JEE Main 2024 (Online) 4th April Morning Shift
Paper was held on Thu, Apr 4, 2024 3:30 AM
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Chemistry

Number of complexes from the following with even number of unpaired "$$\mathrm{d}$$" electrons is ________ $$[\mathrm{V}
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What will be the decreasing order of basic strength of the following conjugate bases? $${ }^{-} \mathrm{OH}, \mathrm{R}
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Given below are two statements : Statements I : Acidity of $$\alpha$$-hydrogens of aldehydes and ketones is responsible
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Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:so
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Identify B and C and how are A and C related?
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Identify the correct set of reagents or reaction conditions '$$X$$' and '$$Y$$' in the following set of transformation.
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In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium
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The element which shows only one oxidation state other than its elemental form is :
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Which of the following is the correct structure of L-Glucose?
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Identify the product in the following reaction:
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Number of molecules/ions from the following in which the central atom is involved in $$\mathrm{sp}^3$$ hybridization is
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The correct sequence of ligands in the order of decreasing field strength is :
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The Molarity (M) of an aqueous solution containing $$5.85 \mathrm{~g}$$ of $$\mathrm{NaCl}$$ in $$500 \mathrm{~mL}$$ wat
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Which among the following is incorrect statement?
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One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode come
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The correct order of first ionization enthalpy values of the following elements is : (A) O (B) N (C) Be (D) F (E) B Choo
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Which of the following nitrogen containing compound does not give Lassaigne's test ?
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Which one of the following molecules has maximum dipole moment?
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What pressure (bar) of $$\mathrm{H}_2$$ would be required to make emf of hydrogen electrode zero in pure water at $$25^{
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Number of elements from the following that CANNOT form compounds with valencies which match with their respective group
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$$2.5 \mathrm{~g}$$ of a non-volatile, non-electrolyte is dissolved in $$100 \mathrm{~g}$$ of water at $$25^{\circ} \mat
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Only $$2 \mathrm{~mL}$$ of $$\mathrm{KMnO}_4$$ solution of unknown molarity is required to reach the end point of a titr
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Consider the following transformation involving first order elementary reaction in each step at constant temperature as
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The enthalpy of formation of ethane $$(\mathrm{C}_2 \mathrm{H}_6)$$ from ethylene by addition of hydrogen where the bond
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$$\mathrm{Xg}$$ of ethylamine is subjected to reaction with $$\mathrm{NaNO}_2 / \mathrm{HCl}$$ followed by water; evolve
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The number of the correct reaction(s) among the following is _______.
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The de-Broglie's wavelength of an electron in the $$4^{\text {th }}$$ orbit is ________ $$\pi \mathrm{a}_0$$. ($$\mathrm
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The number of different chain isomers for C$$_7$$H$$_{16}$$ is __________.
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Number of molecules/species from the following having one unpaired electron is ________. $$\mathrm{O}_2, \mathrm{O}_2^{-
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Consider the following reaction $$\mathrm{MnO}_2+\mathrm{KOH}+\mathrm{O}_2 \rightarrow \mathrm{A}+\mathrm{H}_2 \mathrm{O
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Mathematics

$$\text { Let } f(x)=\left\{\begin{array}{lr} -2, & -2 \leq x \leq 0 \\ x-2, & 0
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One of the points of intersection of the curves $$y=1+3 x-2 x^2$$ and $$y=\frac{1}{x}$$ is $$\left(\frac{1}{2}, 2\right)
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Let $$\alpha \in(0, \infty)$$ and $$A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]
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There are 5 points $$P_1, P_2, P_3, P_4, P_5$$ on the side $$A B$$, excluding $$A$$ and $$B$$, of a triangle $$A B C$$.
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A square is inscribed in the circle $$x^2+y^2-10 x-6 y+30=0$$. One side of this square is parallel to $$y=x+3$$. If $$\l
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Let $$\alpha, \beta \in \mathbf{R}$$. Let the mean and the variance of 6 observations $$-3,4,7,-6, \alpha, \beta$$ be 2
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Let $$f(x)=x^5+2 \mathrm{e}^{x / 4}$$ for all $$x \in \mathbf{R}$$. Consider a function $$g(x)$$ such that $$(g \circ f)
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Let a unit vector which makes an angle of $$60^{\circ}$$ with $$2 \hat{i}+2 \hat{j}-\hat{k}$$ and an angle of $$45^{\cir
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If the domain of the function $$\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _{\mathrm{e}}\left(\frac{3 x^2-8 x+5}{
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Let the point, on the line passing through the points $$P(1,-2,3)$$ and $$Q(5,-4,7)$$, farther from the origin and at a
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The vertices of a triangle are $$\mathrm{A}(-1,3), \mathrm{B}(-2,2)$$ and $$\mathrm{C}(3,-1)$$. A new triangle is formed
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Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is s
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If the solution $$y=y(x)$$ of the differential equation $$(x^4+2 x^3+3 x^2+2 x+2) \mathrm{d} y-(2 x^2+2 x+3) \mathrm{d}
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Let the first three terms 2, p and q, with $$q \neq 2$$, of a G.P. be respectively the $$7^{\text {th }}, 8^{\text {th }
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The sum of all rational terms in the expansion of $$\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$$ is equal to :
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If 2 and 6 are the roots of the equation $$a x^2+b x+1=0$$, then the quadratic equation, whose roots are $$\frac{1}{2 a+
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Let the sum of the maximum and the minimum values of the function $$f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$$ be $$\frac{m}
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If the system of equations $$\begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & x+(\cos \alpha
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Let $$\alpha$$ and $$\beta$$ be the sum and the product of all the non-zero solutions of the equation $$(\bar{z})^2+|z|=
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Let $$f: \mathbf{R} \rightarrow \mathbf{R}$$ be a function given by $$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2}, & x 0\e
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Let the solution $$y=y(x)$$ of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}-y=1+4 \sin x$$ satisfy $$y
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If the shortest distance between the lines $$\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$$ and $$\frac{x-3}{1}=\frac{y-2}{
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Let $$A$$ be a square matrix of order 2 such that $$|A|=2$$ and the sum of its diagonal elements is $$-$$3 . If the poin
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If $$\lim _\limits{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{\mathrm{m}
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Let $$A$$ be a $$3 \times 3$$ matrix of non-negative real elements such that $$A\left[\begin{array}{l}1 \\ 1 \\ 1\end{ar
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If $$\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} \mathrm{~d} x=\frac{1}{\mathrm{a}} \log _{\mathrm{e}}\left
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In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studie
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Let the length of the focal chord PQ of the parabola $$y^2=12 x$$ be 15 units. If the distance of $$\mathrm{PQ}$$ from t
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Let $$\mathrm{ABC}$$ be a triangle of area $$15 \sqrt{2}$$ and the vectors $$\overrightarrow{\mathrm{AB}}=\hat{i}+2 \hat
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Let $$a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=
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Physics

An infinitely long positively charged straight thread has a linear charge density $$\lambda \mathrm{~Cm}^{-1}$$. An elec
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An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :
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A metal wire of uniform mass density having length $$L$$ and mass $$M$$ is bent to form a semicircular arc and a particl
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An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $
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Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two p
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If a rubber ball falls from a height $$h$$ and rebounds upto the height of $$h / 2$$. The percentage loss of total energ
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In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source
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Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\left({ }_0^1 \mathrm{n}\rig
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A body travels $$102.5 \mathrm{~m}$$ in $$\mathrm{n}^{\text {th }}$$ second and $$115.0 \mathrm{~m}$$ in $$(\mathrm{n}+2
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In an experiment to measure focal length ($$f$$) of convex lens, the least counts of the measuring scales for the positi
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The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t
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The equation of stationary wave is : $$y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\fr
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Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two diffe
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P-T diagram of an ideal gas having three different densities $$\rho_1, \rho_2, \rho_3$$ (in three different cases) is sh
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The electric field in an electromagnetic wave is given by $$\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t
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The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omeg
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The value of net resistance of the network as shown in the given figure is :
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A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $$t$$. Which of
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To measure the internal resistance of a battery, potentiometer is used. For $$R=10 \Omega$$, the balance point is observ
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On celcius scale the temperature of body increases by $$40^{\circ} \mathrm{C}$$. The increase in temperature on Fahrenhe
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A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$v$$. The
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An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2
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A hydrogen atom changes its state from $$n=3$$ to $$n=2$$. Due to recoil, the percentage change in the wave length of em
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A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it furthe
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An elastic spring under tension of $$3 \mathrm{~N}$$ has a length $$a$$. Its length is $$b$$ under tension $$2 \mathrm{~
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The magnetic field existing in a region is given by $$\vec{B}=0.2(1+2 x) \hat{k}$$. A square loop of edge $$50 \mathrm{~
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Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thr
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A alternating current at any instant is given by $$i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$$ A. The $$r m s$$ value of
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Twelve wires each having resistance $$2 \Omega$$ are joined to form a cube. A battery of $$6 \mathrm{~V}$$ emf is joined
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Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1=450 \mathrm{~nm}
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