frac{y^2}{4}=1\), in the first quadrant such that the area of triangle formed by \(P\) and the two foci of \(H\) is \(2 \sqrt{13}\). Then, the square of the distance of \(P\) from th...

Let $$R=\left(\begin{array}{ccc}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right)$$ be a non-zero \(3 \times 3\) matrix, where $$x \sin \theta=y \sin \left(\theta+\frac{2 \pi}{3}\right)=z \sin \left(\theta+\frac{4 \pi}{3}\right) \neq 0,...

Consider the system of linear equations \(x+y+z=5, x+2 y+\lambda^2 z=9, x+3 y+\lambda z=\mu\), where \(\lambda, \mu \in \mathbb{R}\). Then, which of the following statement is NOT correct?

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : \(A, B\) and \(C\). A student is required to attempt total 15 questions taking at least 4 questions from e...