JEE Main 2024 (Online) 6th April Morning Shift

Paper was held on
Sat, Apr 6, 2024 3:30 AM

## Chemistry

The number of element from the following that do not belong to lanthanoids is $$\mathrm{Eu}, \mathrm{Cm}, \mathrm{Er}, \

View Question A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak el

View Question Match List I with List II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:soli

View Question At $$-20^{\circ} \mathrm{C}$$ and $$1 \mathrm{~atm}$$ pressure, a cylinder is filled with equal number of $$\mathrm{H}_2

View Question The electron affinity value are negative for
A. $$\mathrm{Be} \rightarrow \mathrm{Be}^{-}$$
B. $$\mathrm{N} \rightarrow

View Question Consider the following complexes
(A) $$\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}$$, (B) $$\left[\mathr

View Question Functional group present in sulphonic acids is :

View Question Match List I with List II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:soli

View Question Given below are two statements :
Statement I : Gallium is used in the manufacturing of thermometers.
Statement II : A th

View Question The density of '$$x$$' $$\mathrm{M}$$ solution ('$$x$$' molar) of $$\mathrm{NaOH}$$ is $$1.12 \mathrm{~g} \mathrm{~mL}^{

View Question Match List I with List II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:soli

View Question Which of the following statements are correct?
A. Glycerol is purified by vacuum distillation because it decomposes at i

View Question Which of the following material is not a semiconductor.

View Question Which of the following is metamer of the given compound (X) ?

View Question In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of interme

View Question Which among the following aldehydes is most reactive towards nucleophilic addition reactions?

View Question DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorr

View Question Given below are two statements :
Statement I : Piciric acid is 2,4,6 - trinitrotoluene.
Statement II : Phenol - 2,4 - di

View Question The major product of the following reaction is P.
$$\mathrm{CH}_3 \mathrm{C}\equiv\mathrm{C}-\mathrm{CH}_3$$ $$\xrightar

View Question Time required for $$99.9 \%$$ completion of a first order reaction is _________ times the time required for completion o

View Question Consider the dissociation of the weak acid HX as given below
$$\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+

View Question An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constan

View Question The major products from the following reaction sequence are product A and product B.
The total sum of $$\pi$$ electrons

View Question The difference in the 'spin-only' magnetic moment values of $$\mathrm{KMnO}_4$$ and the manganese product formed during

View Question $$9.3 \mathrm{~g}$$ of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of

View Question Number of molecules from the following which can exhibit hydrogen bonding is
_________. (nearest integer)

View Question Among $$\mathrm{CrO}, \mathrm{Cr}_2 \mathrm{O}_3$$ and $$\mathrm{CrO}_3$$, the sum of spin-only magnetic moment values o

View Question Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ $$\times 10^{13} \mathr

View Question ## Mathematics

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed

View Question Let a variable line of slope $$m>0$$ passing through the point $$(4,-9)$$ intersect the coordinate axes at the points $$

View Question 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

View Question 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

View Question 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},

View Question 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

View Question 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 $$10 A$$

View Question $$\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

View Question 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

View Question 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}

View Question 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 $

View Question For $$\alpha, \beta \in \mathbb{R}$$ and a natural number $$n$$, let $$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}

View Question Let $$f:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(1)=\lim _\l

View Question $$\int_\limits0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x \text { is equal to }$$

View Question The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found

View Question Let $$y=y(x)$$ be the solution of the differential equation $$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$$, $

View Question The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the

View Question The function $$f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}$$ is

View Question The interval in which the function $$f(x)=x^x, x>0$$, is strictly increasing is

View Question A company has two plants $$A$$ and $$B$$ to manufacture motorcycles. $$60 \%$$ motorcycles are manufactured at plant $$A

View Question 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

View Question 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

View Question If the second, third and fourth terms in the expansion of $$(x+y)^n$$ are 135, 30 and $$\frac{10}{3}$$, respectively, th

View Question Let $$\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}$$. If $$x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)

View Question 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

View Question Let the first term of a series be $$T_1=6$$ and its $$r^{\text {th }}$$ term $$T_r=3 T_{r-1}+6^r, r=2,3$$,
............

View Question 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

View Question 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

View Question 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

View Question 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

View Question ## Physics

A bullet of mass $$50 \mathrm{~g}$$ is fired with a speed $$100 \mathrm{~m} / \mathrm{s}$$ on a plywood and emerges with

View Question The specific heat at constant pressure of a real gas obeying $$P V^2=R T$$ equation is:

View Question The correct truth table for the following logic circuit is :

View Question Electromagnetic waves travel in a medium with speed of $$1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$$. The relative pe

View Question To find the spring constant $$(k)$$ of a spring experimentally, a student commits $$2 \%$$ positive error in the measure

View Question The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the a

View Question A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $

View Question To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of

View Question Which of the following phenomena does not explain by wave nature of light.
A. reflection
B. diffraction
C. photoelectric

View Question Four particles $$A, B, C, D$$ of mass $$\frac{m}{2}, m, 2 m, 4 m$$, have same momentum, respectively. The particle with

View Question In photoelectric experiment energy of $$2.48 \mathrm{~eV}$$ irradiates a photo sensitive material. The stopping potentia

View Question While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $$1 \mathrm{

View Question Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II :

View Question $$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point

View Question An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The ma

View Question A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, th

View Question A train starting from rest first accelerates uniformly up to a speed of $$80 \mathrm{~km} / \mathrm{h}$$ for time $$t$$,

View Question A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the samp

View Question The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

View Question A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of

View Question If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration

View Question A particle is doing simple harmonic motion of amplitude $$0.06 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The m

View Question Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$

View Question Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E /

View Question 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

View Question The refractive index of prism is $$\mu=\sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism

View Question A wire of resistance $$R$$ and radius $$r$$ is stretched till its radius became $$r / 2$$. If new resistance of the stre

View Question When a $$d c$$ voltage of $$100 \mathrm{~V}$$ is applied to an inductor, a $$d c$$ current of $$5 \mathrm{~A}$$ flows th

View Question A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current

View Question