JEE Main 2023 (Online) 29th January Morning Shift

The increasing order of \(\mathrm{pK_a}\) for the following phenols is
(A) 2, 4 - Dinitrophenol
(B) 4 - Nitrophenol
(C) 2, 4, 5 - Trimethylphenol
(D) Phenol
(E) 3-Chlorophenol
Choose the correct answer from the option given below :

Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is _________ \(\times 10^{-1}\).

Number of cyclic tripeptides formed with 2 amino acids A and B is :

The magnetic behaviour of \(\mathrm{Li_2O,Na_2O_2}\) and \(\mathrm{KO_2}\), respectively, are :

The bond dissociation energy is highest for

The number of molecules or ions from the following, which do not have odd number of electrons are _________.
(A) NO\(_2\)
(B) ICl\(_4^ -\)
(C) BrF\(_3\)
(D) ClO\(_2\)
(E) NO\(_2^ +\)
(F) NO

Water decomposes at 2300 K
\(\mathrm{H_2O(g)\to H_2(g)+\frac{1}{2}O_2(g)}\)
The percent of water decomposing at 2300 K and 1 bar is ___________ (Nearest integer).
Equilibrium constant for the reaction is \(2\times10^{-3}\) at 2300 K.

Consider the following reaction approaching equilibrium at 27\(^\circ\)C and 1 atm pressure
\(\mathrm{A+B}\) \(\mathrel{\mathop{\kern0pt\rightleftharpoons} \limits_{{k_r} = {{10}^2}}^{{k_f} = {{10}^3}}}\) \(\mathrm{C+D}\)
The standard Gibb...

For certain chemical reaction \(X\to Y\), the rate of formation of product is plotted against the time as shown in the figure. The number of \(\mathrm{\underline {correct} }\) statement/s from the following is ___________.

(A) Over all ord...

Match List I with List II.

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The major product 'P' for the following sequence of reactions is :

Match List I with List II

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Chiral complex from the following is :
Here en = ethylene diamine

The sum of bridging carbonyls in \(\mathrm{W(CO)_6}\) and \(\mathrm{Mn_2(CO)_{10}}\) is ____________.

The standard electrode potential \(\mathrm{(M^{3+}/M^{2+})}\) for V, Cr, Mn & Co are \(-\)0.26 V, \(-\)0.41 V, + 1.57 V and + 1.97 V, respectively. The metal ions which can liberate \(\mathrm{H_2}\) from a dilute acid are :

Following figure shows dependence of molar conductance of two electrolytes on concentration. \(\Lambda \mathop m\limits^o\) is the limiting molar conductivity.

The number of \(\mathrm{\underline {incorrect} }\) statement(s) from the follo...

Correct statement about smog is :

For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas

What is the value of compressibility factor at point A ?

Identify the correct order for the given property for following compounds.

Choose the correct answer from the option given below :

17 mg of a hydrocarbon (M.F. \(\mathrm{C_{10}H_{16}}\)) takes up 8.40 mL of the H\(_2\) gas measured at 0\(^\circ\)C and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields

The number of double bond/s present in the hydrocarbon is ____...

Which of the given compounds can enhance the efficiency of hydrogen storage tank?

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is \(x\times10^{-1}\). The value of \(x\) is ___________ (Nearest integer).
Assume complete dissociation.

The reaction representing the Mond process for metal refining is _________.

During the borax bead test with \(\mathrm{CuSO_4}\), a blue green colour of the bead was observed in oxidising flame due to the formation of :

"A" obtained by Ostwald's method involving air oxidation of NH\(_3\), upon further air oxidation produces "B", "B" on hydration forms an oxoacid of Nitrogen along with evolution of "A". The oxoacid also produces "A" and gives positive brown...

Compound that will give positive Lassaigne's test for both nitrogen and halogen is :

The correct order of hydration enthalpies is
(A) K\(^+\)
(B) Rb\(^+\)
(C) Mg\(^{2+}\)
(D) Cs\(^+\)
(E) Ca\(^{2+}\)
Choose the correct answer from the options given below :

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15\(^\circ\)C. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at \(-0.8^\circ\) C. The solubility p...

The shortest wavelength of hydrogen atom in Lyman series is \(\lambda\). The longest wavelength is Balmer series of He\(^+\) is

Which of the following salt solutions would coagulate the colloid solution formed when \(\mathrm{FeCl_3}\) is added to \(\mathrm{NaOH}\) solution, at the fastest rate?

Let the equation of the plane P containing the line \(x+10=\frac{8-y}{2}=z\) be \(ax+by+3z=2(a+b)\) and the distance of the plane \(P\) from the point (1, 27, 7) be \(c\). Then \(a^2+b^2+c^2\) is equal to __________.

Let the co-ordinates of one vertex of \(\Delta ABC\) be \(A(0,2,\alpha)\) and the other two vertices lie on the line \({{x + \alpha } \over 5} = {{y - 1} \over 2} = {{z + 4} \over 3}\). For \(\alpha \in \mathbb{Z}\), if the area of $$\Delta...

Let \(\Delta\) be the area of the region \(\left\{ {(x,y) \in {R^2}:{x^2} + {y^2} \le 21,{y^2} \le 4x,x \ge 1} \right\}\). Then \({1 \over 2}\left( {\Delta - 21{{\sin }^{ - 1}}{2 \over {\sqrt 7 }}} \right)\) is equal to

Let \([x]\) denote the greatest integer \(\le x\). Consider the function \(f(x) = \max \left\{ {{x^2},1 + [x]} \right\}\). Then the value of the integral \(\int\limits_0^2 {f(x)dx}\) is

Let \(A=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0,2 x \leq y \leq \sqrt{4-(x-1)^{2}}\right\}\) and \(B=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq y \leq \min \left\{2 x, \sqrt{4-(x-1)^{2}}\right\}\right\} \text {. }\).
Then t...

Let the coefficients of three consecutive terms in the binomial expansion of \((1+2x)^n\) be in the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of those three terms, is __________.

If the co-efficient of \(x^9\) in \({\left( {\alpha {x^3} + {1 \over {\beta x}}} \right)^{11}}\) and the co-efficient of \(x^{-9}\) in \({\left( {\alpha x - {1 \over {\beta {x^3}}}} \right)^{11}}\) are equal, then \((\alpha\beta)^2\) is equ...

Let the tangents at the points \(A(4,-11)\) and \(B(8,-5)\) on the circle \(x^{2}+y^{2}-3 x+10 y-15=0\), intersect at the point \(C\). Then the radius of the circle, whose centre is \(C\) and the line joining \(A\) and \(B\) is its tangent,...

For two non-zero complex numbers \(z_{1}\) and \(z_{2}\), if \(\operatorname{Re}\left(z_{1} z_{2}\right)=0\) and \(\operatorname{Re}\left(z_{1}+z_{2}\right)=0\), then which of the following are possible?
A. $$\operatorname{Im}\left(z_{1}\ri...

Let \(f(x) = x + {a \over {{\pi ^2} - 4}}\sin x + {b \over {{\pi ^2} - 4}}\cos x,x \in R\) be a function which satisfies \(f(x) = x + \int\limits_0^{\pi /2} {\sin (x + y)f(y)dy}\). then \((a+b)\) is equal to

Let \(y=f(x)\) be the solution of the differential equation \(y(x+1)dx-x^2dy=0,y(1)=e\). Then \(\mathop {\lim }\limits_{x \to {0^ + }} f(x)\) is equal to

Let \(f:\mathbb{R}\to\mathbb{R}\) be a differentiable function that satisfies the relation \(f(x+y)=f(x)+f(y)-1,\forall x,y\in\mathbb{R}\). If \(f'(0)=2\), then \(|f(-2)|\) is equal to ___________.

The domain of \(f(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R}\) is

Let \(f:R \to R\) be a function such that \(f(x) = {{{x^2} + 2x + 1} \over {{x^2} + 1}}\). Then

Suppose \(f\) is a function satisfying \(f(x + y) = f(x) + f(y)\) for all \(x,y \in N\) and \(f(1) = {1 \over 5}\). If \(\sum\limits_{n = 1}^m {{{f(n)} \over {n(n + 1)(n + 2)}} = {1 \over {12}}}\), then \(m\) is equal to __________.

Let \(x=2\) be a root of the equation \(x^2+px+q=0\) and \(f(x) = \left\{ {\matrix{ {{{1 - \cos ({x^2} - 4px + {q^2} + 8q + 16)} \over {{{(x - 2p)}^4}}},} & {x \ne 2p} \cr {0,} & {x = 2p} \cr } } \right.\)
Then $$\mathop {\lim }...

If \(p,q\) and \(r\) are three propositions, then which of the following combination of truth values of \(p,q\) and \(r\) makes the logical expression $$\left\{ {(p \vee q) \wedge \left( {( \sim p) \vee r} \right)} \right\} \to \left( {( \s...

Let \(\alpha\) and \(\beta\) be real numbers. Consider a 3 \(\times\) 3 matrix A such that \(A^2=3A+\alpha I\). If \(A^4=21A+\beta I\), then

Consider the following system of equations
\(\alpha x+2y+z=1\)
\(2\alpha x+3y+z=1\)
\(3x+\alpha y+2z=\beta\)
for some \(\alpha,\beta\in \mathbb{R}\). Then which of the following is NOT correct.

If all the six digit numbers \(x_1\,x_2\,x_3\,x_4\,x_5\,x_6\) with \(0< x_1 < x_2 < x_3 < x_4 < x_5 < x_6\) are arranged in the increasing order, then the sum of the digits in the \(\mathrm{72^{th}}\) number is _____________.