List of top Questions asked in JEE Advanced- 2023

Let P be a point on the parabola y2 = 4ax, where a > 0. The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) is 

Let z be a complex number satisfying |z|3 + 2z2 +4zΜ„ - 8= 0 , where zΜ„ denotes the complex conjugate of z. Let the imaginary part of z be non-zero. Match each entry in List-I to the correct entries in List II.
List IList II
(P)|z|2 is equal to(1)12
(Q)|z - zΜ„|2 is equal to(2)4
(R)|z|2 + |z - zΜ„|2 is equal to(3)8
(S)|z + 1|2 is equal to(4)10
  (5)7
The correct option is:
A monochromatic light wave is incident normally on a glass slab of thickness as shown in the figure. The refractive index of the slab increases linearly from n1 to n2 over the height of h. Which of the following statements is/are true about the light wave emerging out of the slab?
Monochromatic light wave
Monochromatic light wave
 
For He+, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm. The wavelength (in nm) of the emitted photon during the transition is ___. 
[Use: Bohr radius, a = 52.9 pm, Rydberg constant, 𝑅H = 2.2 Γ— 10βˆ’18 J, Planck’s constant, h = 6.6 Γ— 10βˆ’34 J s, Speed of light, c = 3 Γ— 108 m sβˆ’1]
The complex(es), which can exhibit the type of isomerism shown by [Pt(NH3)2Br2], is(are) [en = H2NCH2CH2NH2]
Young’s modulus of elasticity π‘Œ is expressed in terms of three derived quantities, namely, the gravitational constant 𝐺, Planck’s constant β„Ž and the speed of light 𝑐, as π‘Œ = π‘π›Όβ„Žπ›½πΊπ›Ύ. Which of the following is the correct option?

Let Ξ²\beta be a real number Consider the
 matrix A=(Ξ²0121βˆ’231βˆ’2)IfA7βˆ’(Ξ²βˆ’1)A6βˆ’Ξ²A5matrix\ A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}If A^7-(\beta-1) A^6-\beta A^5 is a singular matrix, then the value of 9Ξ²9 \beta is _____

Consider the given data with frequency distribution
xi38111054
fi523244





Match each entry in List-I to the correct entries in List-II. 
 List-I List-II
(P)The mean of the above data is(1)2.5
(Q)The median of the above data is(2)5
(R)The mean deviation from the mean of the above data is(3)6
(S)The mean deviation from the median of the above data is(4)2.7
  (5)2.4











The correct option is: 
A thin conducting rod MN of mass 20 gm, length 25 cm, and resistance 10 Ξ© are held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field 𝐡0 = 4 T directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time 𝑑 = 0 and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option. 
[Given: The acceleration due to gravity 𝑔 = 10 m sβˆ’2 and π‘’βˆ’1 = 0.4]
List IList II
(P)At 𝑑 = 0.2 s, the magnitude of the induced emf in Volt(1)0.07
(Q)At 𝑑 = 0.2 s, the magnitude of the magnetic force in Newton(2)0.14
(R)At 𝑑 = 0.2 s, the power dissipated as heat in Watt(3)1.20
(S)The magnitude of terminal velocity of the rod in m sβˆ’1(4)0.12
  (5)2.00 
 

PARAGRAPH "II" A cylindrical furnace has height (𝐻) and diameter (𝐷) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure π‘ƒπ‘Ž and its temperature becomes 𝑇 = 360 𝐾. The hot air with density 𝜌 rises up a vertical chimney of diameter 𝑑 = 0.1 m and height β„Ž = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density πœŒπ‘Ž = 1.2 kg mβˆ’3, pressure π‘ƒπ‘Ž and temperature π‘‡π‘Ž = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in 𝜌 and 𝑇 inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity 𝑔 = 10 m sβˆ’2 and πœ‹ = 3.14] Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _______ gm sβˆ’1.

An annular disk of mass 𝑀, inner radius π‘Ž and outer radius 𝑏 is placed on a horizontal surface with coefficient of friction πœ‡, as shown in the figure. At some time, an impulse ℐ0π‘₯Μ‚ is applied at a height β„Ž above the center of the disk. If β„Ž = β„Žπ‘š then the disk rolls without slipping along the π‘₯-axis.Which of the following statement(s) is(are) correct?
An annular disk of mass 𝑀

For x∈Rx ∈ R, let tanβˆ’1(x)∈tan^{-1} (x) ∈  (βˆ’Ο€2,Ο€2-\frac{\pi}{2},\frac{\pi}{2}). Then the minimum value of function f:R β†’Rf: R \rightarrow R defined by f(x)=f(x) = βˆ«0x tanβˆ’1xe(tβˆ’cos t)1+t2023dt\int_{0}^{x\,tan^{-1}x}\frac{e^{(t-cos\,t)}}{1+t^{2023}}dt  is
A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3β„Ž from the ground, as shown in the figure. A spherical ball of mass π‘š is released on the slide from rest at a height β„Ž from the top of the terrace. The ball leaves the slide with a velocity u^0=u0x^\hat{u}_0=u_0\hat{x} and falls on the ground at a distance 𝑑 from the building making an angle ΞΈ with the horizontal. It bounces off with a velocity of v and reaches a maximum height of β„Ž1. The acceleration due to gravity is 𝑔 and the coefficient of restitution of the ground is 13\frac{1}{\sqrt3}. Which of the following statement(s) is(are) correct?
A slide with a frictionless curved surface

Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is Ο€2\frac{\pi}{2} and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Let a be the area of the triangle ABC. Then the value of (64a)2 is

Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2 Γ— 10βˆ’8 N m radβˆ’1. The angular frequency of the oscillations in 𝑛 Γ— 10βˆ’3 rad sβˆ’1. The value of 𝑛 is _____.

Let  X={(x,y)∈ZΓ—Z:x28+y220<1 and  y2<5x}X = \{ {(x,y) ∈ Z \times Z : \frac{x^2}{8} + \frac {y^2}{20} < 1 \,and \,\,y^2 < 5x} \}. Three distinct points P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle whose area is a positive integer, is
An electric dipole is formed by two charges +q and -q located in the x-y plane at (0,2) mm and (0,-2) mm as shown in the figure. The electric potential at point P(100, 100) mm due to dipole is V0. Now the charges +q and -q are moved to (-1,2)mm and (1,-2)mm respectively. What is the value of the electric potential at point P due to this new dipole?
An electric dipole is formed by two charges +q and -q located in the x-y plane at (0,2) mm and (0,-2) mm

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 Β± 0.1 cm and the distance of its real image from the lens is 20 Β± 0.2 cm. The error in the determination of focal length of the lens is 𝑛 %. The value of 𝑛 is ____ .

The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is___. [Use, molar mass (g molβˆ’1): H = 1, C = 12, O = 16, Si = 28, Cl = 35.5] 

Let Ξ± and Ξ²\alpha\ and\ \beta be real numbers such that βˆ’Ο€4<Ξ²<0<Ξ±<Ο€4-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}. If sin⁑(Ξ±+Ξ²)=13 and cos⁑(Ξ±βˆ’Ξ²)=23\sin (\alpha+\beta)=\frac{1}{3}\ and\ \cos (\alpha-\beta)=\frac{2}{3}, then the greatest integer less than or equal to
(sin⁑αcos⁑β+cos⁑βsin⁑α+cos⁑αsin⁑β+sin⁑βcos⁑α)2\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2 is ____

Let C1 be the circle of radius 1 with the center at the origin. Let C2 be the circle of radius r with center at the point A = (4,1), where 1 < r < 3 . Two distinct common tangents PQ and ST of C1 and C2 are drawn. The tangent PQ touches C1 at P and C2 at Q. The tangent ST touches C1 at S and C2 at T. Midpoints of the line segments PQ and ST are joined to form a line that meets the x-axis at a point B. If AB = √5, then the value of r2 is : 
In the given reaction scheme, P is a phenyl alkyl ether, Q is an aromatic compound; R and S are the major products. 
Reaction Scheme
The correct statement about S is
A thin circular coin of mass 5 gm and radius 43\frac{4}{3} is initially in a horizontal XY - plane. The coin is tossed vertically up (+Z direction) by applying an impulse of Ο€2Γ—10βˆ’2\sqrt{\frac{\pi}{2}\times10^{-2}} N-s at a distance of 23\frac{2}{3} cm from its center. The coin spins about its diameter and moves along the +𝑧 direction. By the time the coin reaches back to its initial position, it completes 𝑛 rotations. The value of 𝑛 is ____. [Given: The acceleration due to gravity 𝑔 = 10 msβˆ’2]
Let T1 and T2 be two distinct common tangents to the ellipse E: x26+y23=1E:  \frac{x^2}{6} + \frac{y^2}{3} = 1 and the parabola P:y2=12xP: y^2 = 12x. Suppose that the tangent T1 touches P and E at the points A1 and A2, respectively and the tangent T2 touches P and E at the points A4 and A3, respectively. Then which of the following statements is(are) true?
A particle of mass m is moving such that its velocity at a point (x,y) is given by v = Ξ± (yi^\hat{i} + 2xj^\hat{j}), where Ξ± is a non-zero constant. What is the resultant force acting on the particle?