JEE Main 2024 (Online) 6th April Morning Shift
Paper was held on Sat, Apr 6, 2024 3:30 AM
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Chemistry

The number of element from the following that do not belong to lanthanoids is $$\mathrm{Eu}, \mathrm{Cm}, \mathrm{Er}, \
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A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak el
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At $$-20^{\circ} \mathrm{C}$$ and $$1 \mathrm{~atm}$$ pressure, a cylinder is filled with equal number of $$\mathrm{H}_2
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The electron affinity value are negative for A. $$\mathrm{Be} \rightarrow \mathrm{Be}^{-}$$ B. $$\mathrm{N} \rightarrow
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Consider the following complexes (A) $$\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}$$, (B) $$\left[\mathr
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Functional group present in sulphonic acids is :
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Given below are two statements : Statement I : Gallium is used in the manufacturing of thermometers. Statement II : A th
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The density of '$$x$$' $$\mathrm{M}$$ solution ('$$x$$' molar) of $$\mathrm{NaOH}$$ is $$1.12 \mathrm{~g} \mathrm{~mL}^{
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Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:soli
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Which of the following statements are correct? A. Glycerol is purified by vacuum distillation because it decomposes at i
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Which of the following material is not a semiconductor.
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Which of the following is metamer of the given compound (X) ?
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In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of interme
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Which among the following aldehydes is most reactive towards nucleophilic addition reactions?
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DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorr
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Given below are two statements : Statement I : Piciric acid is 2,4,6 - trinitrotoluene. Statement II : Phenol - 2,4 - di
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The major product of the following reaction is P. $$\mathrm{CH}_3 \mathrm{C}\equiv\mathrm{C}-\mathrm{CH}_3$$ $$\xrightar
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Time required for $$99.9 \%$$ completion of a first order reaction is _________ times the time required for completion o
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Consider the dissociation of the weak acid HX as given below $$\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+
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An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constan
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The major products from the following reaction sequence are product A and product B. The total sum of $$\pi$$ electrons
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The difference in the 'spin-only' magnetic moment values of $$\mathrm{KMnO}_4$$ and the manganese product formed during
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$$9.3 \mathrm{~g}$$ of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of
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Number of molecules from the following which can exhibit hydrogen bonding is _________. (nearest integer)
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Among $$\mathrm{CrO}, \mathrm{Cr}_2 \mathrm{O}_3$$ and $$\mathrm{CrO}_3$$, the sum of spin-only magnetic moment values o
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Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ $$\times 10^{13} \mathr
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Mathematics

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed
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Let a variable line of slope $$m>0$$ passing through the point $$(4,-9)$$ intersect the coordinate axes at the points $$
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Let $$A=\{n \in[100,700] \cap \mathrm{N}: n$$ is neither a multiple of 3 nor a multiple of 4$$\}$$. Then the number of e
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Let $$C$$ be the circle of minimum area touching the parabola $$y=6-x^2$$ and the lines $$y=\sqrt{3}|x|$$. Then, which o
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If $$A(3,1,-1), B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), C(2,2,1)$$ and $$D\left(\frac{10}{3}, \frac{2}{3},
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Let the relations $$R_1$$ and $$R_2$$ on the set $$X=\{1,2,3, \ldots, 20\}$$ be given by $$R_1=\{(x, y): 2 x-3 y=2\}$$ a
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Let the area of the region enclosed by the curves $$y=3 x, 2 y=27-3 x$$ and $$y=3 x-x \sqrt{x}$$ be $$A$$. Then $$10 A$$
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$$\text { If } f(x)=\left\{\begin{array}{ll} x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0 & , x=0 \end{array}\righ
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The shortest distance between the lines $$\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}$$ and $$\frac{x+1}{2}=\frac{y-1}{1
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Let $$y=y(x)$$ be the solution of the differential equation $$\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x}
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Let $$\alpha, \beta$$ be the distinct roots of the equation $$x^2-\left(t^2-5 t+6\right) x+1=0, t \in \mathbb{R}$$ and $
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For $$\alpha, \beta \in \mathbb{R}$$ and a natural number $$n$$, let $$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}
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Let $$f:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(1)=\lim _\l
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$$\int_\limits0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x \text { is equal to }$$
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The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found
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Let $$y=y(x)$$ be the solution of the differential equation $$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$$, $
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The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the
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The function $$f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}$$ is
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The interval in which the function $$f(x)=x^x, x>0$$, is strictly increasing is
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A company has two plants $$A$$ and $$B$$ to manufacture motorcycles. $$60 \%$$ motorcycles are manufactured at plant $$A
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Let $$x_1, x_2, x_3, x_4$$ be the solution of the equation $$4 x^4+8 x^3-17 x^2-12 x+9=0$$ and $$\left(4+x_1^2\right)\le
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Let a conic $$C$$ pass through the point $$(4,-2)$$ and $$P(x, y), x \geq 3$$, be any point on $$C$$. Let the slope of t
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If the second, third and fourth terms in the expansion of $$(x+y)^n$$ are 135, 30 and $$\frac{10}{3}$$, respectively, th
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Let $$\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}$$. If $$x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)
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Let $$P$$ be the point $$(10,-2,-1)$$ and $$Q$$ be the foot of the perpendicular drawn from the point $$R(1,7,6)$$ on th
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Let the first term of a series be $$T_1=6$$ and its $$r^{\text {th }}$$ term $$T_r=3 T_{r-1}+6^r, r=2,3$$, ............
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For $$n \in \mathrm{N}$$, if $$\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^{-1} n=\frac{\pi}{4}$$, then $$n$$ is equal
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Let $$r_k=\frac{\int_0^1\left(1-x^7\right)^k d x}{\int_0^1\left(1-x^7\right)^{k+1} d x}, k \in \mathbb{N}$$. Then the va
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Let $$\vec{a}=2 \hat{i}-3 \hat{j}+4 \hat{k}, \vec{b}=3 \hat{i}+4 \hat{j}-5 \hat{k}$$ and a vector $$\vec{c}$$ be such th
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Let $$L_1, L_2$$ be the lines passing through the point $$P(0,1)$$ and touching the parabola $$9 x^2+12 x+18 y-14=0$$. L
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Physics

A bullet of mass $$50 \mathrm{~g}$$ is fired with a speed $$100 \mathrm{~m} / \mathrm{s}$$ on a plywood and emerges with
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The specific heat at constant pressure of a real gas obeying $$P V^2=R T$$ equation is:
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The correct truth table for the following logic circuit is :
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Electromagnetic waves travel in a medium with speed of $$1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$$. The relative pe
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To find the spring constant $$(k)$$ of a spring experimentally, a student commits $$2 \%$$ positive error in the measure
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The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the a
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A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $
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To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of
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Which of the following phenomena does not explain by wave nature of light. A. reflection B. diffraction C. photoelectric
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Four particles $$A, B, C, D$$ of mass $$\frac{m}{2}, m, 2 m, 4 m$$, have same momentum, respectively. The particle with
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In photoelectric experiment energy of $$2.48 \mathrm{~eV}$$ irradiates a photo sensitive material. The stopping potentia
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While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $$1 \mathrm{
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Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II :
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$$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point
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An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The ma
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A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, th
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A train starting from rest first accelerates uniformly up to a speed of $$80 \mathrm{~km} / \mathrm{h}$$ for time $$t$$,
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A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the samp
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The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
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A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of
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If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration
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A particle is doing simple harmonic motion of amplitude $$0.06 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The m
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Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$
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Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E /
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For three vectors $$\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$$ and $$\vec{C}=(-8
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The refractive index of prism is $$\mu=\sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism
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A wire of resistance $$R$$ and radius $$r$$ is stretched till its radius became $$r / 2$$. If new resistance of the stre
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When a $$d c$$ voltage of $$100 \mathrm{~V}$$ is applied to an inductor, a $$d c$$ current of $$5 \mathrm{~A}$$ flows th
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A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current
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