List of top Questions asked in JEE Main- 2023

The number of points, where the curve y = x⁵ – 20x³ + 50x + 2 crosses the x-axis, is _____.

Let a curve y = f(x), x ∈ (0, ∞) pass through the points  \(p ( 1\frac{3 }{2} )\) and  Q \( ( a,\frac{1 }{2} )\). If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S (0, c) such that bc = 3, then (PQ)² is equal to ______.

Let f (x) = \(\frac{x}{ (1+x ^n )^{\frac{1}{n} }}\), x∈R-{-1}, n∈N. n>2. 
If fⁿ (x) = (fofof____upto n times) (x), then \(lim ∫^1_ {n→∞ 0} x^{n-2}\)( f ⁿ(x))dx is equal to ___.

Let the eccentricity of an ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), is reciprocal to that of the hyperbola 2x²-2y²=1. if the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is___.

If the lines \(\frac{x−1}{2}=\frac{2−y }{−3} =\frac{ z−3 }{α}\)  and \( \frac{x−4 }{5} =\frac{y−1}{ 2}= \frac{z}{ β}\) intersect, then the magnitude of the minimum value of 8αβ is ___.

The value of tan 9°-tan27°-tan63°+tan81° is____.

A body is dropped on ground from a height ‘h₁’ and after hitting the ground, it rebounds to a height ‘h₂’ If the ratio of velocities of the body just before and after hitting ground is \(4\). then percentage loss in kinetic energy of the body is\(\frac{x}{4}\). The value of x is_____.

A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7× 10⁵ Nm^-2 . The value of mass m is ___ kg. (Take, g = 9.8 ms-2 and π =\(\frac{ 22}{7}\))

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____× 10^-8 H.
(Take, π² = 10)

A beam of light consisting of two wavelengths 7000 Å and 5500 Å is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is n × 10^-5 m. The value of n is_____.

Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is\(\frac{ 9}{x} x 10^{-10}\)m. The value of the x is _____.
(1eV = 1.6 x 10^-19J, \(\frac{1}{4π∈_0}\) = 9 x 10⁹ NM² / C² and electronic charge = 1.6 x 10^-19JC)

As shown in the figure, the voltmeter reads 2V across 5Ω resistor. The resistance of the voltmeter is_____Ω.

As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm2 are joined in such a way that a ≠ b. The equivalent capacitance of the combination is x ∈0 F. The value of x is_____.

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10cm. The maximum tension in the string is found to be \(\frac{x}{40}\) N. The value of x is___.

Number of crystal systems from the following where body centred unit cell can be found, is......
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic.

The number of species having a square planar shape from the following is __
\(XeF_4, SF_4, SiF_4, BF^-_4 BrF^-_4,[Cu(NH_3)_4]^{2+}, [FeCl_4]^{2-}, [PtCl_4]^{2-}\)

Consider the following date
Heat of combustion of H₂(g)           = -241.8 kJ mol^-1 
Heat of combustion of C(s)              = -393.5 kJ mol^-1 
Heat of combustion of C₂H₅OH(1)  = -1234.7 kJ mol^-1
The heat of formation of C₂H₅OH(1) is (-) ____ kJ mol^-1 (Nearest integer)

Consider the following pairs of solution which will be isotonic at the same temperature. The number of pairs of solutions is/are...... 
A. 1 M aq. NaCl and 2 M aq. Urea 
B. 1 M aq. CaCl₂ and 1.5 M aq. KCl 
C. 1.5 M aq. AlCl₃ and 2 M aq. Na₂SO₄ 
D. 2.5 M aq. KCl and 1 M aq. Al₂(SO₄)₃

The equilibrium composition for the reaction PCl₃ + Cl₂ ⇌ PCI5, at 298 K is given below. 
[PCl₃]_eq = 0.2 mol L^-
[Cl₂]eq = 0.1 mol L^-1,
[PCl₅]_eq = 0.40 mol L^-1 
If 0.2 mol of Cl₂ is added at the same temperature, the equilibrium concentrations of PCl5 is ___ × 10^-2 mol L^-1
Given: K_c for the reaction at 298 K is 20

The standard reduction potential at 298 K for the following half cells are given below  
NO − 3 3 − + 4H+ + 3e- → NO(g) +2H2O E0 = 0.97V 
\(V^{2+} (aq) + 2e^-→V\)           E⁰ = -1.19V 
\(Fe^{3+}(aq) + 3e^- → Fe\)        E⁰ = -0.04V 
\(Ag^+ (aq) + e^- → Ag(s)\)      E⁰ = 0.80V 
\(Au^{3+}(aq)+3e^-→Au(s)\) E⁰ = 1.40V 
The number of metal(s) which will be oxidized by  \(N0^-_3\) Oin aqueous solution is______.

The number of colloidal systems from the following, which will have 'liquid' as the dispersion medium, is____.
Gem stones, paints, smoke, cheese, milk, hair cream, insecticide sprays, froth, soap lather.

In an ice crystal, each water molecule is hydrogen bonded to ___ neighbouring molecules

Among the following, the number of compounds which will give positive iodoform reaction is ____ .
(a) 1-Phenylbutan-2-one 
(b) 2-Methylbutan-2-ol 
(c) 3-Methylbutan-2-ol 
(d) 1-Phenylethanol 
(e) 3,3-dimethylbutan-2-one 
(f) 1-Phenylpropan-2-ol

Number of isomeric aromatic amines with synthesized by Gabriel Phthalimide synthesis molecular formula C₈H₁₁N, which can be is ______. jee main 2023