JEE Main 2023 (Online) 29th January Morning Shift

Paper was held on
Sun, Jan 29, 2023 3:30 AM

## Chemistry

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

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

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

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Match List I with List II.
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The correct order of hydration enthalpies is
(A) K$$^+$$
(B) Rb$$^+$$
(C) Mg$$^{2+}$$
(D) Cs$$^+$$
(E) Ca$$^{2+}$$
Choos

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Correct statement about smog is :

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Identify the correct order for the given property for following compounds.
Choose the correct answer from the option gi

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The bond dissociation energy is highest for

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During the borax bead test with $$\mathrm{CuSO_4}$$, a blue green colour of the bead was observed in oxidising flame due

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

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The shortest wavelength of hydrogen atom in Lyman series is $$\lambda$$. The longest wavelength is Balmer series of He$$

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

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Match List I with List II
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The increasing order of $$\mathrm{pK_a}$$ for the following phenols is
(A) 2, 4 - Dinitrophenol
(B) 4 - Nitrophenol
(C)

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"A" obtained by Ostwald's method involving air oxidation of NH$$_3$$, upon further air oxidation produces "B", "B" on hy

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Which of the following salt solutions would coagulate the colloid solution formed when $$\mathrm{FeCl_3}$$ is added to $

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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 val

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

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The standard electrode potential $$\mathrm{(M^{3+}/M^{2+})}$$ for V, Cr, Mn & Co are $$-$$0.26 V, $$-$$0.41 V, + 1.57 V

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

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Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the

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Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is $$x\times10^{-1}$$. The v

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For certain chemical reaction $$X\to Y$$, the rate of formation of product is plotted against the time as shown in the f

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The number of molecules or ions from the following, which do not have odd number of electrons are _________.
(A) NO$$_2$

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Following figure shows dependence of molar conductance of two electrolytes on concentration. $$\Lambda \mathop m\limits^

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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 o

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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 a

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Consider the following reaction approaching equilibrium at 27$$^\circ$$C and 1 atm pressure
$$\mathrm{A+B}$$ $$\mathrel{

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

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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

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## Mathematics

Let $$\lambda \ne 0$$ be a real number. Let $$\alpha,\beta$$ be the roots of the equation $$14{x^2} - 31x + 3\lambda =

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Let $$B$$ and $$C$$ be the two points on the line $$y+x=0$$ such that $$B$$ and $$C$$ are symmetric with respect to the

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Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement

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Let $$f(\theta ) = 3\left( {{{\sin }^4}\left( {{{3\pi } \over 2} - \theta } \right) + {{\sin }^4}(3\pi + \theta )} \rig

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Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players p

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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 th

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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

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

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A light ray emits from the origin making an angle 30$$^\circ$$ with the positive $$x$$-axis. After getting reflected by

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For two non-zero complex numbers $$z_{1}$$ and $$z_{2}$$, if $$\operatorname{Re}\left(z_{1} z_{2}\right)=0$$ and $$\oper

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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_{

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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\}$

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If $$p,q$$ and $$r$$ are three propositions, then which of the following combination of truth values of $$p,q$$ and $$r$

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

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

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Let $$[x]$$ denote the greatest integer $$\le x$$. Consider the function $$f(x) = \max \left\{ {{x^2},1 + [x]} \right\}$

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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) \

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Consider the following system of equations
$$\alpha x+2y+z=1$$
$$2\alpha x+3y+z=1$$
$$3x+\alpha y+2z=\beta$$
for some $$

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If the vectors $$\overrightarrow a = \lambda \widehat i + \mu \widehat j + 4\widehat k$$, $$\overrightarrow b = - 2\w

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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}

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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

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Let $$a_1,a_2,a_3,...$$ be a $$GP$$ of increasing positive numbers. If the product of fourth and sixth terms is 9 and th

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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 $

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Let the coefficients of three consecutive terms in the binomial expansion of $$(1+2x)^n$$ be in the ratio 2 : 5 : 8. The

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If the co-efficient of $$x^9$$ in $${\left( {\alpha {x^3} + {1 \over {\beta x}}} \right)^{11}}$$ and the co-efficient of

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If all the six digit numbers $$x_1\,x_2\,x_3\,x_4\,x_5\,x_6$$ with $$0

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Let $$f:\mathbb{R}\to\mathbb{R}$$ be a differentiable function that satisfies the relation $$f(x+y)=f(x)+f(y)-1,\forall

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Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with s

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Let $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero non-coplanar vectors. Le

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Let the co-ordinates of one vertex of $$\Delta ABC$$ be $$A(0,2,\alpha)$$ and the other two vertices lie on the line $${

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## Physics

Two particles of equal mass '$$m$$' move in a circle of radius '$$r$$' under the action of their mutual gravitational at

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Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$$R$$' is placed inside a l

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In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the cente

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Surface tension of a soap bubble is $$2.0 \times 10^{-2} \mathrm{Nm}^{-1}$$. Work done to increase the radius of soap bu

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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If $$

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The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be

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If a radioactive element having half-life of $$30 \mathrm{~min}$$ is undergoing beta decay, the fraction of radioactive

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A stone is projected at angle $$30^{\circ}$$ to the horizontal. The ratio of kinetic energy of the stone at point of pro

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A block of mass $m$ slides down the plane inclined at angle $$30^{\circ}$$ with an acceleration $$\frac{g}{4}$$. The val

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Match List I with List II :
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A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction

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A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $$30 \math

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Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation.
B. Speed of l

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In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800 \mathrm{~nm}$$. The line

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A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $$\mathrm{z}$

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Which one of the following statement is not correct in the case of light emitting diodes?
A. It is a heavily doped p-n j

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A bicycle tyre is filled with air having pressure of $$270 ~\mathrm{kPa}$$ at $$27^{\circ} \mathrm{C}$$. The approximate

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The threshold wavelength for photoelectric emission from a material is 5500 $$\mathop A\limits^o $$. Photoelectrons will

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Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

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If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given :

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Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same directi

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A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of c

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In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$$\Omega$$ and 3$$\Omega$$. A shun

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A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of p

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A body cools from 60$$^\circ$$C to 40$$^\circ$$C in 6 minutes. If, temperature of surroundings is 10$$^\circ$$C. Then, a

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As shown in the figure, three identical polaroids P$$_1$$, P$$_2$$ and P$$_3$$ are placed one after another. The pass ax

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A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potent

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A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a

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A radioactive element $$_{92}^{242}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucle

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A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact wi

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